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Plane wave representing a particle passing through two slits, resulting in an interference pattern on a screen some distance away from the slits. [1] .

The double-slit experiment is an experiment in quantum mechanics and optics demonstrating the wave-particle duality of electrons , photons , and other fundamental objects in physics. When streams of particles such as electrons or photons pass through two narrow adjacent slits to hit a detector screen on the other side, they don't form clusters based on whether they passed through one slit or the other. Instead, they interfere: simultaneously passing through both slits, and producing a pattern of interference bands on the screen. This phenomenon occurs even if the particles are fired one at a time, showing that the particles demonstrate some wave behavior by interfering with themselves as if they were a wave passing through both slits.

Niels Bohr proposed the idea of wave-particle duality to explain the results of the double-slit experiment. The idea is that all fundamental particles behave in some ways like waves and in other ways like particles, depending on what properties are being observed. These insights led to the development of quantum mechanics and quantum field theory , the current basis behind the Standard Model of particle physics , which is our most accurate understanding of how particles work.

The original double-slit experiment was performed using light/photons around the turn of the nineteenth century by Thomas Young, so the original experiment is often called Young's double-slit experiment. The idea of using particles other than photons in the experiment did not come until after the ideas of de Broglie and the advent of quantum mechanics, when it was proposed that fundamental particles might also behave as waves with characteristic wavelengths depending on their momenta. The single-electron version of the experiment was in fact not performed until 1974. A more recent version of the experiment successfully demonstrating wave-particle duality used buckminsterfullerene or buckyballs , the $C_{60}$ allotrope of carbon.

Waves vs. Particles

Double-slit experiment with electrons, modeling the double-slit experiment.

To understand why the double-slit experiment is important, it is useful to understand the strong distinctions between wave and particles that make wave-particle duality so intriguing.

Waves describe oscillating values of a physical quantity that obey the wave equation . They are usually described by sums of sine and cosine functions, since any periodic (oscillating) function may be decomposed into a Fourier series . When two waves pass through each other, the resulting wave is the sum of the two original waves. This is called a superposition since the waves are placed ("-position") on top of each other ("super-"). Superposition is one of the most fundamental principles of quantum mechanics. A general quantum system need not be in one state or another but can reside in a superposition of two where there is some probability of measuring the quantum wavefunction in one state or another.

Left: example of superposed waves constructively interfering. Right: superposed waves destructively interfering. [2]

If one wave is $A(x) = \sin (2x)$ and the other is $B(x) = \sin (2x)$, then they add together to make $A + B = 2 \sin (2x)$. The addition of two waves to form a wave of larger amplitude is in general known as constructive interference since the interference results in a larger wave.

If one wave is $A(x) = \sin (2x)$ and the other is $B(x) = \sin (2x + \pi)$, then they add together to make $A + B = 0$ $\big($since $\sin (2x + \pi) = - \sin (2x)\big).$ This is known as destructive interference in general, when adding two waves results in a wave of smaller amplitude. See the figure above for examples of both constructive and destructive interference.

Two speakers are generating sounds with the same phase, amplitude, and wavelength. The two sound waves can make constructive interference, as above left. Or they can make destructive interference, as above right. If we want to find out the exact position where the two sounds make destructive interference, which of the following do we need to know?

a) the wavelength of the sound waves b) the distances from the two speakers c) the speed of sound generated by the two speakers

This wave behavior is quite unlike the behavior of particles. Classically, particles are objects with a single definite position and a single definite momentum. Particles do not make interference patterns with other particles in detectors whether or not they pass through slits. They only interact by colliding elastically , i.e., via electromagnetic forces at short distances. Before the discovery of quantum mechanics, it was assumed that waves and particles were two distinct models for objects, and that any real physical thing could only be described as a particle or as a wave, but not both.

In the more modern version of the double slit experiment using electrons, electrons with the same momentum are shot from an "electron gun" like the ones inside CRT televisions towards a screen with two slits in it. After each electron goes through one of the slits, it is observed hitting a single point on a detecting screen at an apparently random location. As more and more electrons pass through, one at a time, they form an overall pattern of light and dark interference bands. If each electron was truly just a point particle, then there would only be two clusters of observations: one for the electrons passing through the left slit, and one for the right. However, if electrons are made of waves, they interfere with themselves and pass through both slits simultaneously. Indeed, this is what is observed when the double-slit experiment is performed using electrons. It must therefore be true that the electron is interfering with itself since each electron was only sent through one at a time—there were no other electrons to interfere with it!

When the double-slit experiment is performed using electrons instead of photons, the relevant wavelength is the de Broglie wavelength $\lambda:$

\[\lambda = \frac{h}{p},\]

where $h$ is Planck's constant and $p$ is the electron's momentum.

Calculate the de Broglie wavelength of an electron moving with velocity $1.0 \times 10^{7} \text{ m/s}.$

Usain Bolt, the world champion sprinter, hit a top speed of 27.79 miles per hour at the Olympics. If he has a mass of 94 kg, what was his de Broglie wavelength?

Express your answer as an order of magnitude in units of the Bohr radius $r_{B} = 5.29 \times 10^{-11} \text{m}$. For instance, if your answer was $4 \times 10^{-5} r_{B}$, your should give $-5.$

Image Credit: Flickr drcliffordchoi.

While the de Broglie relation was postulated for massive matter, the equation applies equally well to light. Given light of a certain wavelength, the momentum and energy of that light can be found using de Broglie's formula. This generalizes the naive formula $p = m v$, which can't be applied to light since light has no mass and always moves at a constant velocity of $c$ regardless of wavelength.

The below is reproduced from the Amplitude, Frequency, Wave Number, Phase Shift wiki.

In Young's double-slit experiment, photons corresponding to light of wavelength $\lambda$ are fired at a barrier with two thin slits separated by a distance $d,$ as shown in the diagram below. After passing through the slits, they hit a screen at a distance of $D$ away with $D \gg d,$ and the point of impact is measured. Remarkably, both the experiment and theory of quantum mechanics predict that the number of photons measured at each point along the screen follows a complicated series of peaks and troughs called an interference pattern as below. The photons must exhibit the wave behavior of a relative phase shift somehow to be responsible for this phenomenon. Below, the condition for which maxima of the interference pattern occur on the screen is derived.

Left: actual experimental two-slit interference pattern of photons, exhibiting many small peaks and troughs. Right: schematic diagram of the experiment as described above. [3]

Since $D \gg d$, the angle from each of the slits is approximately the same and equal to $\theta$. If $y$ is the vertical displacement to an interference peak from the midpoint between the slits, it is therefore true that

\[D\tan \theta \approx D\sin \theta \approx D\theta = y.\]

Furthermore, there is a path difference $\Delta L$ between the two slits and the interference peak. Light from the lower slit must travel $\Delta L$ further to reach any particular spot on the screen, as in the diagram below:

Light from the lower slit must travel further to reach the screen at any given point above the midpoint, causing the interference pattern.

The condition for constructive interference is that the path difference $\Delta L$ is exactly equal to an integer number of wavelengths. The phase shift of light traveling over an integer $n$ number of wavelengths is exactly $2\pi n$, which is the same as no phase shift and therefore constructive interference. From the above diagram and basic trigonometry, one can write

\[\Delta L = d\sin \theta \approx d\theta = n\lambda.\]

The first equality is always true; the second is the condition for constructive interference.

Now using $\theta = \frac{y}{D}$, one can see that the condition for maxima of the interference pattern, corresponding to constructive interference, is

\[n\lambda = \frac{dy}{D},\]

i.e. the maxima occur at the vertical displacements of

\[y = \frac{n\lambda D}{d}.\]

The analogous experimental setup and mathematical modeling using electrons instead of photons is identical except that the de Broglie wavelength of the electrons $\lambda = \frac{h}{p}$ is used instead of the literal wavelength of light.

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Young's Double-Slit Experiment ( AQA A Level Physics )

Revision note.

Double Slit Interference

The interference of two coherent wave sources
A single wave source passing through a double slit
The laser light source is placed behind the single slit
So the light is diffracted, producing two light sources at slits A and B
The light from the double slits is then diffracted, producing a diffraction pattern made up of bright and dark fringes on a screen

3-3-3--laser-light-double-slit-experiment-diagram

The typical arrangement of Young's double-slit experiment

Diffraction Pattern

Constructive interference between light rays forms bright strips, also called fringes , interference fringes or maxima , on the screen
Destructive interference forms dark strips, also called dark fringes or minima , on the screen

$youngs-double-slit-diffraction-pattern$

Young's double slit experiment and the resulting diffraction pattern

Each bright fringe is identical and has the same width and intensity
The fringes are all separated by dark narrow bands of destructive interference

$creation-of-diffraction-pattern-aqa-al-physics$

The constructive and destructive interference of laser light through a double slit creates bright and dark strips called fringes on a screen placed far away

Interference Pattern

The Young's double slit interference pattern shows the regions of constructive and destructive interference:
Each bright fringe is a peak of equal maximum intensity
Each dark fringe is a a trough or minimum of zero intensity
The maxima are formed by the constructive interference of light
The minima are formed by the destructive interference of light

The interference pattern of Young's double-slit diffraction of light

When two waves interfere, the resultant wave depends on the path difference between the two waves
This extra distance is the path difference

Path difference equations, downloadable AS & A Level Physics revision notes

The path difference between two waves is determined by the number of wavelengths that cover their difference in length

For constructive interference (or maxima), the difference in wavelengths will be an integer number of whole wavelengths
For destructive interference (or minima) it will be an integer number of whole wavelengths plus a half wavelength
There is usually more than one produced
n is the order of the maxima or minima; which represents the position of the maxima away from the central maximum
n = 0 is the central maximum
n = 1 represents the first maximum on either side of the central, n = 2 the next one along....

Worked example

WE - Two source interference question image, downloadable AS & A Level Physics revision notes

Determine which orders of maxima are detected at M as the wavelength is increased from 3.5 cm to 12.5 cm.

Worked example - two source interference (2), downloadable AS & A Level Physics revision notes

The path difference is more specifically how much longer, or shorter, one path is than the other. In other words, the difference in the distances. Make sure not to confuse this with the distance between the two paths.

Fringe Spacing Equation

The spacing between the bright or dark fringes in the diffraction pattern formed on the screen can be calculated using the double slit equation:

Double slit interference equation with w, s and D represented on a diagram

D is much bigger than any other dimension, normally several metres long
s is the separation between the two slits and is often the smallest dimension, normally in mm
w is the distance between the fringes on the screen, often in cm. This can be obtained by measuring the distance between the centre of each consecutive bright spot.
The wavelength , λ of the incident light increases
The distance , s between the screen and the slits increases
The separation , w between the slits decreases

WE - Double slit equation question image, downloadable AS & A Level Physics revision notes

Calculate the separation of the two slits.

Fringe Spacing Worked Example, downloadable AS & A Level Physics revision notes

Since w , s and D are all distances, it's easy to mix up which they refer to. Labelling the double-slit diagram with each of these quantities can help ensure you don't use the wrong variable for a quantity.

Interference Patterns

It is different to that produced by a single slit or a diffraction grating

$diffraction-of-white-light-double-slit$

The interference pattern produced when white light is diffracted through a double slit

Each maximum is of roughly equal width
There are two dark narrow destructive interference fringes on either side
All other maxima are composed of a spectrum
The shortest wavelength (violet / blue) would appear nearest to the central maximum because it is diffracted the least
The longest wavelength (red) would appear furthest from the central maximum because it is diffracted the most
As the maxima move further away from the central maximum, the wavelengths of blue observed decrease and the wavelengths of red observed increase

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Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

Wave Optics

Young’s double slit experiment, learning objectives.

By the end of this section, you will be able to:

Explain the phenomena of interference.
Define constructive interference for a double slit and destructive interference for a double slit.

Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see Figure 1).

A beam of light strikes a wall through which a pair of vertical slits is cut. On the other side of the wall, another wall shows a pattern of equally spaced vertical lines of light that are of the same height as the slit.

Figure 1. Young’s double slit experiment. Here pure-wavelength light sent through a pair of vertical slits is diffracted into a pattern on the screen of numerous vertical lines spread out horizontally. Without diffraction and interference, the light would simply make two lines on the screen.

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single λ ) light to clarify the effect. Figure 2 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

Figure a shows three sine waves with the same wavelength arranged one above the other. The peaks and troughs of each wave are aligned with those of the other waves. The top two waves are labeled wave one and wave two and the bottom wave is labeled resultant. The amplitude of waves one and two are labeled x and the amplitude of the resultant wave is labeled two x. Figure b shows a similar situation, except that the peaks of wave two now align with the troughs of wave one. The resultant wave is now a straight horizontal line on the x axis; that is, the line y equals zero.

