Enhancing quadratic optomechanical coupling via a nonlinear medium and lasers

We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser, and the optical cavity mode is driven by a strong laser. We derive an effective Hamiltonian using squeezing transformation and rotating wave approximation. The effective quadratic optomechanical coupling strength can be larger than the decay rate of the cavity mode by adjusting the two optical driving fields. The thermal noise of squeezed cavity mode can be suppressed totally with the help of a squeezed vacuum field. Then a driving field is applied to the mechanical mode. We investigate the equal-time second-order correlations and find there are photon, phonon, and photon-phonon blockades even when the original single-photon quadratic coupling is much smaller than the decay rate of the optical mode. In addition, the sub-Poissonian window of the two-time second-order correlations can be controlled by the mechanical driving field. Finally, we show the squeezing and entanglement of the model could be tuned by the driving fields of the nonlinear medium and mechanical mode.