The Aharonov-Bohm phase is locally generated (like all other quantum phases)

C. Marletto, V. Vedral

Published 2019-06-08Version 1

Aharonov and Bohm noted that the wave-function of a charge acquires a detectable phase when superposed along two paths enclosing an infinite solenoid, even though that wave-function is non-zero exclusively where the solenoid's electric and magnetic fields are zero. This phase was long considered radically different from all other quantum phases, because it seems explainable only via local action of gauge-dependent potentials, not of the gauge-invariant electromagnetic fields. Recently Vaidman proposed a model explaining the phase only in terms of the electron's (magnetic) field at the solenoid, later developed by Kang with a lagrangian treatment. However, this analysis treats the field as semiclassical and is still not local. For it does not explain how the phase, generated by the field-field interaction at the solenoid, is detectable on the charge when closing the interference loop. A quantum treatment of the field is needed for that. In this paper we propose a local model, where the field is treated quantum-mechanically. This shows that the Aharonov-Bohm (AB) phase is generated by the same quantum local mechanism as all other electromagnetic phases. It is mediated by the entanglement between the superposed charge and the EM field, also modelled as a quantum system. Surprisingly, the quantised model produces some experimentally different predictions from the semiclassical accounts of the AB phase, because it predicts that the phase at any point along the charge path is gauge-invariant and locally generated, and therefore in principle detectable by measuring observables of the charge. We also propose a realistic experiment, within current technological reach, where the predicted phase difference along the path is measured, by performing (a partial) quantum state tomography on the charge without closing the interfering charge paths.