A Gravitational Aharonov-Bohm Effect, and its Connection to Parametric Oscillators and Gravitational Radiation

TL;DR

This paper proposes a thought experiment demonstrating a gravitational Aharonov-Bohm effect, explores its connection to gauge invariance and quantum matter, and investigates potential gravitational radiation detection using superconducting parametric oscillators.

Contribution

It introduces a gravitational Aharonov-Bohm effect, links it to gauge invariance, and suggests a novel approach for detecting gravitational radiation with superconducting systems.

Findings

Lower threshold for EM parametric oscillation in separated configurations

Observable dynamical Casimir effect in superconducting cavities

Potential for gravitational microwave generation using parametric oscillators

Abstract

A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, and applied to problem of the interaction of radiation with macroscopically coherent quantum systems, including the problem of gravitational radiation interacting with superconductors. But first we examine the interaction of EM radiation with superconductors in a parametric oscillator consisting of a superconducting wire placed at the center of a high Q superconducting cavity driven by pump microwaves. We find that the threshold for parametric oscillation for EM microwave generation is much lower for the separated configuration than the unseparated one, which then leads to an observable dynamical Casimir effect. We speculate that a separated parametric oscillator for generating coherent GR microwaves could also be built.