Aharonov–Bohm Effect

Quantum interference from a magnetic flux tube — topology without local fields

Parameters

Phase shift Δφ = 2π·Φ/Φ₀
Shifts interference fringes
even though B=0 at particle path.
Aharonov–Bohm (1959): A charged particle travelling around a solenoid acquires a quantum phase Δφ = e·Φ/(ħ) = 2π·Φ/Φ₀, where Φ₀ = h/e is the flux quantum. Although B = 0 everywhere outside the tube, the vector potential A ≠ 0, and it is A — not B — that couples to the wavefunction. The effect shifts double-slit fringes by a fraction of Φ/Φ₀, a purely topological phenomenon confirmed by Tonomura et al. (1986) with toroidal magnets.