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We theoretically study the transparency and amplification of a weak probe field applied to the cavity in hybrid systems formed by a driven superconducting circuit QED system and a mechanical resonator,or a driven optomechanical system and a superconducting qubit.We find that both the mechanical resonator and the superconducting qubit can result in the transparency to a weak probe field in such hybrid systems when a strong driving field is applied to the cavity.We also find that the weak probe field can be amplified in some parameter regimes.We further study the statistical properties of the output field via the degrees of second-order coherence.We find that the nonclassicality of the output field strongly depends on the system parameters.Our studies show that one can control single-photon transmission in the optomechanical system via a tunable artificial atom or in the circuit QED system via a mechanical resonator.

Transparency and amplification in a hybrid system of the mechanical resonator and circuit QED