Figure 2. The amplitudes of waves add. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase, or shifted by half a wavelength.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3a. Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3b. Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

The figure contains three parts. The first part is a drawing that shows parallel wavefronts approaching a wall from the left. Crests are shown as continuous lines, and troughs are shown as dotted lines. Two light rays pass through small slits in the wall and emerge in a fan-like pattern from two slits. These lines fan out to the right until they hit the right-hand wall. The points where these fan lines hit the right-hand wall are alternately labeled min and max. The min points correspond to lines that connect the overlapping crests and troughs, and the max points correspond to the lines that connect the overlapping crests. The second drawing is a view from above of a pool of water with semicircular wavefronts emanating from two points on the left side of the pool that are arranged one above the other. These semicircular waves overlap with each other and form a pattern much like the pattern formed by the arcs in the first image. The third drawing shows a vertical dotted line, with some dots appearing brighter than other dots. The brightness pattern is symmetric about the midpoint of this line. The dots near the midpoint are the brightest. As you move from the midpoint up, or down, the dots become progressively dimmer until there seems to be a dot missing. If you progress still farther from the midpoint, the dots appear again and get brighter, but are much less bright than the central dots. If you progress still farther from the midpoint, the dots get dimmer again and then disappear again, which is where the dotted line stops.

Figure 3. Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) Double slit interference pattern for water waves are nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this. (credit: PASCO)

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 4. Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 4a. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 4b. More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [(1/2) λ , (3/2) λ , (5/2) λ , etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ( λ , 2 λ , 3 λ , etc.), then constructive interference occurs.

Both parts of the figure show a schematic of a double slit experiment. Two waves, each of which is emitted from a different slit, propagate from the slits to the screen. In the first schematic, when the waves meet on the screen, one of the waves is at a maximum whereas the other is at a minimum. This schematic is labeled dark (destructive interference). In the second schematic, when the waves meet on the screen, both waves are at a minimum.. This schematic is labeled bright (constructive interference).

Figure 4. Waves follow different paths from the slits to a common point on a screen. (a) Destructive interference occurs here, because one path is a half wavelength longer than the other. The waves start in phase but arrive out of phase. (b) Constructive interference occurs here because one path is a whole wavelength longer than the other. The waves start out and arrive in phase.

Take-Home Experiment: Using Fingers as Slits

Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?

The figure is a schematic of a double slit experiment, with the scale of the slits enlarged to show the detail. The two slits are on the left, and the screen is on the right. The slits are represented by a thick vertical line with two gaps cut through it a distance d apart. Two rays, one from each slit, angle up and to the right at an angle theta above the horizontal. At the screen, these rays are shown to converge at a common point. The ray from the upper slit is labeled l sub one, and the ray from the lower slit is labeled l sub two. At the slits, a right triangle is drawn, with the thick line between the slits forming the hypotenuse. The hypotenuse is labeled d, which is the distance between the slits. A short piece of the ray from the lower slit is labeled delta l and forms the short side of the right triangle. The long side of the right triangle is formed by a line segment that goes downward and to the right from the upper slit to the lower ray. This line segment is perpendicular to the lower ray, and the angle it makes with the hypotenuse is labeled theta. Beneath this triangle is the formula delta l equals d sine theta.

Figure 5. The paths from each slit to a common point on the screen differ by an amount dsinθ, assuming the distance to the screen is much greater than the distance between slits (not to scale here).

Figure 5 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle θ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be d sin θ , where d is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or d sin θ = mλ, for m = 0, 1, −1, 2, −2, . . . (constructive).

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

[latex]d\sin\theta=\left(m+\frac{1}{2}\right)\lambda\text{, for }m=0,1,-1,2,-2,\dots\text{ (destructive)}\\[/latex],

where λ is the wavelength of the light, d is the distance between slits, and θ is the angle from the original direction of the beam as discussed above. We call m the order of the interference. For example, m = 4 is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6. The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation d sin θ = mλ, for m = 0, 1, −1, 2, −2, . . . .

For fixed λ and m , the smaller d is, the larger θ must be, since [latex]\sin\theta=\frac{m\lambda}{d}\\[/latex]. This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance d apart) is small. Small d gives large θ , hence a large effect.

The figure consists of two parts arranged side-by-side. The diagram on the left side shows a double slit arrangement along with a graph of the resultant intensity pattern on a distant screen. The graph is oriented vertically, so that the intensity peaks grow out and to the left from the screen. The maximum intensity peak is at the center of the screen, and some less intense peaks appear on both sides of the center. These peaks become progressively dimmer upon moving away from the center, and are symmetric with respect to the central peak. The distance from the central maximum to the first dimmer peak is labeled y sub one, and the distance from the central maximum to the second dimmer peak is labeled y sub two. The illustration on the right side shows thick bright horizontal bars on a dark background. Each horizontal bar is aligned with one of the intensity peaks from the first figure.

Figure 6. The interference pattern for a double slit has an intensity that falls off with angle. The photograph shows multiple bright and dark lines, or fringes, formed by light passing through a double slit.

Example 1. Finding a Wavelength from an Interference Pattern

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that m = 3. We are given d = 0.0100 mm and θ = 10.95º. The wavelength can thus be found using the equation d sin θ = mλ for constructive interference.

The equation is d sin θ = mλ . Solving for the wavelength λ gives [latex]\lambda=\frac{d\sin\theta}{m}\\[/latex].

Substituting known values yields

[latex]\begin{array}{lll}\lambda&=&\frac{\left(0.0100\text{ nm}\right)\left(\sin10.95^{\circ}\right)}{3}\\\text{ }&=&6.33\times10^{-4}\text{ nm}=633\text{ nm}\end{array}\\[/latex]

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with λ , so that spectra (measurements of intensity versus wavelength) can be obtained.

Example 2. Calculating Highest Order Possible

Interference patterns do not have an infinite number of lines, since there is a limit to how big m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation d sin θ = mλ ( for m = 0, 1, −1, 2, −2, . . . ) describes constructive interference. For fixed values of d and λ , the larger m is, the larger sin θ is. However, the maximum value that sin θ can have is 1, for an angle of 90º. (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which m corresponds to this maximum diffraction angle.

Solving the equation d sin θ = mλ for m gives [latex]\lambda=\frac{d\sin\theta}{m}\\[/latex].

Taking sin θ = 1 and substituting the values of d and λ from the preceding example gives

[latex]\displaystyle{m}=\frac{\left(0.0100\text{ mm}\right)\left(1\right)}{633\text{ nm}}\approx15.8\\[/latex]

Therefore, the largest integer m can be is 15, or m = 15.

The number of fringes depends on the wavelength and slit separation. The number of fringes will be very large for large slit separations. However, if the slit separation becomes much greater than the wavelength, the intensity of the interference pattern changes so that the screen has two bright lines cast by the slits, as expected when light behaves like a ray. We also note that the fringes get fainter further away from the center. Consequently, not all 15 fringes may be observable.

Section Summary

Young’s double slit experiment gave definitive proof of the wave character of light.
An interference pattern is obtained by the superposition of light from two slits.
There is constructive interference when d sin θ = mλ ( for m = 0, 1, −1, 2, −2, . . . ), where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference.
There is destructive interference when d sin θ = mλ ( for m = 0, 1, −1, 2, −2, . . . ).

Conceptual Questions

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.
Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.
Is it possible to create a situation in which there is only destructive interference? Explain.
Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

The figure shows a photo of a horizontal line of equally spaced red dots of light on a black background. The central dot is the brightest and the dots on either side of center are dimmer. The dot intensity decreases to almost zero after moving six dots to the left or right of center. If you continue to move away from the center, the dot brightness increases slightly, although it does not reach the brightness of the central dot. After moving another six dots, or twelve dots in all, to the left or right of center, there is another nearly invisible dot. If you move even farther from the center, the dot intensity again increases, but it does not reach the level of the previous local maximum. At eighteen dots from the center, there is another nearly invisible dot.

Figure 7. This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)

Problems & Exercises

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?
Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.
What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of 30.0º?
Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45.0º.
Calculate the wavelength of light that has its third minimum at an angle of 30.0º when falling on double slits separated by 3.00 μm.
What is the wavelength of light falling on double slits separated by 2.00 μm if the third-order maximum is at an angle of 60.0º?
At what angle is the fourth-order maximum for the situation in Question 1?
What is the highest-order maximum for 400-nm light falling on double slits separated by 25.0 μm?
Find the largest wavelength of light falling on double slits separated by 1.20 μm for which there is a first-order maximum. Is this in the visible part of the spectrum?
What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?
(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?
(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10.0º, at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

The figure shows a schematic of a double slit experiment. A double slit is at the left and a screen is at the right. The slits are separated by a distance d. From the midpoint between the slits, a horizontal line labeled x extends to the screen. From the same point, a line angled upward at an angle theta above the horizontal also extends to the screen. The distance between where the horizontal line hits the screen and where the angled line hits the screen is marked y, and the distance between adjacent fringes is given by delta y, which equals x times lambda over d.

Figure 8. The distance between adjacent fringes is [latex]\Delta{y}=\frac{x\lambda}{d}\\[/latex], assuming the slit separation d is large compared with λ .

Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8.
Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8).

coherent: waves are in phase or have a definite phase relationship

constructive interference for a double slit: the path length difference must be an integral multiple of the wavelength

destructive interference for a double slit: the path length difference must be a half-integral multiple of the wavelength

incoherent: waves have random phase relationships

order: the integer m used in the equations for constructive and destructive interference for a double slit

Selected Solutions to Problems & Exercises

3. 1.22 × 10 −6 m

9. 1200 nm (not visible)

11. (a) 760 nm; (b) 1520 nm

13. For small angles sin θ − tan θ ≈ θ (in radians).

For two adjacent fringes we have, d sin θ m = mλ and d sin θ m + 1 = ( m + 1) λ

Subtracting these equations gives

[latex]\begin{array}{}d\left(\sin{\theta }_{\text{m}+1}-\sin{\theta }_{\text{m}}\right)=\left[\left(m+1\right)-m\right]\lambda \\ d\left({\theta }_{\text{m}+1}-{\theta }_{\text{m}}\right)=\lambda \\ \text{tan}{\theta }_{\text{m}}=\frac{{y}_{\text{m}}}{x}\approx {\theta }_{\text{m}}\Rightarrow d\left(\frac{{y}_{\text{m}+1}}{x}-\frac{{y}_{\text{m}}}{x}\right)=\lambda \\ d\frac{\Delta y}{x}=\lambda \Rightarrow \Delta y=\frac{\mathrm{x\lambda }}{d}\end{array}\\[/latex]

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The discovery of light's wave-particle duality

The observation of interference effects definitively indicates the presence of overlapping waves. Thomas Young postulated that light is a wave and is subject to the superposition principle; his great experimental achievement was to demonstrate the constructive and destructive interference of light (c. 1801). In a modern version of Young’s experiment, differing in its essentials only in the source of light, a laser equally illuminates two parallel slits in an otherwise opaque surface. The light passing through the two slits is observed on a distant screen. When the widths of the slits are significantly greater than the wavelength of the light, the rules of geometrical optics hold—the light casts two shadows, and there are two illuminated regions on the screen. However, as the slits are narrowed in width, the light diffracts into the geometrical shadow, and the light waves overlap on the screen. (Diffraction is itself caused by the wave nature of light, being another example of an interference effect—it is discussed in more detail below.)

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The superposition principle determines the resulting intensity pattern on the illuminated screen. Constructive interference occurs whenever the difference in paths from the two slits to a point on the screen equals an integral number of wavelengths (0, λ, 2λ,…). This path difference guarantees that crests from the two waves arrive simultaneously. Destructive interference arises from path differences that equal a half-integral number of wavelengths (λ/2, 3λ/2,…). Young used geometrical arguments to show that the superposition of the two waves results in a series of equally spaced bands, or fringes, of high intensity, corresponding to regions of constructive interference, separated by dark regions of complete destructive interference.

An important parameter in the double-slit geometry is the ratio of the wavelength of the light λ to the spacing of the slits d . If λ/ d is much smaller than 1, the spacing between consecutive interference fringes will be small, and the interference effects may not be observable. Using narrowly separated slits, Young was able to separate the interference fringes. In this way he determined the wavelengths of the colours of visible light. The very short wavelengths of visible light explain why interference effects are observed only in special circumstances—the spacing between the sources of the interfering light waves must be very small to separate regions of constructive and destructive interference.

Observing interference effects is challenging because of two other difficulties. Most light sources emit a continuous range of wavelengths, which result in many overlapping interference patterns, each with a different fringe spacing. The multiple interference patterns wash out the most pronounced interference effects, such as the regions of complete darkness. Second, for an interference pattern to be observable over any extended period of time, the two sources of light must be coherent with respect to each other. This means that the light sources must maintain a constant phase relationship. For example, two harmonic waves of the same frequency always have a fixed phase relationship at every point in space, being either in phase, out of phase, or in some intermediate relationship. However, most light sources do not emit true harmonic waves; instead, they emit waves that undergo random phase changes millions of times per second. Such light is called incoherent . Interference still occurs when light waves from two incoherent sources overlap in space, but the interference pattern fluctuates randomly as the phases of the waves shift randomly. Detectors of light, including the eye, cannot register the quickly shifting interference patterns, and only a time-averaged intensity is observed. Laser light is approximately monochromatic (consisting of a single wavelength) and is highly coherent; it is thus an ideal source for revealing interference effects.

