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 number, 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 multicomponent 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 find potential applications in microwave quantum sensing, quantum telecommunication, and quantum information protocols.