  We propose a realization of a quantum heat engine in a hybrid
microwave-optomechanical system that is the analog of a classical straight-twin
engine. It exploits a pair of polariton modes that operate as out-of-phase
quantum Otto cycles. A third polariton mode that is essential in the coupling
of the optical and microwave fields is maintained in a quasi-dark mode to
suppress disturbances from the mechanical noise. We also find that the
fluctuations in the contributions to the total work from the two polariton
modes are characterized by quantum correlations that generally lead to a
reduction in the extractable work compared to its classical version.
