Gravitational Wave Detection via a Planar Levitated Sensor in a Fabry-Perot Cavity

A particle trapped in an optical standing wave inside a Fabry-Perot cavity has been proposed as a detector for gravitational waves with frequencies from 10-300 kHz, which may be sourced by axion clouds surrounding spinning black holes or primordial black hole mergers. While the original proposal for such an experiment used standard heuristic estimates to compute the expected detector sensitivity, a thorough treatment of the signal and noise properties of such a detector has not yet been carried out. In this work, we expand the standard two-photon carrier-sideband formalism for studying optical setups to incorporate levitated dielectric particles. We then use this formalism to compute dynamical properties of such levitated sensors and extract transfer functions from various noise ports to readout channels. Finally, using the transfer functions which describe the experiment, we calculate noise budgets for the strain sensitivity of the experiment, including both classical and quantum noise sources.