Aharonov-Bohm Effect — Quantum Mechanics in 60 Seconds #Shorts

追加: 2026-05-22

[00:00:00]An electron beam splits and travels two paths around an obstacle. On the right, a detector. Standard interferometer.

[00:00:07]Standard fringes.

[00:00:08]Now, place a tiny solenoid between the paths. Inside it sits a strong magnetic field, trapped flux phi pointing along the axis. The electrons travel only outside the solenoid where the magnetic field is exactly zero. They feel no Lorentz force. Classically, nothing should happen. Launch the beam. The two paths recombine and form an interference pattern on the detector. The textbook double path fringes. But, the vector potential A is not zero outside the solenoid. It circulates around the flux like a whirlpool. And the electrons swim right through it. Each path picks up a phase from the integral of A along it.

[00:00:43]The difference between the two paths equals E times the enclosed flux divided by N, a topological signature of the trapped field. Turn up the flux to half a flux quantum. The fringes slide by exactly half a period. Maxima land where minima used to be. Crank phi to one full flux quantum, and the pattern returns shifted by an entire fringe. The number of fringes shifted counts the quanta of flux trapped inside. Tonomura proved this in 1986 with a superconducting torus that shielded the field perfectly.

[00:01:12]The electrons saw zero B everywhere.

[00:01:15]And the shift was still there. A is physical. B is its curvature.