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Description
A dielectric particle optically trapped inside a Fabry-Perot cavity has been proposed as a detector for gravitational waves with frequencies from ~10-300 kHz. While standard treatments of levitated optomechanics experiments proceed assuming the levitated particle sources only a perturbative effect on the cavity fields, the atypical properties of the sensors targeted for levitation may break such assumptions. In this work, we establish a framework for studying this class of experiments, which extends the vacuum two-photon formalism of Corbitt et al. to include moving dielectrics. Notably, our framework relaxes the constraint that the insertion of the dielectric particle must modify the cavity fields only perturbatively. We proceed to demonstrate that the proposed plate-like particles can indeed modify the cavity fields in a non-perturbative manner, emphasizing the necessity of our treatment. We highlight the expanded space of optical and dynamical phenomenology these particles open which is inaccessible by conventional levitated sensors. Finally, we study the response of the experiment to external perturbations (including gravitational waves), laying the groundwork for the construction of sensitivity estimates in future work.