After 1802, Young’s measurements of the wavelengths of visible light could be combined with the relatively crude determinations of the speed of light available at the time in order to calculate the approximate frequencies of light. For example, the frequency of green light is about 6 × 10 14 Hz ( hertz , or cycles per second). This frequency is many orders of magnitude larger than the frequencies of common mechanical waves. For comparison, humans can hear sound waves with frequencies up to about 2 × 10 4 Hz. Exactly what was oscillating at such a high rate remained a mystery for another 60 years.

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154 Young’s Double Slit Experiment

[latexpage]

Learning Objectives

Explain the phenomena of interference.
Define constructive interference for a double slit and destructive interference for a double slit.

Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single $\lambda $) light to clarify the effect. (Figure) shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in (Figure) (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in (Figure) (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in (Figure) . Each slit is a different distance from a given point on the screen. Thus different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in (Figure) (a). If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in (Figure) (b). More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths [$\left(1/2\right)\lambda $, $\left(3/2\right)\lambda $, $\left(5/2\right)\lambda $, etc.], then destructive interference occurs. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ($\lambda $, $2\lambda $, $3\lambda $, etc.), then constructive interference occurs.

(Figure) shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. If the screen is a large distance away compared with the distance between the slits, then the angle $\theta $ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The difference between the paths is shown in the figure; simple trigonometry shows it to be $d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta $, where $d$ is the distance between the slits. To obtain constructive interference for a double slit , the path length difference must be an integral multiple of the wavelength, or

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

where $\lambda $ is the wavelength of the light, $d$ is the distance between slits, and $\theta $ is the angle from the original direction of the beam as discussed above. We call $m$ the order of the interference. For example, $m=4$ is fourth-order interference.

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in (Figure) . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

For fixed $\lambda $ and $m$, the smaller $d$ is, the larger $\theta $ must be, since $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }/d$. This is consistent with our contention that wave effects are most noticeable when the object the wave encounters (here, slits a distance $d$ apart) is small. Small $d$ gives large $\theta $, hence a large effect.

Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of $\text{10}\text{.}\text{95º}$ relative to the incident beam. What is the wavelength of the light?

The third bright line is due to third-order constructive interference, which means that $m=3$. We are given $d=0\text{.}\text{0100}\phantom{\rule{0.25em}{0ex}}\text{mm}$ and $\theta =\text{10}\text{.}\text{95º}$. The wavelength can thus be found using the equation $d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }$ for constructive interference.

The equation is $d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }$. Solving for the wavelength $\lambda $ gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with $\lambda $, so that spectra (measurements of intensity versus wavelength) can be obtained.

Interference patterns do not have an infinite number of lines, since there is a limit to how big $m$ can be. What is the highest-order constructive interference possible with the system described in the preceding example?

Strategy and Concept

The equation $d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)$ describes constructive interference. For fixed values of $d$ and $\lambda $, the larger $m$ is, the larger $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta $ is. However, the maximum value that $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta $ can have is 1, for an angle of $\text{90º}$. (Larger angles imply that light goes backward and does not reach the screen at all.) Let us find which $m$ corresponds to this maximum diffraction angle.

Solving the equation $d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }$ for $m$ gives

Taking $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =1$ and substituting the values of $d$ and $\lambda $ from the preceding example gives

Therefore, the largest integer $m$ can be is 15, or

Section Summary

Young’s double slit experiment gave definitive proof of the wave character of light.
An interference pattern is obtained by the superposition of light from two slits.
There is constructive interference when $d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)$, where $d$ is the distance between the slits, $\theta $ is the angle relative to the incident direction, and $m$ is the order of the interference.
There is destructive interference when $d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\left(m+\frac{1}{2}\right)\lambda \phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.5em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots \right)$.

Conceptual Questions

Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

Is it possible to create a situation in which there is only destructive interference? Explain.

(Figure) shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

$0\text{.}\text{516º}$

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of $\text{30}\text{.}0º$?

$1\text{.}\text{22}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}$

Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of $\text{45}\text{.}0º$.

Calculate the wavelength of light that has its third minimum at an angle of $\text{30}\text{.}0º$ when falling on double slits separated by $3\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μm}$. Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics .

What is the wavelength of light falling on double slits separated by $2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μm}$ if the third-order maximum is at an angle of $\text{60}\text{.}0º$?

At what angle is the fourth-order maximum for the situation in (Figure) ?

$2\text{.}\text{06º}$

What is the highest-order maximum for 400-nm light falling on double slits separated by $\text{25}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{μm}$?

Find the largest wavelength of light falling on double slits separated by $1\text{.}\text{20}\phantom{\rule{0.25em}{0ex}}\text{μm}$ for which there is a first-order maximum. Is this in the visible part of the spectrum?

1200 nm (not visible)

What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

(b) 1520 nm

(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of $\text{10}\text{.}0º$, at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?

(Figure) shows a double slit located a distance $x$ from a screen, with the distance from the center of the screen given by $y$. When the distance $d$ between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta $, with $\theta $ in radians), the distance between fringes is given by $\text{Δ}y=\mathrm{x\lambda }/d$.

For small angles $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta -\text{tan}\phantom{\rule{0.25em}{0ex}}\theta \approx \theta \phantom{\rule{0.25em}{0ex}}\left(\text{in radians}\right)$.

For two adjacent fringes we have,

Subtracting these equations gives

Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in (Figure) .

Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see (Figure) ).

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Chapter 27 Wave Optics

27.3 Young’s Double Slit Experiment

Explain the phenomena of interference.
Define constructive interference for a double slit and destructive interference for a double slit.

When light passes through narrow slits, it is diffracted into semicircular waves, as shown in Figure 3 (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in Figure 3 (b). Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below.

Take-Home Experiment: Using Fingers as Slits

Similarly, to obtain destructive interference for a double slit , the path length difference must be a half-integral multiple of the wavelength, or

$\boldsymbol{d \;\textbf{sin} \;\theta = m +}$

The equations for double slit interference imply that a series of bright and dark lines are formed. For vertical slits, the light spreads out horizontally on either side of the incident beam into a pattern called interference fringes, illustrated in Figure 6 . The intensity of the bright fringes falls off on either side, being brightest at the center. The closer the slits are, the more is the spreading of the bright fringes. We can see this by examining the equation

$\boldsymbol{d \;\textbf{sin} \;\theta = m \theta , \;\textbf{for} \; m = 0, \;1, \; -1, \; 2, \; -2, \; \dots}.$

Example 1: Finding a Wavelength from an Interference Pattern

$\boldsymbol{10.95 ^{\circ}}$

Substituting known values yields

$$\begin{array}{r @{{}={}}l} \boldsymbol{\lambda} & \boldsymbol{\frac{(0.0100 \;\textbf{mm})(\textbf{sin} 10.95^{\circ})}{3}} \\[1em] & \boldsymbol{6.33 \times 10^{-4} \;\textbf{mm} = 633 \;\textbf{nm}}. \end{array}$

Example 2: Calculating Highest Order Possible

Strategy and Concept

$\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda \; (\textbf{for} \; m = 0, \; 1, \; -1, \; 2, \; -2, \; \dots)}$

Section Summary

Young’s double slit experiment gave definitive proof of the wave character of light.
An interference pattern is obtained by the superposition of light from two slits.

$\boldsymbol{d \;\textbf{sin} \;\theta = m \lambda \;(\textbf{for} \; m = 0, \; 1, \; -1, \;2, \; -2, \dots)}$

Conceptual Questions

1: Young’s double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

2: Suppose you use the same double slit to perform Young’s double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.

3: Is it possible to create a situation in which there is only destructive interference? Explain.

4: Figure 7 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses.

Problems & Exercises

2: Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

$\boldsymbol{30.0 ^{\circ}}$

7: At what angle is the fourth-order maximum for the situation in Problems & Exercises 1 ?

$\boldsymbol{25.0 \;\mu \textbf{m}}$

10: What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

11: (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

$\boldsymbol{10.0^{\circ}}$

14: Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 8 .

15: Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 8 ).

$\boldsymbol{0.516 ^{\circ}}$

9: 1200 nm (not visible)

11: (a) 760 nm

(b) 1520 nm

$\boldsymbol{\textbf{sin} \;\theta - \;\textbf{tan} \;\theta \approx \theta}$

For two adjacent fringes we have,

$\boldsymbol{d \;\textbf{sin} \;\theta _{\textbf{m}} = m \lambda}$

Subtracting these equations gives

$\begin{array}{r @{{}={}}l} \boldsymbol{d (\textbf{sin} \; \theta _{\textbf{m} + 1} - \textbf{sin} \; \theta _{\textbf{m}})} & \boldsymbol{[(m + 1) - m] \lambda} \\[1em] \boldsymbol{d(\theta _{{\textbf{m}} + 1} - \theta _{\textbf{m}})} & \boldsymbol{\lambda} \end{array}$

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What Is The Double-Slit Experiment?

The double-slit experiment, observation affects reality, the various interpretations:.

The double-slit experiment shows the duality of the quantum world. A photon’s wave/particle duality is affected when it is observed.

Light has been one of the major areas of inquiry for physicists since we first began questioning the world around us. Understandably so, as it is the medium by which we see, measure and understand the world. It holds a powerful symbolism in our imaginations, is reflected in our religions and is famously quoted in our scriptures.

Rigorous science has enlightened our ignorance about Light. Until the 1800s, light was thought to be made up of particles, attested by Newtonian physics.

This came rather intuitively, as we see light traveling in a straight line, like bullets coming out of a gun.

Prison cell interior , sunrays coming through a barred window - Illustration(nobeastsofierce)S

However, nature is often weirder than our expectations and light’s weird behavior was first shown by Thomas Young in his now heavily worked upon and immortalized double-slit experiment. This experiment provides some fascinating insights into the minute workings of nature and has challenged everything we know about light, matter, and reality itself. Let’s revisit the experiment that has baffled legendary scientists – including Einstein!

What Is Light? Matter Or Energy?

What Is Diffraction And Diffraction Grating?

Interferometer: What Is The Michelson Interferometer Experiment?

What Is Quantum Mechanics?

Without Magic, Could You Get Through Platform 9 ¾?

Gravitation,Waves,Around,Black,Hole,In,Space,3d,Illustration

What Is Quantum Physics?

Quantum Entanglement: Explained in REALLY SIMPLE Words

Photoelectric Effect Explained in Simple Words for Beginners

What Would Happen If You Traveled At The Speed of Light?

What is the Heisenberg Uncertainty Principle: Explained in Simple Words

Quantum Physics: Here’s Why Movies Always Get It Wrong

Time Dilation - Einstein's Theory Of Relativity Explained!

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Quantum mechanics
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The double-slit experiment

This article is an extended version of the article “The double-slit experiment” that appeared in the September 2002 issue of Physics World (p15). It has been further extended to include three letters about the history of the double-slit experiment with single electrons that were published in the May 2003 issue of the magazine.

What is the most beautiful experiment in physics? This is the question that Robert Crease asked Physics World readers in May – and more than 200 replied with suggestions as diverse as Schrödinger’s cat and the Trinity nuclear test in 1945. The top five included classic experiments by Galileo, Millikan, Newton and Thomas Young. But uniquely among the top 10, the most beautiful experiment in physics – Young’s double-slit experiment applied to the interference of single electrons – does not have a name associated with it.

Most discussions of double-slit experiments with particles refer to Feynman’s quote in his lectures: “We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.” Feynman went on to add: “We should say right away that you should not try to set up this experiment. This experiment has never been done in just this way. The trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in. We are doing a “thought experiment”, which we have chosen because it is easy to think about. We know the results that would be obtained because there are many experiments that have been done, in which the scale and the proportions have been chosen to show the effects we shall describe”.

It is not clear that Feynman was aware that the first double-slit experiment with electrons had been carried out in 1961, the year he started his lectures (which were published in 1963). More surprisingly, perhaps, Feynman did not stress that an interference pattern would build up even if there was just one electron in the apparatus at a time. (This lack of emphasis was unusual because in the same lecture Feynman describes the electron experiment – and other double-slit experiments with water waves and bullets – in considerable detail).

So who actually carried out the first double-slit experiment with single electrons? Not surprisingly many thought or gedanken experiments are named after theorists – such as the Aharonov-Bohm effect, Bell’s inequality, the Casimir force, the Einstein-Podolsky-Rosen paradox, Schrödinger’s cat and so on – and these names rightly remain even when the experiment has been performed by others in the laboratory. However, it seems remarkable that no name whatsoever is attached to the double-slit experiment with electrons. Standard reference books are silent on this question but a study of the literature reveals several unsung experimental heroes.

Back to Young

Young carried out his original double-slit experiment with light some time in the first decade of the 1800s, showing that the waves of light from the two slits interfered to produce a characteristic fringe pattern on a screen. In 1909 Geoffrey Ingram (G I) Taylor conducted an experiment in which he showed that even the feeblest light source – equivalent to “a candle burning at a distance slightly exceeding a mile” – could lead to interference fringes. This led to Dirac’s famous statement that “each photon then interferes only with itself”.

In 1927 Clinton Davisson and Lester Germer observed the diffraction of electron beams from a nickel crystal – demonstrating the wave-like properties of particles for the first time – and George (G P) Thompson did the same with thin films of celluloid and other materials shortly afterwards. Davisson and Thomson shared the 1937 Nobel prize for “discovery of the interference phenomena arising when crystals are exposed to electronic beams”, but neither performed a double-slit experiment with electrons.

