Abstract
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in {\it time-dependent} potentials . In particular, we focus on the case of a charged particle moving in the time varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential ({\it i.e.} $\oint A_\mu dx ^\mu$) and field ({\it i.e.} $\frac{1}{2}\int F_{\mu \nu} d \sigma ^{\mu \nu}$) forms of the Aharanov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space-time loop, amplitude of the electromagnetic wave) under which the time varying Aharonov-Bohm effect could be observed.
Highlights
We investigate the Aharonov–Bohm phase difference picked up by charged particles that go around a closed space–time loop in the presence of the time-dependent potentials and fields of an electromagnetic plane wave
Aharonov–Bohm phase of a charged particle traveling around a closed space–time loop, given in Figs. 1, 2 and 3, in the presence of a time-varying electromagnetic field, given by a plane wave traveling in the ±z direction and with a polarization in the x direction
Our work is a generalization of earlier work, [11,12], in that we consider both the electric and the magnetic Aharonov–Bohm effects, and we are able to see the interplay between the two
Summary
We investigate the Aharonov–Bohm phase difference picked up by charged particles that go around a closed space–time loop in the presence of the time-dependent potentials and fields of an electromagnetic plane wave. The type I Aharonov–Bohm effect is when the charged particle develops a phase while moving through a region that is free of electric and magnetic fields, as in the original time-independent, infinite solenoid set-up. For the usual static magnetic Aharonov–Bohm effect, the line integral of the 3-vector potential, A, is related to the surface area of the magnetic field via Stokes’ theorem in 3D, A·dx = B·da In order for this magnetic Aharonov–Bohm phase to be non-zero, the magnetic field, B, must have a component along the area normal direction, da. For the wave traveling in the z-direction, and for the area of the loop which has a projection in the x z plane, both the magnetic field in the y-direction and the electric field in the xdirection will give non-zero contributions to the time-varying Aharonov–Bohm phase. In our set-up both the magnetic and electric Ahronov–Bohm phases play a role
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