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We study theoretically the generation of mechanical squeezing and optomechanical entanglement in a double-cavity optomechanical system involving a modulated optical parametric amplifier (OPA). Owing to the cooperation of the modulated OPA and the auxiliary cavity, the mechanical squeezing can be realized in both the resolved-sideband and unresolved-sideband regimes. Particularly, the strong mechanical squeezing can be generated in the resolved-sideband regime with the assistance of the modulated OPA. Moreover, under the joint effect of the auxiliary cavity and the modulated OPA, the optomechanical entanglement can be greatly enhanced in the unresolved-sideband regime. It is noted that both the mechanical squeezing and optomechanical entanglement have strong robustness against the high dissipation of the cavity and thermal noise. [ABSTRACT FROM AUTHOR]

In this paper, the macroscopic quantum entanglement and squeezing in an unresolved‐sideband atom‐optomechanical system with a modulated optical parametric amplifier (OPA) inside the cavity are studied. Increasing the parametric gain of the OPA, the quantum‐classical correspondence between the atom‐mirror entanglement and classical nonlinear dynamics can be found. The critical point where the system experiences the transition from periodic oscillation to period‐doubling motion can be characterized by the singularity of the atom–mirror entanglement. Furthermore, the dependence of the atom–mirror entanglement and mechanical squeezing on the detuning and the parametric gain of the OPA as well as the environment temperature are investigated in detail. It is found that the atom‐mirror entanglement can be enhanced and the mechanical squeezing can be generated by modulating the OPA. [ABSTRACT FROM AUTHOR]