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

Abstract

A thought experiment is proposed to demonstrate the existence of a gravitational, vector AharonovBohm effect. We begin the analysis starting from four Maxwell-like equations for weak gravitational fields interacting with slowly moving matter. 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. Some room-temperature data will be presented demonstrating the splitting of a single microwave cavity resonance into a spectral doublet due to the insertion of a central wire. This would represent an unseparated kind of parametric oscillator, in which the signal and idler waves would occupy the same volume of space. We then propose a separated parametric oscillator experiment, in which the signal and idler waves are generated in two disjoint regions of space, which are separated from each other by means of an impermeable superconducting membrane. 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.

Dynamical Casimir effect and the possibility of laser-like generation of gravitational radiation

“…Could the "new engineering or a new idea or both," as suggested in the above quotation from MTW, be "quantum engineering," in which somehow replaces G and c, so that the necessity for the use of astrophysical sources for the generation of gravitational waves could somehow be avoided? Here we propose a possibly affirmative answer to this question that involves the laser-like generation of gravitational radiation via the process of the dynamical Casimir effect [7].…”

“…In particular, this zeropoint energy should apply to gravitational waves, as well as to electromagnetic waves. In the case of gravitational waves, note that the size of the zero-point energy (7) is independent of Newton's constant G and of the speed of light c.…”

“…Thus the piston can impart energy into this gas. As a result, the action of the piston can parametrically amplify the radiation contained inside the resonator [13], so that it can become, via an exponential growth mechanism [7], a macroscopically observable beam of coherent radiation, just like in a laser.…”

“…A more detailed derivation of the threshold power ( 15) is given in [7], and yields the following result:…”

Electromagnetic coupling to centimeter-scale mechanical membrane resonators via RF cylindrical cavities

“…These results suggest that optomechanics with SRF microwave frequency cavities might hold promise for future systems which can exploit their extremely high Q-factors. We add that future configurations using membrane-SRF-cavities schemes might pave the way for macroscopic parametric amplifier/oscillator systems [24,25], which could then be used to perform experiments probing the quantum/classical boundary. Finally, hybrid systems that coherently couple microwave fields to optical fields [26] and, therefore, efficiently transfer squeezed states from the microwave to the optical regime, might also be a feasible future application for such SRF cavity systems.…”