Aharonov–Bohm effect

Quantum particles such as electrons are described by wavefunctions. When a coherent electron wave is split into two paths and later recombined, a relative phase difference between the paths can shift the resulting interference fringes. In the magnetic Aharonov–Bohm setup, the paths pass on opposite sides of a region containing magnetic flux, such as the interior of a solenoid, while the electrons themselves avoid that region. The interference pattern depends on the enclosed flux, although the magnetic field may be zero along the accessible paths.

In classical electromagnetism, a charged particle's magnetic force is determined by the magnetic field at its location. In the quantum description, the electromagnetic vector potential enters the particle's Hamiltonian and can affect the phase accumulated along a path. For a loop around the enclosed flux, the relative phase is proportional to the electric charge and magnetic flux, expressed in units of Planck's constant. The vector potential is gauge-dependent, so care is needed when interpreting it; the measured interference is gauge-invariant. Modern treatments show that the effect can also be described using the electromagnetic field of the full isolated system, while giving up a strictly local description of the particle alone.

Aharonov and Bohm proposed the effect in 1959. Richard Chambers reported an electron-interference experiment in 1960, but early experiments faced concerns that stray magnetic fields from finite magnets might influence the electrons. In 1986, Akira Tonomura and colleagues used electron holography with a tiny toroidal magnet surrounded by superconducting and copper layers. The superconducting layer confined the magnetic field to the magnet, while the electrons were prevented from entering it. The measured phase behavior provided strong experimental confirmation of the predicted effect under those conditions.

The Aharonov–Bohm effect demonstrates that quantum interference can reveal information about electromagnetic structure not captured by considering classical forces along each particle path alone. It has influenced discussion of electromagnetic potentials and gauge theories, and related phase effects have been studied in mesoscopic conductors and other quantum systems. The magnetic effect is one member of a broader family that also includes an electric version; the details and experimental conditions differ among these variants.