In the early 1950s Ladislaus Laszlo Marton of the US National Bureau of Standards (now NIST) in Washington, DC demonstrated electron interference but this was in a Mach-Zehnder rather than a double-slit geometry. These were the early days of the electron microscope and physicists were keen to exploit the very short de Broglie wavelength of electrons to study objects that were too small to be studied with visible light. Doing gedanken or thought experiments in the laboratory was further down their list of priorities.

A few years later Gottfried Möllenstedt and Heinrich Düker of the University of Tübingen in Germany used an electron biprism – essentially a very thin conducting wire at right angles to the beam – to split an electron beam into two components and observe interference between them. (Möllenstedt made the wires by coating fibres from spiders’ webs with gold – indeed, it is said that he kept spiders in the laboratory for this purpose). The electron biprism was to become widely used in the development of electron holography and also in other experiments, including the first measurement of the Aharonov-Bohm effect by Bob Chambers at Bristol University in the UK in 1960.

But in 1961 Claus Jönsson of Tübingen, who had been one of Möllenstedt’s students, finally performed an actual double-slit experiment with electrons for the first time ( Zeitschrift für Physik 161 454). Indeed, he demonstrated interference with up to five slits. The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( American Journal of Physics 57 117-120). Whereas Jönsson’s experiment was analogous to Young’s original experiment, Tonomura’s was similar to G I Taylor’s. (Note added on 7 May: Pier Giorgio Merli, Giulio Pozzi and GianFranco Missiroli carried out double-slit interference experiments with single electrons in Bologna in the 1970s; see Merli et al. in Further reading and the letters from Steeds, Merli et al. , and Tonomura at the end of this article.)

Since then particle interference has been demonstrated with neutrons, atoms and molecules as large as carbon-60 and carbon-70. And earlier this year another famous experiment in optics – the Hanbury Brown and Twiss experiment – was performed with electrons for the first time (again at Tübingen!). However, the results are profoundly different this time because electrons are fermions – and therefore obey the Pauli exclusion principle – whereas photons are bosons and do not.

Credit where it’s due

So why are Jönsson, Tonomura and the other pioneers of the double-slit experiment not well known? One obvious reason is that Jönsson’s results were first published in German in a German journal. Another reason might be that there was little incentive to perform the ultimate thought experiment in the lab, and little recognition for doing so. When Jönsson’s paper was translated into English 13 years later and published in the American Journal of Physics in 1974 (volume 42, pp4-11), the journal’s editors, Anthony (A P) French and Edwin Taylor, described it as a “great experiment”, but added that there are “few professional rewards” for performing what they describe as “real, pedagogically clean fundamental experiments.”

It is worth noting that the first double-slit experiment with single electrons by Tonomura and co-workers was also published in the American Journal of Physics , which publishes articles on the educational and cultural aspects of physics, rather than being a research journal. Indeed, the journal’s information for contributors states: “We particularly encourage manuscripts on already published contemporary research that can be used directly or indirectly in the classroom. We specifically do not publish articles announcing new theories or experimental results.”

French and Taylor’s editorial also confirms how little known Jönsson’s experiment was at the time: “For decades two-slit electron interference has been presented as a thought experiment whose predicted results are justified by their remote and somewhat obscure relation to real experiments in which electrons are diffracted by crystals. Few such recent presentations acknowledge that the two-slit electron interference experiment has now been done and that the results agree with the expectation of quantum physics in all detail.”

However, it should be noted that the history of physics is complicated and that events are rarely as clear-cut as we might like. For instance, it is widely claimed that Young performed his double-slit experiment in 1801 but he did not publish any account of it until his Lectures on Natural Philosophy in 1807. It also appears as if Davisson and a young collaborator called Charles Kunsman observed electron diffraction in 1923 – four years before Davisson and Germer – without realising it.

Final thoughts

Gedanken or thought experiments have played an important role in the history of quantum physics. It is unlikely that the whole area of quantum information would be as lively as it is today – both theoretically and experimentally – if a small band of physicists had not persevered and actually demonstrated quantum phenomena with individual particles.

At one time the Casimir force, which has yet to be measured with an accuracy of better than 15% in the geometry first proposed by Hendrik Casimir in 1948, might also have been viewed as purely a pedagogical experiment – a gedanken experiment with little relevance to real experimental physics. However, it is now clear that applications as varied as nanotechnology and experimental tests of theories of “large” extra dimensions require a detailed knowledge of the Casimir force .

The need for “real, pedagogically clean fundamental experiments” is clearly as great as ever.

This is a longer version of the article “The double-slit experiment” that appeared in the print version of the September issue of Physics World, on page 15. Three letters that appeared in the May 2003 issue of the magazine have been added to the end of this version of the article.

T Young 1802 On the theory of light and colours (The 1801 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 92 12-48

T Young 1804 Experiments and calculations relative to physical optics (The 1803 Bakerian Lecture) Philosophical Transactions of the Royal Society of London 94 1-16

T Young 1807 A Course of Lectures on Natural Philosophy and the Mechanical Arts (J Johnson, London)

G I Taylor 1909 Interference fringes with feeble light Proceedings of the Cambridge Philosophical Society 15 114-115

P A M Dirac 1958 The Principles of Quantum Mechanics (Oxford University Press) 4th edn p9

R P Feynman, R B Leighton and M Sands 1963 The Feynman Lecture on Physics (Addison-Wesley) vol 3 ch 37 (Quantum behaviour)

A Howie and J E Fowcs Williams (eds) 2002 Interference: 200 years after Thomas Young’s discoveries Philosophical Transactions of the Royal Society of London 360 803-1069

R P Crease 2002 The most beautiful experiment Physics World September pp19-20. This article contains the results of Crease’s survey for Physics World ; the first article about the survey appeared on page 17 of the May 2002 issue.

Electron interference experiments

Visit www.nobel.se/physics/laureates/1937/index.html for details of the Nobel prize awarded to Clinton Davisson and George Thomson

L Marton 1952 Electron interferometer Physical Review 85 1057-1058

L Marton, J Arol Simpson and J A Suddeth 1953 Electron beam interferometer Physical Review 90 490-491

L Marton, J Arol Simpson and J A Suddeth 1954 An electron interferometer Reviews of Scientific Instruments 25 1099-1104

G Möllenstedt and H Düker 1955 Naturwissenschaften 42 41

G Möllenstedt and H Düker 1956 Zeitschrift für Physik 145 377-397

G Möllenstedt and C Jönsson 1959 Zeitschrift für Physik 155 472-474

R G Chambers 1960 Shift of an electron interference pattern by enclosed magnetic flux Physical Review Letters 5 3-5

C Jönsson 1961 Zeitschrift für Physik 161 454-474

C Jönsson 1974 Electron diffraction at multiple slits American Journal of Physics 42 4-11

A P French and E F Taylor 1974 The pedagogically clean, fundamental experiment American Journal of Physics 42 3

P G Merli, G F Missiroli and G Pozzi 1976 On the statistical aspect of electron interference phenomena American Journal of Physics 44 306-7

A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron build-up of an interference pattern American Journal of Physics 57 117-120

H Kiesel, A Renz and F Hasselbach 2002 Observation of Hanbury Brown-Twiss anticorrelations for free electrons Nature 418 392-394

Atoms and molecules

O Carnal and J Mlynek 1991 Young’s double-slit experiment with atoms: a simple atom interferometer Physical Review Letters 66 2689-2692

D W Keith, C R Ekstrom, Q A Turchette and D E Pritchard 1991 An interferometer for atoms Physical Review Letters 66 2693-2696

M W Noel and C R Stroud Jr 1995 Young’s double-slit interferometry within an atom Physical Review Letters 75 1252-1255

M Arndt, O Nairz, J Vos-Andreae, C Keller, G van der Zouw and A Zeilinger 1999 Wave-particle duality of C 60 molecules Nature 401 680-682

B Brezger, L Hackermüller, S Uttenthaler, J Petschinka, M Arndt and A Zeilinger 2002 Matter-wave interferometer for large molecules Physical Review Letters 88 100404

Review articles and books

G F Missiroli, G Pozzi and U Valdrè 1981 Electron interferometry and interference electron microscopy Journal of Physics E 14 649-671. This review covers early work on electron interferometry by groups in Bologna, Toulouse, Tübingen and elsewhere.

A Zeilinger, R Gähler, C G Shull, W Treimer and W Mampe 1988 Single- and double-slit diffraction of neutrons Reviews of Modern Physics 60 1067-1073

A Tonomura 1993 Electron Holography (Springer-Verlag, Berlin/New York)

H Rauch and S A Werner 2000 Neutron Interferometry: Lessons in Experimental Quantum Mechanics (Oxford Science Publications)

The double-slit experiment with single electrons

The article “A brief history of the double-slit experiment” (September 2002 p15; correction October p17) describes how Claus Jönsson of the University of Tübingen performed the first double-slit interference experiment with electrons in 1961. It then goes on to say: “The next milestone – an experiment in which there was just one electron in the apparatus at any one time – was reached by Akira Tonomura and co-workers at Hitachi in 1989 when they observed the build up of the fringe pattern with a very weak electron source and an electron biprism ( Am. J. Phys. 57 117-120)”.

In fact, I believe that “the first double-slit experiment with single electrons” was performed by Pier Giorgio Merli, GianFranco Missiroli and Giulio Pozzi in Bologna in 1974 – some 15 years before the Hitachi experiment. Moreover, the Bologna experiment was performed under very difficult experimental conditions: the intrinsic coherence of the thermionic electron source used by the Bologna group was considerably lower than that of the field-emission source used in the Hitachi experiment.

The Bologna experiment is reported in a film called “Electron Interference” that received the award in the physics category at the International Festival on Scientific Cinematography in Brussels in 1976. A selection of six frames from the film ( see figure ) was also used for a short paper, “On the statistical aspect of electron interference phenomena”, that was submitted for publication in May 1974 and published two years later (P G Merli, G F Missiroli and G Pozzi 1976 Am. J. Phys. 44 306-7).

John Steeds Department of Physics, University of Bristol [email protected]

The history of science is not restricted to the achievements of big scientists or big scientific institutions. Contributions can also be made by researchers with the necessary background, curiosity and enthusiasm. In the period 1973-1974 we were investigating practical applications of electron interferometry with a Siemens Elmiskop 101 electron microscope that had been carefully calibrated at the CNR-LAMEL laboratory in Bologna, where one of us (PGM) was based ( J. Phys. E7 729-32).

These experiments followed earlier work at the Istituto di Fisica in 1972-73 in which the electron biprism was inserted in a Siemens Elmiskop IA and then used both for didactic ( Am. J. Phys. 41 639-644) and research experiments ( J. Microscopie 18 103-108). We used the Elmiskop 101 for many experiments including, for instance, the observation of the electrostatic field associated with p-n junctions ( J. Microscopie 21 11-20).

During this period we learnt that Professors Angelo and Aurelio Bairati in the Institute of Anatomy at the University of Milan had bought an image intensifier that could be used with the Elmiskop 101. Out of curiosity, and also realizing the conceptual importance of interference experiments with single photons or electrons, we asked if we could attempt to perform an interference experiment with single electrons in the Milan laboratory. Our results formed the basis of the film “Electron interference” and were also published in 1976 ( Am. J. Phys. 44 306-7).

Following the publication of the paper by Tonomura and co-workers in 1989, which did not refer to our 1976 paper (although it did contain an incorrect reference to our film), the American Journal of Physics published a letter from Greyson Gilson of Submicron Structures Inc. The letter stated: “Tonomura et al. seem to believe that they were the first to perform a successful two-slit interference experiment using electrons and also that they were the first to observe the cumulative build-up of the resulting electron interference pattern. Although their demonstration is very admirable, reports of similar work have appeared in this Journal for about 30 years (see, for examples, Refs. 2-7.) It seems inappropriate to permit the widespread misconception that such experiments have not been performed and perhaps cannot be performed to continue.” (G Gilson 1989 Am. J. Phys. 57 680). Three of the seven papers that Gilson refers to were from our group in Bologna.

The main subject of our 1976 paper and the 1989 paper from the Hitachi group are the same: the single-electron build-up of the interference pattern and the statistical aspect of the phenomena. Obviously the electron-detection system used by the Hitachi group in 1989 was more sophisticated than the one we used in 1974. However, the sentence on page 118 of the paper by Tonomura et al. , which states that in our film we “showed the electron arrival in each frame without recording the cumulative arrivals”, is not correct: this can be seen by watching the film and looking at figure 1 of our 1976 paper (a version of which is shown here ).

Finally, it is also worth noting that the first double-slit experiment with single electrons was actually a by-product of research into the practical applications of electron interferometry.

Pier Giorgio Merli LAMEL, CNR Bologna, Italy [email protected] Giulio Pozzi Department of Physics, University of Bologna [email protected] GianFranco Missiroli Department of Physics, University of Bologna [email protected]

The Bologna group photographed the monitor of a sensitive TV camera as they changed the intensity of an electron beam. They observed that a few light flashes of electrons appeared at low intensities, and that interference fringes were formed at high intensities. They also mentioned that they were able to increase the storage time up to “values of minutes”. Historically, they are the first to report such experiments concerning the formation of interference patterns as far as I know.

