Cavity optomechanics with ultra-cold Bose gases for quasiparticle state manipulation and prospects for sensing applications

Ensembles of ultra-cold atoms have been proven to be versatile tools for high precision sensing applications. Here, we present a method for manipulation and readout of the state of trapped clouds of ultra-cold bosonic atoms. In particular, we discuss the creation of coherent and squeezed states of quasiparticles and the coupling of quasiparticle modes through an external cavity field. This enables operations like state swapping and beam splitting which can be applied to realize a Mach-Zehnder interferometer (MZI) in frequency space. We present two explicit example applications in sensing: the measurement of the healing length of the condensate with the MZI scheme, and the measurement of an oscillating force gradient with a pulsed optomechanical readout scheme. Furthermore, we calculate fundamental limitations based on parameters of state-of-the-art technology.