Quantum-Limited Amplification of Cavity Optomechanics without Resolved Sideband Condition

We propose a scheme to realize the phase-preserving amplification without the restriction of resolved sideband condition. As a result, our gain-bandwidth product is about one magnitude larger than the existing proposals. In our model, an additional cavity is coupled to the cavity-optomechanical system. Therefore our operating frequency is continuously tunable via adjusting the coupling coefficient of the two cavities.