Later, similar experiments were conducted by Hannes Lichte, then at Tübingen and now at Dresden. Important experiments on electron interference were also carried out by Valentin Fabrikant and co-workers at the Moscow Institute for Energetics in 1949 and later by Takeo Ichinokawa of Waseda University in Tokyo.

Our experiments at Hitachi (A Tonomura, J Endo, T Matsuda, T Kawasaki and H Ezawa 1989 Demonstration of single-electron buildup of an interference pattern Am. J. Phys. 57 117–120) differed from these experiments in the following respects:

(a) Our experiments were carried out from beginning to end with constant and extremely low electron intensities – fewer than 1000 electrons per second – so there was no chance of finding two or more electrons in the apparatus at the same time. This removed any possibility that the fringes might be due to interactions between the electrons, as had been suspected by some physicists, such as Sin-Itiro Tomonaga.

(b) We developed a position-sensitive electron-counting system that was modified from the photon-counting image acquisition system produced by Hamamatsu Photonics. In this system, the formation of fringes could be observed as a time series; the electrons were accumulated over time to gradually form an interference pattern on the monitor (similar to a long exposure with a photographic film). The electrons arrived at random positions on the detector only once in a while and it took more than 20 minutes for the interference pattern to form (see figure). To film the build-up process, the electron source, the electron biprism and the rest of the experiment therefore had to be extremely stable: if the interference pattern had drifted by a fraction of fringe spacing over the exposure time, the whole fringe pattern would have disappeared.

(c) The electrons arriving at the detector were detected with almost 100% efficiency. Counting losses and noise in conventional TV cameras mean that it is difficult to know if each flash of the screen really corresponds to an individual electron. Therefore, the detection error in our experiment was limited to less than 1%.

We believe that we carried out the first experiment in which the build-up process of an interference pattern from single-electron events could be seen in real time as in Feynman’s famous double-slit Gedanken experiment under the condition, we emphasize, that there was no chance of finding two or more electrons in the apparatus.

Akira Tonomura Hitachi Advanced Research Laboratory, Saitama, Japan [email protected]

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The double-slit experiment: Is light a wave or a particle?

The double-slit experiment is universally weird.

The double-slit experiment shows light waves rippling across between two slits and interfering with each other.

How does the double-slit experiment work?

Interference patterns from waves, particle patterns, double-slit experiment: quantum mechanics, history of the double-slit experiment, additional resources.

The double-slit experiment is one of the most famous experiments in physics and definitely one of the weirdest. It demonstrates that matter and energy (such as light) can exhibit both wave and particle characteristics — known as the particle-wave duality of matter — depending on the scenario, according to the scientific communication site Interesting Engineering .

According to the University of Sussex , American physicist Richard Feynman referred to this paradox as the central mystery of quantum mechanics.

We know the quantum world is strange, but the two-slit experiment takes things to a whole new level. The experiment has perplexed scientists for over 200 years, ever since the first version was first performed by British scientist Thomas Young in 1801.

Related: 10 mind-boggling things you should know about quantum physics

Christian Huygens was the first to describe light as traveling in waves whilst Isaac Newton thought light was composed of tiny particles according to Las Cumbres Observatory . But who is right? British polymath Thomas Young designed the double-slit experiment to put these theories to the test.

To appreciate the truly bizarre nature of the double-split experiment we first need to understand how waves and particles act when passing through two slits.

When Young first carried out the double-split experiment in 1801 he found that light behaved like a wave.

Firstly, if we were to shine a light on a wall with two parallel slits — and for the sake of simplicity, let's say this light has only one wavelength.

As the light passes through the slits, each, in turn, becomes almost like a new source of light. On the far side of the divider, the light from each slit diffracts and overlaps with the light from the other slit, interfering with each other.

double slit experiment showing interference pattern made from light waves.

According to Stony Brook University , any wave can create an interference pattern, whether it be a sound wave, light wave or waves across a body of water. When a wave crest hits a wave trough they cancel each other out — known as destructive interference — and appear as a dark band. When a crest hits a crest they amplify each other — known as constructive interference — and appear as a bright band. The combination of dark and bright bands is known as an interference pattern and can be seen on the sensor screen opposite the slits.

This interference pattern was the evidence Young needed to determine that light was a wave and not a particle as Newton had suggested.

But that is not the whole story. Light is a little more complicated than that, and to see how strange it really is we also need to understand what pattern a particle would make on a sensor field.

If you were to carry out the same experiment and fire grains of sand or other particles through the slits, you would end up with a different pattern on the sensor screen. Each particle would go through a slit end up in a line in roughly the same place (with a little bit of spread depending on the angle the particle passed through the slit).

double-slit experiment showing the pattern made from particles passing through two slits

Clearly, waves and particles produce a very different pattern, so it should be easy to distinguish between the two right? Well, this is where the double-slit experiment gets a little strange when we try and carry out the same experiment but with tiny particles of light called photons. Enter the realm of quantum mechanics.

The smallest constituent of light is subatomic particles called photons. By using photons instead of grains of sand we can carry out the double-slit experiment on an atomic scale.

If you block off one of the slits, so it is just a single-slit experiment, and fire photons through to the sensor screen, the photons will appear as pinprick points on the sensor screen, mimicking the particle patterns produced by sand in the previous example. From this evidence, we could suggest that photons are particles.

double-slit experiment photons fired through just one slit with the other slit blocked off.

Now, this is where things start to get weird.

If you unblock the slit and fire photons through both slits, you start to see something very similar to the interference pattern produced by waves in the light example. The photons appear to have gone through the pair of slits acting like waves.

But what if you launch photons one by one, leaving enough time between them that they don't have a chance of interfering with each other, will they behave like particles or waves?

At first, the photons appear on the sensor screen in a random scattered manner, but as you fire more and more of them, an interference pattern begins to emerge. Each photon by itself appears to be contributing to the overall wave-like behavior that manifests as an interference pattern on the screen — even though they were launched one at a time so that no interference between them was possible.

double-slit experiment firing photons through both slits

It's almost as though each photon is "aware" that there are two slits available. How? Does it split into two and then rejoin after the slit and then hit the sensor? To investigate this, scientists set up a detector that can tell which slit the photon passes through.

Again, we fire photons one at a time at the slits, as we did in the previous example. The detector finds that about 50% of the photons have passed through the top slit and about 50% through the bottom, and confirms that each photon goes through one slit or the other. Nothing too unusual there.

But when we look at the sensor screen on this experiment, a different pattern emerges.

double-slit experiment with detector turned on

This pattern matches the one we saw when we fired particles through the slits. It appears that monitoring the photons triggers them to switch from the interference pattern produced by waves to that produced by particles.

If the detection of photons through the slits is apparently affecting the pattern on the sensor screen, what happens if we leave the detector in place but switch it off? (Shh, don't tell the photons we're no longer spying on them!)

This is where things get really, really weird.

Same slits, same photons, same detector, just turned off. Will we see the same particle-like pattern?

No. The particles again make a wave-like interference pattern on the sensor screen.

double-slit experiment with the detector switched off

The atoms appear to act like waves when you're not watching them, but as particles when you are. How? Well, if you can answer that, a Nobel Prize is waiting for you.

In the 1930s, scientists proposed that human consciousness might affect quantum mechanics. Mathematician John Von Neumann first postulated this in 1932 in his book " The Mathematical Foundations of Quantum Mechanics ." In the 1960s, theoretical physicist, Eugene Wigner conceived a thought experiment called Wigner's friend — a paradox in quantum physics that describes the states of two people, one conducting the experiment and the observer of the first person, according to science magazine Popular Mechanics . The idea that the consciousness of a person carrying out the experiment can affect the result is knowns as the Von Neumann–Wigner interpretation.

Though a spiritual explanation for quantum mechanic behavior is still believed by a few individuals, including author and alternative medicine advocate Deepak Chopra , a majority of the science community has long disregarded it.

As for a more plausible theory, scientists are stumped.

Furthermore —and perhaps even more astonishingly — if you set up the double-slit experiment to detect which slit the photon went through after the photon has already hit the sensor screen, you still end up with a particle-type pattern on the sensor screen, even though the photon hadn't yet been detected when it hit the screen. This result suggests that detecting a photon in the future affects the pattern produced by the photon on the sensor screen in the past. This experiment is known as the quantum eraser experiment and is explained in more detail in this informative video from Fermilab .

We still don't fully understand how exactly the particle-wave duality of matter works, which is why it is regarded as one of the greatest mysteries of quantum mechanics.

British polymath Thomas Young first performed the double-slit experiment in 1801.

The first version of the double-slit experiment was carried out in 1801 by British polymath Thomas Young, according to the American Physical Society (APS). His experiment demonstrated the interference of light waves and provided evidence that light was a wave, not a particle.

Young also used data from his experiments to calculate the wavelengths of different colors of light and came very close to modern values.

Despite his convincing experiment that light was a wave, those who did not want to accept that Isaac Newton could have been wrong about something criticized Young. (Newton had proposed the corpuscular theory, which posited that light was composed of a stream of tiny particles he called corpuscles.)

According to APS, Young wrote in response to one of the critics, "Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible."

Since the development of quantum mechanics, physicists now acknowledge light to be both a particle and a wave.

Explore the double-slit experiment in more detail with this article from the University of Cambridge, which includes images of electron patterns in a double-slit experiment. Discover the true nature of light with Canon Science Lab . Read about fragments of energy that are not waves or particles — but could be the fundamental building blocks of the universe — in this article from The Conversation . Dive deeper into the two-slit experiment in this article published in the journal Nature .

Bibliography

Grangier, Philippe, Gerard Roger, and Alain Aspect. " Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. " EPL (Europhysics Letters) 1.4 (1986): 173.

Thorn, J. J., et al. "Observing the quantum behavior of light in an undergraduate laboratory. " American Journal of Physics 72.9 (2004): 1210-1219.

Ghose, Partha. " The central mystery of quantum mechanics. " arXiv preprint arXiv:0906.0898 (2009).

Aharonov, Yakir, et al. " Finally making sense of the double-slit experiment. " Proceedings of the National Academy of Sciences 114.25 (2017): 6480-6485.

Peng, Hui. " Observations of Cross-Double-Slit Experiments. " International Journal of Physics 8.2 (2020): 39-41.

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Published: 03 September 2024

Quantum double slit experiment with reversible detection of photons

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Quantum mechanics
Single photons and quantum effects

Principle of quantum superposition permits a photon to interfere with itself. As per the principle of causality, a photon must pass through the double-slit prior to its detection on the screen to exhibit interference. In this paper, a double-slit quantum interference experiment with reversible detection of Einstein–Podolsky–Rosen quantum entangled photons is presented. Where a photon is first detected on a screen without passing through a double-slit, while the second photon is propagating towards the double-slit. A detection event on the screen cannot affect the second photon with any signal propagating at the speed of light, even after its passage through the double-slit. After the detection of the first photon on the screen, the second photon is either passed through the double-slit or diverted towards a stationary photon detector. Therefore, the question of whether the first photon carries the which-path information of the second photon in the double-slit is eliminated. No single photon interference is exhibited by the second photon, even if another screen is placed after the double-slit.

Quantum double-double-slit experiment with momentum entangled photons

Which-way identification by an asymmetrical double-slit experiment with monochromatic photons

Revisiting self-interference in Young’s double-slit experiments

Introduction.

In 1801, Young’s double-slit interference experiment proved that light behaves as a wave 1 , 2 . A first experimental observation of interference with very low intensity of light was reported by Taylor 3 . However, quantum mechanically, light consists of discrete energy packets known as photons, which can exhibit particle- or wave-like behaviour. According to the principle of quantum superposition, a single particle can exist at different locations simultaneously 4 , 5 . This counter-intuitive law of nature gives wave nature to a particle, and by its consequence, a particle can interfere with itself, i.e. all quantum superimposed states of a particle interfere with each other. In a single particle quantum double-slit experiment, a single particle is passed through a double-slit, and an interference pattern gradually emerges on the screen by accumulating particle detections by repeating the experiment. Each detection of a particle on the screen determines its position on the screen, whereas this measurement cannot determine the path of a particle in the double-slit. However, the interference pattern cannot be formed, when the which-path information of a particle is measured or stored by modifying the experiment. The casual temporal order of this experiment signifies a detection on the screen after the passage of a particle through the double-slit. This casual self interference was demonstrated experimentally with electrons 6 , 7 , 8 , 9 , neutrons 10 , 11 , photons 12 , 13 and positrons 14 . Quantum mechanics exerts no restriction on the self interference of macromolecules, which is experimentally demonstrated 15 , 16 , 17 , 18 , 19 , 20 . An experiment demonstrating self interference of two-photon amplitudes in a double-double-slit is performed with momentum entangled photons 21 , 22 . Another version of a double-slit experiment is realised by placing a double-slit in the path of one photon, where the interference pattern is formed only when both photons are measured 23 , 24 , 25 , 26 , 27 , 28 , 29 . However, in these experiments, both photons are measured after one of them is passed through the double-slit.

