Improving mechanical squeezing in a dissipative optomechanical system with quadratic dispersive coupling

We theoretically investigate that mechanical quantum squeezing in a dissipative optomechanical system, driven by two driving tones, can be improved through quadratic dispersive coupling (QDC) which appears by adjusting a membrane in an appropriate position of an optical cavity. The analytical expressions are derived for revealing the intrinsic mechanism of the mechanical squeezing improvement. Remarkably, compared with the case without QDC, an optimal condition involved the QDC is found to considerably enhance the mechanical squeezing, without reducing the purity of the mechanical squeezed state which even increases at low temperature. We also show that, in this scheme, the mechanical squeezing is still improved by QDC and beyond 3 dB even though the temperature rises. This improvement effect can be reflected by the broader frequency band of the measurable squeezing output field from the cavity. This provides a new opportunity to explore high-precision measurements and quantum nature of macroscopic objects.