Synchronization dynamics of two nanomechanical membranes within a Fabry-Perot cavity

Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an appropriate definition of the phase difference operator for the resonators, we study synchronization in the quantum case through the covariance matrix formalism. We find that for sufficiently large driving, quantum synchronization is robust with respect to quantum fluctuations and to thermal noise up to not too large temperatures. Under synchronization, the two membranes are never entangled, while quantum discord behaves similarly to quantum synchronization, that is, it is larger when the variance of the phase difference is smaller

Improving photon blockade, entanglement and mechanical-cat-state generation in a generalized cross-Kerr optomechanical circuit

We propose a feasible experimental scheme to improve the few-photon optomechanical effects, including photon blockade and mechanical-Schrodinger cat-state generation, as well as photon-phonon entanglement in a tripartite microwave optomechanical circuit. The system under consideration is formed by a single-Cooper-pair transistor, a microwave LC resonator, and a micromechanical resonator. Our scheme is based on an additional higher-order (generalized) nonlinear cross-Kerr type of coupling, linearly dependent on photon number while quadratically dependent on mechanical phonon one, which can be realized via adjusting the gate charge of the Cooper-pair transistor. We show, both analytically and numerically, that the presence of both cross-Kerr and generalized cross-Kerr nonlinearities not only may give rise to the enhancement of one- and two-photon blockades as well as photon induced tunneling but can also provide more controllability over them. Furthermore, it is shown that in the regime of zero optomechanical coupling, with the aid of generalized cross-Kerr nonlinearity, one can generate multi-components mechanical superposition states which exhibit robustness against system dissipations. We also study the steady-state entanglement between the microwave and mechanical modes, the results of which signify the role of generalized cross-Kerr nonlinearity in enhancing the entanglement in the regime of large-red detuning. The proposed generalized cross-Kerr optomechanical system can be found potential applications in microwave quantum sensing, quantum telecommunication, and quantum information protocols