Double-slit experiment

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The double-slit experiment consists of letting light diffract through two slits producing fringes on a screen. These fringes or interference patterns have light and dark regions corresponding to where the light waves have constructively and destructively interfered. The experiment can also be performed with a beam of electrons or atoms, showing similar interference patterns; this is taken as evidence of the "wave-particle duality" predicted by quantum physics. Note, however, that a double-slit experiment can also be performed with water waves in a ripple tank; the explanation of the observed wave phenomena does not require quantum mechanics in any way. The phenomenon is quantum mechanical only when quantum particles - such as atoms, electrons, or photons - manifest as waves.

1 Importance to physics
2 Explanation of experiment
3 Replicating Young's experiment
4 Quantum version of experiment
5 Conditions for interference
6 Results observed
7 Shape of interference fringes
8 See also
9 References
10 External links

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Importance to physics

Although the double-slit experiment is now often referred to in the context of quantum mechanics, it was originally performed by the English scientist Thomas Young some time around 1805 in an attempt to resolve the question of whether light was composed of particles (the "corpuscular" theory), or rather consisted of waves travelling through some aether, just as sound waves travel in air.

The interference patterns observed in the experiment seemed to discredit the corpuscular theory, and the wave theory of light remained well accepted until the early 20th century, when evidence began to accumulate which seemed instead to confirm the particle theory of light.

The double-slit experiment, and its variations, then became a classic Gedankenexperiment (thought experiment) for its clarity in expressing the central puzzles of quantum mechanics; although in this form the experiment was not actually performed with anything other than light until 1961, when Claus Jönsson of the University of Tübingen performed it with electrons. (C Jönsson, Zeitschrift für Physik 161, 454; C. Jönsson 1974 "Electron diffraction at multiple slits", American Journal of Physics 42 4-11), and not until 1974 in the form of "one electron at a time", in a laboratory at the University of Milan, by researchers led by Pier Giorgio Merli, of LAMEL-CNR Bologna.

The results of the 1974 experiment were published and even made into a short film, but did not receive wide attention. The experiment was repeated in 1989 by Tonomura et al at Hitachi in Japan. Their equipment was better, reflecting 15 years of advances in electronics and a dedicated development effort by the Hitachi team. Their methodology was more precise and elegant, and their results agreed with the results of Merli's team. Although Tonomura asserted that the Italian experiment had not detected electrons one at a time - a key to demonstrating the wave-particle paradox - single electron detection is clearly visible in the photos and film taken by Merli and his group.

In September 2002, the double-slit experiment of Claus Jönsson was voted "the most beautiful experiment" by readers of Physics World.

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Explanation of experiment

Image:YoungsDoubleSlit.png

In Young's original experiment, sunlight passes first through a single slit, and then through two thin vertical slits in otherwise solid barriers, and is then viewed on a rear screen.

When either slit is covered, a single peak is observed on the screen from the light passing through the other slit.

But when both slits are open, instead of the sum of these two singular peaks that would be expected if light were made of particles, a pattern of light and dark fringes is observed.

Image:Fringespos.png This pattern of fringes was best explained as the interference of the light waves as they recombined after passing through the slits, much as waves in water recombine to create peaks and swells. In the brighter spots, there is "constructive interference", where two "peaks" in the light wave coincide as they reach the screen. In the darker spots, "destructive interference" occurs where a peak and a trough occur together.

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Replicating Young's experiment

This experiment can easily be demonstrated in just the way that Young demonstrated it to the Royal Society of London. An assistant outside used mirrors to direct sunlight at a pinhole opening. The beam from the opening was then bisected by "a slip of card". To make things easier, a modern experimenter could replace the sunlight and mirrors with a laser pointer covered, except for a pinhole, by black paper. Splitting the beam with a small strip of notecard will produce a visible interference pattern when the beam is projected across the room. [1]

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Quantum version of experiment

By the 1920s, various other experiments (such as the photoelectric effect) had demonstrated that light interacts with matter only in discrete, "quantum"-sized packets called photons.

If sunlight is replaced with a light source that is capable of producing just one photon at a time, and the screen is sensitive enough to detect a single photon, Young's experiment can, in theory, be performed one photon at a time -- with identical results.

If either slit is covered, the individual photons hitting the screen, over time, create a pattern with a single peak. But if both slits are left open, the pattern of photons hitting the screen, over time, again becomes a series of light and dark fringes. This result seems to both confirm and contradict the wave theory. On the one hand, the interference pattern confirms that light still behaves much like a wave, even though we send it one particle at a time. On the other hand, each time a photon with a certain energy is emitted, the screen detects a photon with the same energy. Under the Copenhagen Interpretation of quantum theory, an individual photon is seen as passing through both slits at once, and interfering with itself, producing the interference pattern.

