Photon-photon interactions in a largely detuned optomechanical cavity

We propose to realize effective beam-splitter-like and two-mode-squeezing photon-photon interactions in an optomechanical interface by exploiting detuned driving lasers. In this interface, the transitions between the optical and the mechanical states are significantly suppressed by the large energy offsets, therefore protecting the photon-photon interactions from mechanical dissipations. Moreover, the destructive quantum interference between the eigenmodes of the interface is capable of reducing the effects of initial mechanical thermal occupations. This optomechanical interface can serve as a universal block for photon state engineering and hybrid quantum networks in high-temperature thermal bath and without the requirement of cooling the mechanical oscillator to the ground state.