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In this paper, we study theoretically a hybrid optomechanical systemconsisting of a degenerate optical parametric amplifier inside a driven opticalcavity with a moving end mirror which is modeled as a stiffening Duffing-likeanharmonic quantum mechanical oscillator. By providing analytical expressionsfor the critical values of the system parameters corresponding to the emergenceof the multistability behavior in the steady-state response of the system, weshow that the stiffening mechanical Duffing anharmonicity reduces the width ofthe multistability region while the optical parametric nonlinearity can beexploited to drive the system toward the multistability region. We also showthat for appropriate values of the mechanical anharmonicity strength thesteady-state mechanical squeezing and the ground-state cooling of themechanical resonator can be achieved. Moreover, we find that the presence ofthe nonlinear gain medium can lead to the improvement of the mechanicalanharmonicity-induced cooling of the mechanical motion, as well as to themechanical squeezing beyond the standard quantum limit of 3 dB.

laser physics

Steady-state mechanical squeezing and ground-state cooling of a Duffing  anharmonic oscillator in an optomechanical cavity assisted by a nonlinear  medium