A remarkable refinement of the double-slit experiment consists of putting a detector at each of the two slits, to determine which slit the photon passes through on its way to the screen (If the photon or electron passes through only one slit - which it must do, as, by definition, a photon or an electron is a quanta, or "packet" of energy which cannot be subdivided - then logically it cannot interfere with itself and produce an interference pattern). When the experiment is arranged in this way, the fringes disappear.

The Copenhagen interpretation posits the existence of probability waves which describe the likelihood of finding the particle at a given location. Until the particle is detected at any location along this probability wave, it effectively exists at every point. Thus, when the particle could be passing through either of the two slits, it will actually pass through both, and so an interference pattern results. But if the particle is detected at one of the two slits, then it can no longer be passing through both - it must exist at one or the other, and so no interference pattern appears.

This is similar to the path integral formulation of quantum mechanics provided by Richard Feynman (although Feynman stresses that this is merely a mathematical description, not an attempt to describe some "real" process that we cannot see), in which a particle such as a photon takes every possible path through space-time to get from point A to point B. In the double-slit experiment, point A might be the emitter, and point B the screen upon which the interference pattern appears, and a particle takes every possible path - through both slits at once - to get from A to B. When a detector is placed at one of the slits, the situation changes, and we now have a different point B at the detector, and a new path between the detector and the screen - upon which the interference pattern no longer appears).

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Conditions for interference

A necessary condition for obtaining an interference pattern in a double-slit experiment concerns the difference in pathlength between two paths that light can take to reach a zone of constructive interference on the viewing screen. This difference must be the wavelength of the light that is used, or a multiple of this wavelength. (See illustration. [2]) If a beam of sunlight is let in, and that beam is allowed to fall immediately on the double slit, then the fact that the Sun is not a point source degrades the interference pattern. The light from a source that is not a point source behaves like the light of many point sources side by side. Each can create an interference pattern, but the interference patterns of each of the many-side-by-side sources does not coincide on the screen, so they average each other out, and no interference pattern is seen.

The presence of the first slit is necessary to ensure that the light reaching the double slit is light from a single point source. The path length from the single slit to the double slit is equally important for obtaining the interference pattern as the path from the double slit to the screen.

Newton's rings show that light does not have to be coherent in order to produce an interference pattern. Newton's rings can be readily obtained with plain sunlight.<ref>Newton's rings. Newton's Rings from Eric Weisstein's World of Physics</ref> More rings are discernible if for example light from a Sodium lamp is used, since Sodium lamp light is only a narrow band of the spectrum. Light from a Sodium lamp is incoherent. Other examples of interference patterns from incoherent light are the colours of soap bubbles and of oil films on water.

In general, interference patterns are clearer when monochromatic or near-monochromatic light is used. Laserlight is as monochromatic as light can be made, therefore laserlight is used to obtain an interference pattern.

If the two slits are illuminated by coherent waves, but with polarizations perpendicular with respect to each other, the interference pattern disappears.

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Results observed

The bright bands observed on the screen happen when the light has interfered constructively -- where a crest of a wave meets a crest. The dark regions show destructive interference -- a crest meets a trough.

<math>\frac{\lambda}{s} = \frac{x}{D} \,</math>

where

λ is the wavelength of the light

s is the separation of the slits

x is the distance between the bands of light (also called fringe distance)

D is the distance from the slits to the screen

This is only an approximation and depends on certain conditions.

It is possible to work out the wavelength of light using this equation and the above apparatus. If s and D are known and x is observed, then λ can be easily calculated.

A detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics is given in the article on Englert-Greenberger duality.

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Shape of interference fringes

The theoretical shapes of the interference fringes observed in Young's double slit experiment are straight lines which is easily proved.

In case two pinholes are used instead of slits, as in the original Young's experiment, hyperbolic fringes are observed. This is because the difference in paths travelled by the light from the two sources is a constant for a fringe which is the property of a hyperbola.

If the two sources are placed on a line perpendicular to the screen, the shape of the interference fringes is circular as the individual paths travelled by light from the two sources are always equal for a given fringe. This can be done in simpler way by placing a mirror parallel to a screen at a distance and a source of light just above the mirror. (Note the extra phase difference of π due to reflection at the interface of a denser medium)

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