  We analyze the phase conjugate coupling of a pair of optomechanical
oscillator modes driven by the time-dependent beat-note due to 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, but these features are limited by
quantum effects due to the non-commutative nature of quantum mechanical
operators. The effects are measurable by read-out 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 external forces acting on the
system.
