Gravitational wave signal and noise response of an optically levitated sensor in a Fabry-P\'erot cavity

TL;DR

This paper provides a detailed relativistic analysis of an optically levitated sensor in a Fabry-Pérot cavity for high-frequency gravitational wave detection, revealing key asymmetries and noise coupling features.

Contribution

It introduces a gauge-independent derivation of GW interaction with levitated sensors and identifies how sensor positioning affects noise coupling and sensitivity.

Findings

Strain signal depends asymmetrically on trap position, maximized near input mirror.

Coupling of input-mirror displacements to the strain signal can be suppressed.

Results clarify physical origin and inform design principles for high-frequency GW detectors.

Abstract

Optically levitated sensors inside a Fabry-P\'erot cavity have been proposed for high-frequency gravitational-wave (GW) detection, though their configuration for gravitational wave sensitivity exhibits counterintuitive features. We provide a new detailed general relativistic derivation of the interaction between a gravitational wave and a levitated object in an optical cavity, demonstrating gauge independence of the observable response. We find a strong asymmetric dependence of the strain signal on trap position, maximized when the sensor is located near the input mirror, in agreement with previous results. A key new result of this work is the consequence of this asymmetry on the noise coupling: the coupling of input-mirror displacements to the strain signal can be highly suppressed relative to that of end-mirror displacements and common-mode mirror motion. These results clarify the physical origin of the gravitational wave interaction with such a sensor and establish crucial design principles for optical levitation based high-frequency GW detectors.