Squeezing of a Mechanical Oscillator in a Dissipative Optomechanical System with Duffing Nonlinearity

ABSTRACT The quadrature‐squeezed state of a macroscopic mechanical oscillator plays a key role in enhancing the precision of quantum measurements. Here, we theoretically demonstrate that the steady‐state displacement squeezing of a membrane in a purely dissipative optomechanical system can be generated via the Duffing nonlinearity of the membrane when the cavity is driven by a red‐detuned laser. The mechanical squeezing results from a combination of the Duffing nonlinearity and the cooling of the membrane induced by the red‐detuned laser. We find that the maximum achievable squeezing is over 6 dB at a temperature of 10 mK in the resolved‐sideband regime. We show that a larger Duffing nonlinear strength or a smaller cavity decay rate causes the strong displacement squeezing exceeding 3 dB to emerge at a lower input laser power. And the strong mechanical squeezing beyond 3 dB can be achieved at a temperature of 10 mK even outside the resolved sideband regime. The generated mechanical squeezing is robust against the thermal noise of the membrane. Moreover, we show that the mechanical squeezing can be detected directly through homodyning detection of the cavity output field.