Phonon-phonon interaction and Parametric down-conversion generation in multimode optomechanical systems


 We studied the process of polariton conversion in a 3-mode nonlinear optomechanical system. Compared with the standard 2-mode optomechanical system, we find a much larger conversion rate of polariton modes can be achieved under typical dissipation conditions. To obtain a transparent understanding of the relevant physical process, we show that in the large detuned case the cavity can be eliminated adiabatically, resulting in a parametric down-conversion (PDC) interaction between two phononic polariton modes. By tuning cavity detuning, the nonlinear interaction can be enhanced with the frequency-matching condition. Results from analytical treatment based on the effective PDC model agree with the numerical simulation. Such a system provides potential applications in nonlinear phononics.