Robust mechanical squeezing beyond 3  dB in a quadratically coupled optomechanical system

We demonstrate the dissipation-enabled generation of strong mechanical squeezing in a cavity optomechanical system by periodically modulating the amplitude of a single-tone laser driving the system. The Bogoliubov mode of the quadratically coupled mechanical oscillator cools down to its ground state due to optomechanical sideband cooling, which contributes to strong squeezing exceeding the 3 dB standard quantum limit. This sideband cooling mechanism is further optimized by numerically maximizing the ratio of the coupling sidebands. Then we look at the crucial role of the cavity mode dissipation in inducing enhanced squeezing. We also verify our results with the analytical solution (under adiabatic approximation) and the exact numerical solution. Compared with previous setups, the quadratic coupling between the mechanical oscillator and the optical mode gives rise to robust mechanical squeezing and strong optomechanical entanglement even for a large thermal occupancy of the mechanical mode.