Measuring Electromagnetic Vector Potential via Weak Value

TL;DR

This paper demonstrates that the electromagnetic vector potential, previously thought unmeasurable directly due to gauge invariance, can actually be measured using weak value techniques, revealing its physical reality.

Contribution

It introduces a method to measure the electromagnetic vector potential directly via weak values, challenging the traditional view of its gauge dependence.

Findings

Vector potential can be measured directly using weak values.

The measurement is the difference in weak values of canonical momentum.

This approach confirms the physical reality of the vector potential.

Abstract

Electromagnetic vector potential has physical significance in quantum mechanics as revealed by the Aharonov-Bohm effect for charged particles. However, till date it is thought that we cannot measure the vector potential directly as this is not a gauge invariant quantity. Contrary to this belief, here we show that one can indeed measure the electromagnetic vector potential using the notion of weak value. We show that it is simply the difference between the weak value of the canonical momentum of a charged particle in the presence and absence of magnetic field. This suggests that the vector potential is not only a physical entity but can be measured directly in the experiment.