Theory of phase-mixing amplification in an optomechanical system

The investigation of the ultimate limits imposed by quantum mechanics on amplification represents an important topic both on a fundamental level and from the perspective of potential applications. We discuss here a novel regime for bosonic linear amplifiers - beside phase-insensitive and phase-sensitive amplification - which we term here phase-mixing amplification. Furthermore, we show that phase-mixing amplification can be realised in a cavity optomechanical setup, constituted by a mechanical resonator which is dispersively coupled to an optomechanical cavity asymmetrically driven around both mechanical sidebands. While, in general, this amplifier is phase-mixing, for a suitable choice of parameters, the amplifier proposed here operates as a phase-sensitive amplifier. We show that both configurations allow amplification with an added noise below the quantum limit of (phase-insensitive) amplification in a parameter range compatible with current experiments in microwave circuit optomechanics. In particular, we show that introducing phase-mixing amplification typically allows for a significant reduction of the added noise.