An analytical model for the detection of levitated nanoparticles in optomechanics

Interferometric position detection of levitated particles is crucial for the centre-of-mass (CM) motion cooling and manipulation of levitated particles. In combination with balanced detection and feedback cooling, this system has provided picometer scale position sensitivity, zeptonewton force detection, and sub-millikelvin CM temperatures. In this article, we develop an analytical model of this detection system and compare its performance with experimental results allowing us to explain the presence of spurious frequencies in the spectra.