Multimode strong-coupling quantum optomechanics

We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong-coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators, we show that the system can classically exhibit bistability and bifurcations, and we explore how these manifest themselves in interference, entanglement, and correlation in the quantum theory, while revealing the impact of decoherence of the mechanical system due to cavity fluctuations and coherent driving.