Quantum phase shift from electromagnetic potential in field-free region
Predicted by Yakir Aharonov and David Bohm in 1959, this effect demonstrates that quantum particles can be affected by electromagnetic potentials even in regions where the fields are zero. An electron beam splits to pass on either side of a solenoid (where B=0 outside), yet the interference pattern shifts depending on the magnetic flux enclosed—revealing the fundamental role of the vector potential A in quantum mechanics.
At Φ = ½Φ₀, the phase shift is exactly π, causing destructive interference where there was previously constructive, and vice versa—the fringes shift by half a period. This effect was experimentally confirmed by Tonomura et al. (1986) using superconducting shielding to completely exclude electrons from the magnetic field region.