In this paper, a quantum double-slit experiment with reversible detection of photons is presented, which is carried out with continuous variable Einstein–Podolsy–Rosen (EPR) 30 quantum entangled photon pairs. A reversible detection implies that a photon of a quantum entangled pair is first detected on a screen while the other photon is propagating towards a double-slit, and later it can pass either through the double-slit or it can be diverted towards a stationary single photon detector. The experiment is configured such that the detection of a first photon on the screen cannot affect the second photon through any local communication, even after its interaction with the double-slit. This is because the second photon is separated from the detection event by a lightlike interval. Since the second photon passes through the double-slit after the detection of the first photon therefore, the first photon carried no which-path information of the second photon in the double-slit. The second photon is detected by stationary single photon detectors, which are placed at fixed locations throughout the interference experiment. The interference pattern is produced on the screen by repeating the experiment each time with a new EPR entangled pair, provided those photon detections on the screen are considered when the second photon is detected by a stationary detector positioned after the double-slit. However, position measurements of individual photons do not produce any interference pattern, even if the detector placed after the double-slit is displaced gradually to count photons at different locations. The experiment is performed with continuous variable EPR entangled photon pairs produced simultaneously in a Beta Barium Borate (BBO) nonlinear crystal by Type-I spontaneous parametric down conversion (SPDC) in a noncollinear configuration 31 , 32 , 33 , 34 , 35 , 36 , 37 . A real double-slit is used in this experiment, whereas the quantum entangled pair production rate is intentionally reduced to keep one entangled photon pair in the experiment until its detection. The second EPR entangled pair of photons is produced considerably later than the detection of the first entangled pair of photons. In addition, this paper presents a theoretical analysis of the experiment.

Concept and analysis

The EPR state is a continuous variable entangled quantum state of two particles, where both particles are equally likely to exist at all position and momentum locations. A one-dimensional EPR state in position basis is written as $|\alpha \rangle =\int ^{\infty }_{-\infty }|x\rangle _{1}|x+{\textbf {x}}_{o}\rangle _{2} \textrm{d}x$ , where subscripts 1 and 2 represent particle-1 and particle-2, respectively. A constant ${\textbf {x}}_{o}$ corresponds to the position difference of particles. The same EPR state is expressed in momentum basis as $|\alpha \rangle =\int ^{\infty }_{-\infty }e^{i \frac{p x_{o}}{\hslash }}|p\rangle _{1}|-p\rangle _{2}\textrm{d}p$ , where particles have opposite momenta, and $\hslash =h/2\pi$ is the reduced Planck’s constant. Therefore, both position and momentum of each particle are completely unknown. If the position of any one particle is measured, then the EPR state is randomly collapsed onto $|x'\rangle _{1}|x'+{\textbf {x}}_{o}\rangle _{2}$ where a prime on x indicates a single measured position value from the integral range. Therefore, the measured positions of particles are correlated, i.e. they are separated by ${\textbf {x}}_{o}$ irrespective of $x'$ . Instead of position, if momentum, which is a complementary observable to the position, of a particle is measured, then the EPR state is randomly collapsed onto $| p'\rangle _{1}|-p'\rangle _{2}$ , where both the particles exhibit opposite momenta irrespective of $p'$ thus, their measured momenta are correlated.

A schematic diagram of the experiment, where a screen corresponds to a single photon detector capable of detecting locations of photon detection events. A screen is placed considerably closer to the source than a beam splitter and a double-slit.

In this paper, the EPR state of two photons in three-dimensions, propagated away from a finite size of source, is evaluated as follows: Consider a schematic of the experiment shown in Fig. 1 , where EPR entangled photons are produced by a finite source size. Photon-1 is detected on a screen, which can record the position of a detected photon as a point on the screen. This measurement corresponds to a position measurement of photon-1 while photon-2 is propagating towards a double-slit, and later it passes through a 50:50 beam splitter. The reflected probability amplitude of photon-2 is incident on a single photon detector-3, which is placed at the focal point of a convex lens. Whereas the transmitted probability amplitude is passed through a double-slit and incident on a single photon detector-2. The detector-2 is stationary, and it measures the position of photon-2 behind the double-slit. Each single photon detector is equipped with a very narrow aperture in order to measure the position of a photon around a location.

To evaluate the EPR state of two photons emanating from a three-dimensional source of finite extension, consider a source placed around the origin of a right-handed Cartesian coordinate system, as shown in Fig. 1 . Two photons are produced simultaneously from each point in the source as a consequence of the EPR constraint. Corresponding to an arbitrary point $\mathbf {r'}$ within the source, a two-photon probability amplitude to find photon-1 at a point $o_{a}$ in region- a left to the source and photon-2 at a point $o_{b}$ in region- b right to the source is written as $\frac{e^{ip_{1}|\textbf{r}_{a}-\textbf{r}'|/\hslash }}{|\textbf{r}_{a}-\textbf{r}'|}\frac{e^{ip_{2}|\textbf{r}_{b}-\textbf{r}'|/\hslash }}{|\textbf{r}_{b}-\textbf{r}'|}$ 38 , 39 , where $p_{1}$ and $p_{2}$ are magnitudes of momentum of photon-1 and of photon-2, respectively, and $\textbf{r}_{a}$ and $\textbf{r}_{b}$ are the position vectors of points $o_{a}$ and $o_{b}$ from the origin. Since the source size is finite, the total finite amplitude to find a photon at $o_{a}$ and a photon at $o_{b}$ is a linear quantum superposition of amplitudes originating from all points located in the source, which is written as

where both photons have the same linear polarisation state. A case for different polarisation states of photons leads to a hyper-entangled state, which is reported in Refs. 40 , 41 . However, for this experiment, an EPR entanglement is sufficient. Therefore, both photons are assumed to have the same linear polarisation state along the y -axis, which is omitted in this analysis. In Eq. ( 1 ), $A_{o}$ is a constant, and $\psi (x',y',z')$ is the probability amplitude of a pair production at a position $r'(x',y',z')$ in the source. This amplitude is constant for an infinitely extended EPR state at any arbitrary position vector $\textbf{r}'$ in the source. This integral represents the amplitude of two photons emanating from a three-dimensional photon pair source of finite size. It leads to a two-photon amplitude, which corresponds to the probability amplitude to find two photons together at different locations. Further, the magnitudes of momenta of photons are considered to be equal $p_{1}=p_{2}=p$ , for the degenerate photon pair production. The amplitude of pair production $\psi (x',y',z')$ is considered to be a three-dimensional Gaussian function such that, $\psi (x',y',z')= a e^{-(x'^2+y'^2)/\sigma ^2}e^{-z'^2/w^2}$ , where a is a constant, $\sigma$ and w are the widths of the Gaussian.

To evaluate the integral, consider two planes oriented perpendicular to the z -axis such that a plane-1 is located at a distance $s_{1}$ and a plane-2 is located at a distance $s_{2}$ from the origin. These planes are not shown in Fig. 1 however, a screen can be placed in a plane-1 and a double-slit can be placed in a plane-2. The amplitude to find photon-1 on plane-1 and photon-2 on plane-2 is evaluated as follows: Consider the distances of planes from the origin are such that, $\sigma ^{2}p/h s_{1}\ge 1$ and $\sigma ^{2}p/h s_{2} \ge 1$ , where the magnitudes of $s_{1}$ and $s_{2}$ are considerably larger than $\sigma$ and w . This approximation is valid for the experimental considerations of this paper. Since the double-slit and the detectors are placed close to the z -axis therefore, Eq. ( 1 ) can be written as

where $\Phi (x_{1},y_{1}; x_{2}, y_{2})$ is a two-photon position amplitude with variables of its argument separated by a semicolon denoting a position of photon-1 on plane-1 and of photon-2 on plane-2. After solving the integral, $\Phi (x_{1},y_{1}; x_{2}, y_{2})$ is written as

where $c_{n}$ is a constant and tan( $\Phi$ )=–p(s 1 +s 2 )σ 2 /2 ℏ s 1 s 2 . It is evident from Eq. ( 3 ) that both photons can be found at arbitrary positions. Once a photon is detected at a well-defined location ( $x'_{i}, y'_{i}$ ), where a label $i\in \{1,2\}$ corresponds to any single measured photon, then its position is determined. This measurement collapses the total wavefunction of both photons. Note that when a photon is detected at a well-defined position, even then the amplitude to find the other photon in the position space is delocalised, i.e. the projected position wavefunction has a nonzero spread. This wavefunction projection happens immediately once a photon is detected.

The second order quantum interference is exhibited if photon-1 detections are retained on the screen with the condition that photon-2 is detected after the double-slit by a stationary detector-2 as shown in Fig. 1 . However, this stationary detector will not always detect photon-2 since, photon has a nonzero amplitude to exist at different positions even after passing through the double-slit. The conditional detection corresponds to a joint measurement of photons. If all photon-1 detections on the screen are considered, then the interference pattern does not appear. Single photon interference is suppressed on the screen as well as after the double-slit, since photons are EPR entangled. To evaluate the second order interference pattern, consider a screen placed at $z=-s_{1}$ and a double-slit placed at $z=s_{2}$ with their planes oriented perpendicular to the z -axis. If the transmission function of the double-slit is $A_{T}(x_{2},y_{2})$ then the joint amplitude to detect photon-1 on the screen at a position $(x_{1}, y_{1})$ and photon-2 by a stationary detector-2 is written as

where an integration represents a projection onto a quantum superposition of position states of the photon-2 in the plane of the double-slit. A phase multiplier $B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }$ represents a phase acquired by a photon to reach detector-2 from the double-slit plane. The distance between detector-2 location ( $x_{o}, y_{o}, z_{o}$ ) and an arbitrary point location ( $x_{2}, y_{2}, s_{2}$ ) in the double-slit plane is $r_{d}=(D^{2}+(x_{2}-x_{o})^{2}+ (y_{2}-y_{o})^{2})^{1/2}$ , where $D=z_{o}-s_{2}$ is the distance of detector-2 from the double-slit. Note that $x_{o}$ is different than the symbol ${\textbf {x}}_{o}$ which is denoting separation of particles in the one-dimensional EPR state. Thus, the second order interference pattern depends on the position of detector-2. For a double-slit with slit separation d along the x -axis and infinite extension along the y -axis, the transmission function is given by $A_{T}(x_{2},y_{2})= [\delta (x_{2}-d/2)+\delta (x_{2}+d/2)]/\sqrt{2}$ . In the following experiment, each slit of the double-slit is largely extended along the y -axis as compared to its width. The effect of slit width and position resolution of single photon detectors is considered in the analysis of the following experiment. It is also evident that the two-photon interference pattern exhibits a shift when the position of the stationary detector-2 is shifted.

Experimental results

An experiment is performed with continuous variable EPR entangled photons of equal wavelength 810 nm, which are produced by the Type-I SPDC in a negative-uniaxial BBO nonlinear crystal. An experimental diagram of the setup is shown in Fig. 2 , where the x -axis is perpendicular to the optical table passing through the crystal. This experimental setup is a folded version of a diagram shown in Fig. 1 , where folding is along the x -axis such that photons propagate close to the angle of the conical emission pattern in a horizontal plane parallel to the optical table. Furthermore, photons propagating at a small inclination w.r.t. a horizontal plane pass through the double-slit. A vertical linearly polarised laser beam, along the x -axis, of wavelength 405 nm is expanded ten times to obtain a beam diameter of 8 mm at the full-width-half-maximum. The expanded laser beam is passed through the BBO crystal, whose optic-axis can be precisely tilted in a vertical plane passing through the crystal. This configuration results in noncollinear spontaneous down-converted photon pair emission in a broad conical pattern, where both the photons of each pair have the same linear polarisation state perpendicular to the polarisation state of the pump photons. The down-converted photons are EPR entangled in a plane perpendicular to the symmetry axis of the cone. The pump laser beam, after passing through the nonlinear crystal, is absorbed by a beam dumper to minimise unwanted background light.

An experimental diagram, where EPR entangled pairs of photons are emanated in a conical emission pattern. The paths of entangled photons are represented by red lines. The pump laser beam, after passing through the crystal, is represented by a narrow white line for clarity. The x -axis is perpendicular to the optical table and passing though the nonlinear crystal.

