Visual Examples: The Double Slit Experiment I

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The double slit experiment is known as an archetypical quantum effect. It displays the famous wave-particle duality in the sense that the pattern of fringes clearly indicates the presence of some interference phenomenon, and therefore the presence of waves, while the pattern is made up from discrete detection events, as if hit by particles.

A pattern of points as results from a double slit experiment.

This is a pattern found in a double slit experiment performed at the Hitachi Labs, Japan, in 1987. The different stages correspond to different numbers of electrons: 10, 100, 3000, 20 000, and 70 000. (Figure scanned from [1].)

Pattern of points from an actual experiment.

A bit of history: The double slit experiment with photons was introduced by Thomas Young in the beginning of the 19th century as a proof for the wave nature of light. But it is difficult to perform with single particles. What you see in Young's experiment is a continuous glow on the screen with intensity proportional to |psi|2, but no single dots, because they count by billions.

When performing this experiment with electrons, the slits must be extremely narrow and very close to each other, because the wave length of an electron is considerably smaller than that of a photon. This was carried out first in 1927 by Clinton Davisson and Lester Germer, who used the atomic lattice of a crystal as their slits (not two slits in this case, but thousands; the pattern is somewhat different then, but still features the characteristic fringes).

In 1987, a team at the Hitachi Labs in Tokyo, Japan, could do an interference experiment with single electrons [1]. They detected the position of arrival of every single electron on the screen, and could see how the pattern arises from single points, as shown in the picture above. There was only one electron at a time traveling through the arrangement.

Because the wave length is so small, they did it not with slits but with a positively charged thread, which by Coulomb force attracts passing-by electrons. Half of the wave packet passes on the right and is deflected to the left, whereas the other half passes on the left and is deflected to the right, such that the two packets interfere and, again, form an interference pattern completely analogous to the one based on two slits.

The |psi|^2 distribution.

This is what the wave function looks like. The wave function takes values in the complex numbers, but only the modulus square is represented in this plot, whereas the phase is ignored. Black corresponds to values close to zero, bright means larges values. One clearly discerns the two slits on the left hand side, and the interference pattern on the right.

The |psi|^2 distribution.

A different plot of |psi|2. Now the value is represented as height of the surface. The color does not encode information.

The possible trajectories of a Bohmian particle.

These are the paths, one of which the actual particle follows, according to Bohmian mechanics. Each path passes through one of the slits (left hand side); and hits the screen (right hand side) at a random position that appears |psi|2 distributed, displaying the famous diffraction fringes. Although one cannot know in advance through which slit the particle will pass, one can decide afterwards: it passes through the upper slit if and only if it hits the screen on the upper half, that is, above the symmetry axis.

This simple mechanism achieves what has so very often been claimed impossible: to explain the diffraction pattern in terms of trajectories.

By Roderich Tumulka.

[1] A. Tonomura, J. Endo, H. Ezawa, T. Matsuda, T. Kawasaki: Am. J. Phys. 57 (2), p. 117 (1989)

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