Aharonov-Bohm phases in a quantum LC circuit

Abstract

We study novel types of contributions to the partition function of the Maxwell system defined on a small compact manifold. These contributions, often not addressed in the perturbative treatment with physical photons, emerge as a result of tunneling transitions between topologically distinct but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that this effect is highly sensitive to a small external electric field, which should be contrasted with the conventional Casimir effect where the vacuum photons are essentially unaffected by any external field. Furthermore, photons will be emitted from the vacuum in response to a time-dependent electric field, similar to the dynamical Casimir effect in which real particles are radiated from the vacuum due to the time-dependent boundary conditions. We also propose an experimental setup using a quantum LC circuit to detect this novel effect. We expect physical electric charges to appear on the capacitor plates when the system dimension is such that coherent Aharonov-Bohm phases can be maintained over macroscopically large distances.