A screen is represented by a movable single photon detector-1 ( $D_{1}$ ), which is placed close to the crystal at a distance of 26.4 cm to detect photon-1 at about 5.68 ns prior to the detection of photon-2. The aperture of a single photon detector $D_{1}$ is an elongated single-slit of width 0.1 mm along the x -axis, which represents an effective detector width. It also corresponds to the resolution of the position measurements along the x -axis. This detector can be displaced parallel to the x -axis in steps of 0.1 mm to detect photons at different positions. Photon-1 is passed through a band-pass filter of band-width 10 nm at the centre wavelength 810 nm prior to its detection. Photon-2 is incident on a 50:50 polarisation independent beam splitter, which is placed at a distance of 93.8 cm from the crystal. A double-slit with an orientation of single slits perpendicular to the x -axis is placed after the beam splitter at a distance of 3 cm. Another elongated single-slit aperture of width 0.1 mm along the x -axis is placed after the double-slit at a distance of 23 cm from the double-slit in front of an optical fibre coupler. After passing through the double-slit, photon-2 is filtered by a band-pass filter of band-width 10 nm at the centre wavelength 810 nm. It is then passed through the aperture and directed towards a single photon detector-2 ( $D_{2}$ ) with a multimode optical fibre of length 0.5 m. This single-slit aperture can be displaced along the x -axis with a resolution of 0.1 mm. However, it is positioned at a predetermined location during one complete interference pattern data collection. In this experimental configuration, photon-1 is detected much earlier while photon-2 is propagating towards the beam splitter. Detection of photon-1 cannot affect photon-2 through any signalling limited by the speed of light until it reaches at an optical fibre coupler placed after the double-slit. Photon-2 arrives at the beam splitter 2.26 ns after the detection of photon-1, and from the beam splitter, its transmitted amplitude takes about 0.1 ns to arrive at the double-slit. The reflected amplitude of photon-2 is detected after passing through a band-pass filter by another optical fibre coupled single photon detector-3 ( $D_{3}$ ) without any aperture. Photons are focused on an optical fibre input with a convex lens, which projects the incident quantum state of photon-2 onto an eigen-state of the transverse momentum, provided photon-2 is detected by a single photon detector $D_{3}$ . Distance of the lens from the beam splitter is 25 cm, where this lens and the single photon detector $D_{3}$ are positioned at predetermined fixed locations throughout the experiment.

( a ) Quantum interference pattern obtained by measuring the coincidence detection of photons by a variable position single photon detector $D_{1}$ and a stationary single photon detector $D_{2}$ , where a solid line represents the theoretically evaluated interference pattern. ( b ) Coincidence detection of photons results in no interference, when photon-2 is detected by a stationary single photon detector $D_{3}$ and photon-1 is detected by $D_{1}$ . Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The shift in the two-photon quantum interference pattern when, ( a ) single photon detector $D_{2}$ position is $x_{o} = +0.11$ mm, ( b ) $D_{2}$ position is $x_{o} = -0.11$ mm. Single photons do not interfere in this experiment. Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The experiment is performed with 19 mW power of the pump laser beam, which is incident on the crystal. Each single photon detector output is connected to an electronic time correlated single photon counter (TCSPC), which measures the single and coincidence photon counts with 81 ps temporal resolution. A selected width of time window for the coincidence detection of photons is 81 ns. Single photon counts of each detector and coincidence photon counts of $D_{1}$ and $D_{2}$ , $D_{1}$ and $D_{3}$ are measured for 60 s. These measurements are repeated ten times to obtain an average of photon counts. A two-photon quantum interference pattern with a reversible detection of photons is shown in Fig. 3 a, where open circles represent the measured coincidence photon counts of single photon detectors $D_{1}$ and $D_{2}$ and the single photon counts of $D_{1}$ . Whereas, a solid line corresponds to the theoretical calculation of two-photon quantum interference using Eq. ( 4 ) by considering the finite width of each slit of the double-slit and position resolution of $D_{2}$ . A position of $D_{2}$ relative to the double slit is $(x_{o}, D)$ in a vertical plane with $D=23$ cm. The two-photon quantum interference pattern exhibits a shift as the position $x_{o}$ of $D_{2}$ is displaced, which is due to the phase-shift multiplier term $B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }$ in Eq. ( 4 ). The slit separation of the double-slit is 0.75 mm and the width of each slit is 0.15 mm. A fixed position of a single photon detector $D_{2}$ is taken to be the reference point with $x_{o}=0$ . There is no single photon interference pattern produced in this experiment by scanning the detector $D_{1}$ or $D_{2}$ . When photon-1 is detected, photon-2 is still propagating towards the beam splitter, and later its transmitted amplitude is detected by a fixed position single photon detector $D_{2}$ at a time lapse of 5.68 ns after the detection of a photon-1. On the other hand, if the reflected amplitude of photon-2 is detected by a single photon detector $D_{3}$ then $D_{2}$ will not measure any photon. In this case, photon-2 is not passed through the double-slit, and therefore, no two-photon quantum interference results as shown in Fig. 3 b, which shows coincidence counts of single photon detectors $D_{1}$ and $D_{3}$ and the single counts of $D_{1}$ . A choice of whether to detect a photon after the double-slit or not is naturally and randomly occurring due to the presence of a beam splitter in the path of photon-2 after its detection. A path superposition quantum state of photon-2 after the beam splitter is projected either onto the transmitted or the reflected path due to a single photon detection by a detector $D_{2}$ or $D_{3}$ , respectively. The main characteristic of two-photon quantum interference is that it exhibits a shift of the entire pattern as the single photon detector $D_{2}$ is displaced to another fixed position. This shift in the pattern is shown in Fig. 4 when, (a) $D_{2}$ is placed at a position $x_{o}= 0.11$ mm, (b) $D_{2}$ is placed at a position $x_{o}=-0.11$ mm with same D . This shift is also observed experimentally in the quantum ghost interference experiment by Strekalov et al. 23 . As a consequence of the EPR entanglement, there is no single photon interference. Therefore, the experiment in this paper presents a quantum two-photon interference with a reversible detection of photons, which has no classical counterpart.

This paper presents a two-photon double-slit experiment with the reversible detection of photons. Continuous variable EPR entangled photons are produced by the Type-I SPDC process, where photon-1 is detected on a screen while photon-2 is propagating towards a beam splitter. At a later time, photon-2 is produced in a quantum superposition of reflected and transmitted path amplitudes at the beam splitter. The transmitted amplitude is passed through the double-slit, and if this amplitude is detected by a detector-2 then the path quantum superposition state of photon-2 is collapsed onto the transmitted path. Then detector-3 does not detect this photon. Since photon-2 interacted with the double-slit considerably later than the detection of photon-1 therefore, it is ruled out that photon-1 has carried the path information of photon-2 in the double-slit to suppress the single photon interference. In addition, a position measurement of photon-1 cannot affect photon-2 through any signal propagating with speed, which is limited by the speed of light. If photon-2 is detected by a detector-3 then the quantum superposition state is collapsed onto the reflected path. Therefore, detector-2 does not detect photon-2, which results in no interference in single photon and two-photon measurements.

It is very important to expand the beam diameter of the pump laser beam to produce a continuous variable EPR quantum entangled state. It also leads to a broader envelope of the interference pattern. To achieve low background counts limited by the dark counts of the single photon detectors, the pump laser beam should have minimal scattering from optical components, and it should be properly dumped after passing through the crystal. A source of EPR entangled photons consists of a thin crystal in Type-1 SPDC configuration, where down-converted photons have the same linear polarisation. The nonlinear crystal is anti-reflection coated for wavelengths of pump and down-converted photons to reduce scattering and back reflection. The nonlinear crystal is kept at room temperature without any temperature control. Its optical-axis is precisely aligned w.r.t. the polarisation vector of the pump laser beam to obtain a broad conical emission pattern of down-converted photons with a full cone angle of 9.5°. The optical power of the pump laser beam is 19 mW, which is x -polarised. Single-slit apertures, which are placed in front of $D_{1}$ and an input coupler of an optical fibre of $D_{2}$ , are attached to translational stages to displace them precisely to collect photons corresponding to different positions of apertures. To increase the number of photons passing through the double slit, a double slit consists of two elongated single slits separated by a distance of 0.75 mm along the x -axis, where the width of each slit is 0.15 mm. In the experimental configuration, photons are EPR entangled in a plane perpendicular to the direction of propagation of the pump laser beam. The efficiency of each single photon detector is about 65 %. The single photon detector $D_{1}$ equipped with a convex lens is directly collecting photons and it is placed close to the crystal. Whereas, the single photon detectors $D_{2}$ and $D_{3}$ are coupled to multimode optical fibres of length 0.5 m. The input of each optical fibre is attached to respective optical fibre couplers, each consisting of a convex lens of diameter 1 cm. Photons are collected by the lenses after passing through the single-slit apertures to measure the position of photons by $D_{1}$ and $D_{2}$ . However, a coupler of a single photon detector $D_{3}$ is not equipped with any aperture. A band-pass optical filter of band-width 10 nm at centre wavelength 810 nm is placed at the input of each single photon detector to filter the unwanted scattered photons of the pump laser and background light.

Data availability

All data generated or analysed during this study are included in this article.

Young, T. The 1801 Bakerian Lecture: On the theory of light and colours. Philos. Trans. R. Soc. Lond. 92 , 12–48 (1802).

ADS Google Scholar

Young, T. The 1803 Bakerian Lecture: Experiments and calculations relative to physical optics. Philos. Trans. R. Soc. Lond. 94 , 1–16 (1804).

Taylor, G. I. Interference fringes with feeble light. Proc. Camb. Philos. Soc. 15 , 114–115 (1909).

Google Scholar

Dirac, P. The Principles of Quantum Mechanics (Oxford University Press, 1930), 4 edn.

Feynman, M. A., Leighton, R. B. & Sands, M. L. The Feynman Lectures on Physics , vol. 3 (Addison-Wesley, 1963), second edn.

Donati, O., Missiroli, G. P. & Pozzi, G. An experiment on electron interference. Am. J. Phys. 41 , 639–644 (1973).

Article ADS Google Scholar

Frabboni, S., Gazzadi, G. C. & Pozzi, G. Nanofabrication and the realization of Feynman’s two-slit experiment. Appl. Phys. Lett. 93 , 073108 (2008).

Rodolfo, R. The merli–missiroli–pozzi two-slit electron-interference experiment. Phys. Perspect. 14 , 178–195 (2012).

Frabboni, S. et al. The Young-Feynman two-slits experiment with single electrons: Build-up of the interference pattern and arrival-time distribution using a fast-readout pixel detector. Ultramicroscopy 116 (2012).

Rauch, H. Particle and/or wave features in neutron interferometry. J. Phys.: Conf. Ser. 361 , 012019 (2012).

Zeilinger, A., Gahler, R., Shull, C. G., Treimer, W. & Mampe, W. Single and double-slit diffraction of neutrons. Rev. Mod. Phys. 60 , 1067–1073 (1988).

Article ADS CAS Google Scholar

Grangier, P., Roger, G. & Aspect, A. Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. Europhys. Lett. 1 , 173 (1986).

Zeilinger, A. Experiment and the foundations of quantum physics. Rev. Mod. Phys. 71 , S288–S297 (1999).

Article CAS Google Scholar

Sala, S. et al. First demonstration of antimatter wave interferometry. Sci. Adv. 5 (2019).

Arndt, M. et al. Wave-particle duality of ${\rm c}_{60}$ molecules. Nature 401 , 680–682 (1999).

Article ADS PubMed CAS Google Scholar

Fein, Y. Y. et al. Quantum superposition of molecules beyond 25 kDa. Nat. Phys. 15 , 1242–1245 (2019).

Cotter, J. P. et al. In search of multipath interference using large molecules. Sci. Adv. 3 (2017).

Hornberger, K., Gerlich, S., Haslinger, P., Nimmrichter, S. & Arndt, M. Colloquium: Quantum interference of clusters and molecules. Rev. Mod. Phys. 84 , 157–173 (2012).

Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nature. Phys. 10 , 271–277 (2014).

Shayeghi, A. et al. Matter-wave interference of a native polypeptide. Nat. Commun. 11 , 1447 (2020).

Article ADS PubMed PubMed Central CAS Google Scholar

Kaur, M. & Singh, M. Quantum double-double-slit experiment with momentum entangled photons. Sci. Rep. 10 , 11427 (2020).

Article PubMed PubMed Central CAS Google Scholar

Greenberger, D. M., Horne, M. A. & Zeilinger, A. Multiparticle interferometry and the superposition principle. Phys. Today 46 , 8 (1993).

Article Google Scholar

Strekalov, D. V., Sergienko, A. V., Klyshko, D. N. & Shih, Y. H. Observation of two-photon “ghost’’ interference and diffraction. Phys. Rev. Lett. 74 , 3600–3603 (1995).

Ribeiro, P. H. S., Pádua, S., Machado da Silva, J. C. & Barbosa, G. A. Controlling the degree of visibility of Young’s fringes with photon coincidence measurements. Phys. Rev. A 49 , 4176–4179 (1994).

Souto Ribeiro, P. H. & Barbosa, G. A. Direct and ghost interference in double-slit experiments with coincidence measurements. Phys. Rev. A 54 , 3489–3492 (1996).

Chingangbam, P. & Qureshi, T. Ghost interference and quantum erasure. Progress Theoret. Phys. 127 , 383–392 (2012).

Gatti, A., Brambilla, E. & Lugiato, L. A. Entangled imaging and wave-particle duality: From the microscopic to the macroscopic realm. Phys. Rev. Lett. 90 , 133603 (2003).

Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. W. Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92 , 210403 (2004).

Article ADS PubMed Google Scholar

Mandel, L. Quantum effects in one-photon and two-photon interference. Rev. Mod. Phys. 71 , S274–S282 (1999).

Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47 , 777–780 (1935).

