We consider a hybrid quantum many-body system formed by both a vibrationalmode of a nanomembrane, which interacts optomechanically with light in acavity, and an ultracold atom gas in the optical lattice of the out-coupledlight. After integrating over the light field, an effective Hamiltonian revealsa competition between the localizing potential force and the membranedisplacement force. For increasing atom-membrane interaction we find anonequilibrium quantum phase transition from a localized non-motional phase ofthe atom cloud to a phase of collective motion. Near the quantum criticalpoint, the energy of the lowest collective excitation vanishes, while the orderparameter of the condensate becomes non-zero in the symmetry-broken state. Theeffect occurs when the atoms and the membrane are non-resonantly coupled.
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