Phase conjugation in quantum optomechanics

We analyze the phase-conjugate coupling of a pair of optomechanical oscillator modes driven by the time-dependent beat note of a two-color optical field. The dynamics of the direct and phase-conjugate modes exhibit familiar time-reversed qualities, leading to opposite sign temperatures for the modes in the classical regime of operation. These features are limited by quantum effects due to the noncommutative nature of quantum-mechanical operators. The effects are measurable by readout of the oscillator via a qubit. As a potential application of this system in sensing, we discuss a protocol applying phase-conjugate swaps to cancel or reduce external forces on the system.