The Kink of Gravitational Waves in a Vibrating Detector: An Emergent Berry Phase

Abstract

The detection of gravitational waves (GWs) has marked an advent of new era in the domain of astrophysics and general relativity. Using the framework of interaction between GWs and a point particle-like detector, within linearized gravity approach, we build a toy model which has potential to detect GWs. The detector is in simultaneous interaction with GWs and an external time-dependent (tunable) two-dimensional harmonic potential. We discover that in adiabatic approximation, gravitational wave interaction can lead to a geometric phase in the quantum states of the detector which can be controlled by tuning the frequency of the external harmonic potential. We argue that such geometric phase detection may serve as a manifestation of the footprint of GWs. More importantly, our theoretical model may be capable of providing a layout to build a future detector for the detection of very small frequency (≤ 5 Hz) GWs.

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

“…The total Berry phase of the system does not depend upon the choice of the coordinate basis and as can be observed from equation (116), it is dependent upon the cross polarization of the gravitational wave. This is quite contrary to the claim made in [38] which states that the Berry phase is generated entirely by the plus polarization of the gravitational wave and does not depend upon the cross polarization of the gravitational wave. Therefore, our analysis with a gravitational wave carrying the cross polarization only is not in accord with the claim made in [38].…”

“…It is quite easily understandable that the total Berry phase of the system is independent of the choice of the coordinate basis. Contrary to the claim made in [38], we do observe that for different values of n + and n − , there exists a Berry phase which is dependent on the cross polarization of the gravitational wave. Hence, not only the plus polarization, the cross polarization also carries signatures of a geometric phase.…”

“…Similar results for the Berry phases were obtained using a completely different method in [38]. The presence of the Christoffel symbol 01 1 G in the expressions for the Berry phases corresponding to the two spatial directions in the above two equations indicates the possibility that observing a non-zero Berry phase in this set up is equivalent to detecting a gravitational wave.…”

“…The approach that we have taken to obtain the Berry phase is based on finding the Lewis invariant and Lewis phase and then making an adiabatic approximation. This approach differs from the one in [38] where similar results for the Berry phase were obtained using a ladder operator approach. The main objective of our study is to show that a non-trivial Berry phase in the setup that we have considered, can prove to be an effective tool for the detection of gravitational waves.…”

“…The connection between Berryʼs phase and Lewisʼs phase for the quadratic Hamiltonians was first explored in the work [31]. Few more interesting investigations of such phases have been performed especially in the case of quantum harmonic oscillators [32][33][34][35][36][37][38]. Information theoretic viewpoint of the computation of such phases can be found in [39,40].…”