Self-Interference

The superposition of waves from several sources, such as light or water waves, is known as interference, resulting in a characteristic pattern of alternating high and low intensity. While we are familiar with this phenomenon in relation to light or water waves, it can also be observed with electrons.

In quantum mechanics, a single electron or photon (a particle of light) can interfere with itself. This can be demonstrated using the double-slit experiment.

Single electrons are accelerated and pass through a double slit. An interference pattern with alternating maxima and minima is observed on the screen behind it, demonstrating that the electron behaves like a wave.  The position of the maxima and minima is determined by the distance between the slits, their width, and the energy of the electrons.

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Illustration of the double-slit experiment, on the left electrons are emitted and accelerated, on the right is the arrangement with double slit and observation screen on which the electrons are measured. Picture: Ruth Bründler, UZH.

Measurement on the observation screen: The positions of individual particles can be seen in the figure below. When many electrons are measured, the pattern shown in the figure below results: a typical interference pattern. No individual particles can be seen at locations with low wave intensity. This means that individual particles exhibit interference effects, i.e. they can interfere with themselves. This phenomenon can only be explained by quantum mechanics: the particle is described by its wave function, which indicates the probability of detecting the particle at a given location. If the particle's path is divided (e.g. by a lattice), this leads to a superposition of waves and the corresponding interference effects.

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Observation of interference effects Image: Proc. Natl. Acad. Sci. U.S.A. 102(42), 2005. doi:10.1073/pnas.0504720102

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The double-slit experiment with electrons is one of the most famous in physics. It amazingly demonstrates that particles such as electrons can behave like waves. In the experiment, individual electrons are fired from an electron source towards a wall with two narrow slits in it. A detector behind this registers where the electrons hit. This could be a fluorescent screen, for example.

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Experimental setup of the double-slit experiment. Image: Ruth Bründler, UZH.

Classically, one would expect the electrons to pass through either the left or right slit, producing two separate stripes on the screen.
However, if the experiment is allowed to run for long enough, so that many electrons fly through the slits one after the other, an interference pattern forms on the screen. This pattern consists of light and dark stripes, which are typical of the superposition of waves. It therefore appears as if each electron has interfered with itself.

If you try to measure which slit each electron passes through, however, the interference pattern disappears. You get two simple stripes again.

In quantum mechanics, this phenomenon is known as wave-particle duality. Electrons behave like waves or particles depending on the measurement. Before measurement, the state of an electron is not fixed, but exists in a superposition of both possible paths. It is only when it is measured that the electron “decides” which path to take.

Video : The individual dots on the fluorescent screen correspond to the signal of individual electrons in the double-slit experiment. After about a minute you can see the typical interference pattern expected for waves. (Video: Vega Science Trust, lecture by Akira Tonomura)

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• The 1920's in cosmopolitan Zurich
• Quantum Mechanics and Zurich
• Erwin Schrödinger and Walter Heitler
• Wolfgang Pauli and Gregor Wentzel
• Wave or particle?
• Self-Interference
• Entanglement
• Superposition
• How do quanta get into mechanics?
• Everything out of focus
• Tunneling
• Nobel Prizes
• Technical Applications
• Research at UZH: Particle Physics
• Research at UZH: Condensed Matter