Normal Mode Splitting and Antibunching in Stokes and Anti-Stokes Processes in Cavity Optomechanics: Radiation Pressure Induced Four-Wave Mixing Cavity Optomechanics

We study Stokes and anti-Stokes processes in cavity optomechanics in the regime of strong coupling. The Stokes and anti-Stokes signals exhibit prominently the normal-mode splitting. We report gain for the Stokes signal. We also report lifetime splitting when the pump power is less than the critical power for normal-mode splitting. The nonlinear Stokes processes provide a useful method for studying strong coupling regime of cavity optomechanics. We also investigate the correlations between the Stokes and anti-Stokes photons produced spontaneously by the optomechanical system. At zero temperature, our nanomechanical system leads to the correlations between the spontaneously generated photons exhibiting photon antibunching and those violating the Cauchy-Schwartz inequality.