Steady-state mechanical squeezing in an optomechanical system via Duffing nonlinearity

Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum effects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be generated in an optomechanical system with mechanical nonlinearity and red-detuned monochromatic driving on the cavity mode. The squeezing is achieved as the joint effect of nonlinearity-induced parametric amplification and cavity cooling and is robust against thermal fluctuations of the mechanical mode. We also show that the mechanical squeezing can be detected via an ancilla cavity mode.