Response and sensitivity of a gravitational wave detector featuring an optically-trapped particle 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 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 provide a detailed derivation of the counter-intuitive result of the original proposal regarding the broken symmetry in the Fabry-Perot cavity: that the maximum signal ratio is obtained when the particle is trapped near the input mirror. We then employ the Finesse simulation package to analyze the response of such a detector to an incident gravitational wave, as well as the role of dominant noise sources in a fully frequency-dependent way as a function of detector parameters. The complete noise budget calculation reveals that the detection laser, which is also used for cooling the levitated sensor, sources additional contributions to the detector response function which can be exploited to substantially improve the experiment's sensitivity beyond previous estimates.