Enhancing nanomechanical squeezing by atomic interactions in a hybrid atom-optomechanical system

In a hybrid atom-optomechanical system, the optical coupling of a mechanical mode of a nanomembrane in an optical cavity with a distant interacting atom gas permits highly non-classical quantum many-body states. We show that the mechanical mode can be squeezed by the back-action of internal excitations of the atoms in the gas. A Bogoliubov approach reveals that these internal excitations form a fluctuating environment of quasi-particle excitations for the mechanical mode with a gaped spectral density. Nanomechanical squeezing arises due to quasi-particle excitations in the interacting atom gas when the mechanical frequency is close to resonance with the internal atomic transitions. Interestingly, nanomechanical squeezing is enhanced by atom-atom interactions.