Gravitational Wave Response and Noise Budget for a Levitated Sensor Detector

At present, the only experimental configurations to observe signatures of gravitational waves (GWs) are kilometer-scale Michelson interferometers, used in the LIGO and Virgo observatories, and global-scale pulsar timing arrays. However, there is a vast landscape of proposed devices, distinct from the current observatory paradigm and ranging in size from tabletop to millions of kilometers, which aim to detect GWs in the future. One such proposal currently under construction is the Levitated Sensor Detector (LSD), which will implement optically-levitated nanoparticles trapped within Fabry-Perot cavities to create a resonant, narrow-band, but tunable high-frequency GW detector. The principles of operation of such a device have been studied previously at leading order; in this work, we derive the response of the nanoparticles levitated in the LSD to incident GWs in a fully relativistic treatment. Furthermore, we study the transfer functions from experimental degrees of freedom to observable variables using the Finesse simulation program. Finally, considering anticipated noise sources in the LSD, we produce a preliminary noise budget for its operation and consider prospects for detecting proposed high frequency GW sources.