Quantum dynamics of two-optical modes and a single mechanical mode optomechanical system: Selective energy exchange

We study the quantum dynamics of an optomechanical setup comprising two optical modes and one mechanical mode. We show that the same system can undergo a dynamical phase transition analogous to Dicke–Hepp–Lieb superradiant type phase transition. We found that the coupling between the momentum quadratures of the two optical fields gives rise to a new dynamical critical point. We show that selective energy exchange between any two modes is possible by coherent control of the coupling parameters. In addition we also demonstrate the occurrence of normal mode splitting (NMS) in the mechanical displacement spectrum.