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We consider how nonlinear interaction effects can manifest themselves and even be enhanced in a strongly driven optomechanical system. Using a Keldysh Green's function approach, we calculate modifications to the cavity density of states due to both linear and nonlinear optomechanical interactions, showing that strong modifications can arise even for a weak nonlinear interaction. We show how this quantity can be directly probed in an optomechanically induced transparency-type experiment. We also show how the enhanced interaction can lead to nonclassical behavior, as evidenced by the behavior of g(2) correlation functions.
Lemonde et al. (Fri,) studied this question.