Monken, C. H., Ribeiro, P. H. S. & Pádua, S. Transfer of angular spectrum and image formation in spontaneous parametric down-conversion. Phys. Rev. A 57 , 3123–3126 (1998).

Walborn, S. P., de Oliveira, A. N., Thebaldi, R. S. & Monken, C. H. Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion. Phys. Rev. A 69 , 023811 (2004).

Schneeloch, J. & Howell, J. C. Introduction to the transverse spatial correlations in spontaneous parametric down-conversion through the biphoton birth zone. J. Opt. 18 , 053501 (2016).

Walborn, S. P., Monken, C. H., Pádua, S. & Souto-Ribeiro, P. H. Spatial correlations in parametric down-conversion. Phys. Rep. 495 , 87–139 (2010).

Hong, C. K. & Mandel, L. Theory of parametric frequency down conversion of light. Phys. Rev. A 31 , 2409 (1985).

Horne, M. A., Shimony, A. & Zeilinger, A. Two-particle interferometry. Phys. Rev. Lett. 62 , 2209–2212 (1989).

Joobeur, A., Saleh, B. E. A., Larchuk, T. S. & Teich, M. C. Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment. Phys. Rev. A 53 , 4360–4371 (1996).

Horne, M. A. & Zeilinger, A. in Microphys. Real. Quant. Form. (Kluwer Academic, Dordrecht, 1988).

Horne, M. A. in Experimental Metaphysics (Kluwer Academic, Dordrecht, 1997).

Kaur, M. & Singh, M. Quantum imaging of a polarisation sensitive phase pattern with hyper-entangled photons. Sci. Rep. 11 , 23636 (2021).

Saxena, A., Kaur, M., Devrari, V. & Singh, M. Quantum ghost imaging of a transparent polarisation sensitive phase pattern. Sci. Rep. 12 , 21105 (2022).

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Acknowledgements

Mandip Singh acknowledges research funding by the Department of Science and Technology, Quantum Enabled Science and Technology grant for project No. Q.101 of theme title “Quantum Information Technologies with Photonic Devices”, DST/ICPS/QuST/Theme-1/2019 (General).

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Vipin Devrari & Mandip Singh

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MS setup the experiment and made its theoretical model, VD took data and analysed data, MS wrote this manuscript. Both authors discussed the experiment.

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Devrari, V., Singh, M. Quantum double slit experiment with reversible detection of photons. Sci Rep 14 , 20438 (2024). https://doi.org/10.1038/s41598-024-71091-1

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IIT JEE Study Material
Youngs Double Slit Experiment

Young's Double Slit Experiment

What is young’s double slit experiment.

Young’s double slit experiment uses two coherent sources of light placed at a small distance apart. Usually, only a few orders of magnitude greater than the wavelength of light are used. Young’s double slit experiment helped in understanding the wave theory of light , which is explained with the help of a diagram. As shown, a screen or photodetector is placed at a large distance, ‘D’, away from the slits.

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The original Young’s double slit experiment used diffracted light from a single source passed into two more slits to be used as coherent sources. Lasers are commonly used as coherent sources in modern-day experiments.

Position of Fringes
Shape of Fringes
Intensity of Fringes

Special Cases

Displacement of Fringes

Each source can be considered a source of coherent light waves . At any point on the screen at a distance ‘y’ from the centre, the waves travel distances l 1 and l 2 to create a path difference of Δl at the point. The point approximately subtends an angle of θ at the sources (since the distance D is large, there is only a very small difference between the angles subtended at sources).

Derivation of Young’s Double Slit Experiment

Consider a monochromatic light source ‘S’ kept at a considerable distance from two slits: s 1 and s 2 . S is equidistant from s 1 and s 2 . s 1 and s 2 behave as two coherent sources as both are derived from S.

The light passes through these slits and falls on a screen which is at a distance ‘D’ from the position of slits s 1 and s 2 . ‘d’ is the separation between two slits.

If s 1 is open and s 2 is closed, the screen opposite to s 1 is closed, and only the screen opposite to s 2 is illuminated. The interference patterns appear only when both slits s 1 and s 2 are open.

When the slit separation (d) and the screen distance (D) are kept unchanged, to reach P, the light waves from s 1 and s 2 must travel different distances. It implies that there is a path difference in Young’s double slit experiment between the two light waves from s 1 and s 2 .

Approximations in Young’s double slit experiment

Approximation 1: D > > d: Since D > > d, the two light rays are assumed to be parallel.
Approximation 2: d/λ >> 1: Often, d is a fraction of a millimetre, and λ is a fraction of a micrometre for visible light.

Under these conditions, θ is small. Thus, we can use the approximation sin θ = tan θ ≈ θ = λ/d.

∴ path difference, Δz = λ/d

This is the path difference between two waves meeting at a point on the screen. Due to this path difference in Young’s double slit experiment, some points on the screen are bright, and some points are dark.

Now, we will discuss the position of these light and dark fringes and fringe width.

Position of Fringes in Young’s Double Slit Experiment

Position of bright fringes.

For maximum intensity or bright fringe to be formed at P,

Path difference, Δz = nλ (n = 0, ±1, ±2, . . . .)

i.e., xd/D = nλ

The distance of the n th bright fringe from the centre is

x n = nλD/d

Similarly, the distance of the (n-1) th bright fringe from the centre is

x (n-1) = (n -1)λD/d

Fringe width, β = x n – x (n-1) = nλD/d – (n -1)λD/d = λD/d

(n = 0, ±1, ±2, . . . .)

Position of Dark Fringes

For minimum intensity or dark fringe to be formed at P,

Path difference, Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, . . . .)

i.e., x = (2n +1)λD/2d

The distance of the n th dark fringe from the centre is

x n = (2n+1)λD/2d

x (n-1) = (2(n-1) +1)λD/2d

Fringe width, β = x n – x (n-1) = (2n + 1) λD/2d – (2(n -1) + 1)λD/2d = λD/d

Fringe Width

The distance between two adjacent bright (or dark) fringes is called the fringe width.

If the apparatus of Young’s double slit experiment is immersed in a liquid of refractive index (μ), then the wavelength of light and fringe width decreases ‘μ’ times.

If white light is used in place of monochromatic light, then coloured fringes are obtained on the screen, with red fringes larger in size than violet.

Angular Width of Fringes

Let the angular position of n th bright fringe is θ n, and because of its small value, tan θ n ≈ θ n

Similarly, the angular position of (n+1) th bright fringe is θ n+1, then

∴ The angular width of a fringe in Young’s double slit experiment is given by,

Angular width is independent of ‘n’, i.e., the angular width of all fringes is the same.

Maximum Order of Interference Fringes

But ‘n’ values cannot take infinitely large values as it would violate the 2 nd approximation.

i.e., θ is small (or) y < < D

When the ‘n’ value becomes comparable to d/ λ, path difference can no longer be given by d γ/D.

Hence for maxima, path difference = nλ

The above represents the box function or greatest integer function.

Similarly, the highest order of interference minima

The Shape of Interference Fringes in YDSE

From the given YDSE diagram, the path difference between the two slits is given by

The above equation represents a hyperbola with its two foci as, s 1 and s 2 .

The interference pattern we get on the screen is a section of a hyperbola when we revolve the hyperbola about the axis s 1 s 2 .

If the screen is a yz plane, fringes are hyperbolic with a straight central section.

If the screen is xy plane , the fringes are hyperbolic with a straight central section.

The Intensity of Fringes in Young’s Double Slit Experiment

For two coherent sources, s 1 and s 2 , the resultant intensity at point p is given by

I = I 1 + I 2 + 2 √(I 1 . I 2 ) cos φ

Putting I 1 = I 2 = I 0 (Since, d<<<D)

I = I 0 + I 0 + 2 √(I 0 .I 0 ) cos φ

I = 2I 0 + 2 (I 0 ) cos φ

I = 2I 0 (1 + cos φ)

For maximum intensity

phase difference φ = 2nπ

Then, path difference $\begin{array}{l}\Delta x=\frac{\lambda }{{2}{\pi }}\left( {2}n{\pi } \right)\end{array} $ = nλ

The intensity of bright points is maximum and given by

I max = 4I 0

For minimum intensity

φ = (2n – 1) π

Phase difference φ = (2n – 1)π

Thus, the intensity of minima is given by

If I 1 ≠ I 2 , I min ≠ 0.

Rays Not Parallel to Principal Axis:

From the above diagram,

Using this, we can calculate different positions of maxima and minima.

Source Placed beyond the Central Line:

If the source is placed a little above or below this centre line, the wave interaction with S 1 and S 2 has a path difference at point P on the screen.

Δ x= (distance of ray 2) – (distance of ray 1)

= bd/a + yd/D → (*)

We know Δx = nλ for maximum

Δx = (2n – 1) λ/2 for minimum

By knowing the value of Δx from (*), we can calculate different positions of maxima and minima .

Displacement of Fringes in YDSE

When a thin transparent plate of thickness ‘t’ is introduced in front of one of the slits in Young’s double slit experiment, the fringe pattern shifts toward the side where the plate is present.

The dotted lines denote the path of the light before introducing the transparent plate. The solid lines denote the path of the light after introducing a transparent plate.

Where μt is the optical path.

Then, we get,

Term (1) defines the position of a bright or dark fringe; term (2) defines the shift that occurred in the particular fringe due to the introduction of a transparent plate.

Constructive and Destructive Interference

For constructive interference, the path difference must be an integral multiple of the wavelength.

Thus, for a bright fringe to be at ‘y’,

Or, y = nλD/d

Where n = ±0,1,2,3…..

The 0th fringe represents the central bright fringe.

Similarly, the expression for a dark fringe in Young’s double slit experiment can be found by setting the path difference as

Δl = (2n+1)λ/2

This simplifies to

(2n+1)λ/2 = y d/D

y = (2n+1)λD/2d

Young’s double slit experiment was a watershed moment in scientific history because it firmly established that light behaved like a wave.

The double slit experiment was later conducted using electrons , and to everyone’s surprise, the pattern generated was similar as expected with light. This would forever change our understanding of matter and particles, forcing us to accept that matter, like light, also behaves like a wave.

Wave Optics

Young’s double slit experiment.

Frequently Asked Questions on Young’s Double Slit Experiment

What was the concept explained by young’s double slit experiment.

Young’s double slit experiment helps in understanding the wave theory of light.

What are the formulas derived from Young’s double slit experiment?

For constructive interference, dsinθ = mλ , for m = 0,1,-1,2,-2

For destructive interference, dsinθ = (m+½)λ, for m = 0,1,-1,2,-2 Here, d is the distance between the slits. λ is the wavelength of the light waves.

What is called a fringe width?

The distance between consecutive bright or dark fringe is called the fringe width.

What kind of source is used in Young’s double slit experiment?

A coherent source is used in Young’s double slit experiment.

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Calculating total number of fringes in Young's Double Slit Experiment

I know that the $n^{th}$ order maxima can be given by $\frac{n\lambda D}{d}$ . But theoretically n can go up to infinity and the intensity will go down. However, is there any way to approximate the visible bright spots that can be observed in experiments?

visible-light
double-slit-experiment
interference

3 $\begingroup$ Depends how good your source and detector are (not even counting things like lock-in amplifiers). $\endgroup$ – Jon Custer Commented Mar 6, 2019 at 18:45
$\begingroup$ total number of bright fringes = 2[ $\frac{d}{\lambda}\$] + 1 where [ . ] Is the greatest integer function $\endgroup$ – OhMyGauss Commented May 19, 2020 at 10:37

3 Answers 3

In Young's slits, the two beams that interfere have a width limited by the diffraction by the slits. The fringes are visible only in the common part of the two beams.

By neglecting the distance between the slits, the angular width associated with the diffraction is $2(\lambda /a)$ and the angular width of a fringe is $\lambda /d$

As the central fringe is bright, we will roughly have $N=1+2d/a$ visible fringes. It is an approaching reasoning that may forget certain elements!

Sorry for my poor english !

$\begingroup$ what does "d" and "a" refer to? $\endgroup$ – MSKB Commented Feb 17, 2022 at 6:04

I assume that you want to approximate the number of observable maxima. For very narrow slits the number of maxima is $n <= d/\lambda$ on each side of the central maximum. So the number of maxima is 2n+1. These are all observable. The individual slits also produce $m <=w/\lambda$ maxima. For a narrow slit m=0. The total number of maxima is then 2n+2m+1. This formula does not take into account that maxima may be merged.

Of course this is what you can observe under very good conditions. Intense monochromatic light, a perfect slit, low background, and a good detector will be required if you want to see them all.

1 $\begingroup$ However, is there any way to approximate the visible bright spots that can be observed in experiments? $\endgroup$ – BioPhysicist Commented Mar 6, 2019 at 19:01
1 $\begingroup$ I'm not asking anything. I'm quoting the question above that you have not answered. $\endgroup$ – BioPhysicist Commented Mar 6, 2019 at 19:15
1 $\begingroup$ No... I do not think you have answered the question... The OP is asking about how many you could see in some experimental set up. Not the theoretical limit regardless of intensity of the farthest bright spot. $\endgroup$ – BioPhysicist Commented Mar 6, 2019 at 19:19

This is variation in number of fringe widths with wavelength

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