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Directional amplifiers are crucial nonreciprocal devices in both classicaland quantum information processing. Here we propose a scheme for realizing adirectional amplifier between optical and microwave fields based on anoptomechanical system with optical gain, where an active optical cavity and twopassive microwave cavities are, respectively, coupled to a common mechanicalresonator via radiation pressure. The two passive cavities are coupled viahopping interaction to facilitate the directional amplification between theactive and passive cavities. We obtain the condition of achieving opticaldirectional amplification and find that the direction of amplification can becontrolled by the phase differences between the effective optomechanicalcouplings. The effects of the gain rate of the active cavity and the effectivecoupling strengths on the maximum gain of the amplifier are discussed. We showthat the noise added to this amplifier can be greatly suppressed in the largecooperativity limit.

Directional amplifier in an optomechanical system with optical gain