Nonlinear optical response in multiple-mode coupling nanomechanical system

We theoretically investigate the optical Kerr nonlinear effect in a multiple-mechanical-mode-coupling hybrid quantum system, where a hybrid quantum dot-nanomechanical resonator (QD-NR) system driven by two-tone fields interacts with another two NRs with same or different frequencies. There are two kinds coupling in the system, i.e., the exciton-phonon coupling (the interaction of QD and NR) and phonon-phonon coupling (the interaction between NRs). It is demonstrated that the optical Kerr effect can be regulated in different parametric regimes including the resonance, detuning, different or identical resonators, and Rabi frequency. The physical origin of the controllable optical Kerr nonlinear effect comes from mechanically induced coherent population oscillation, and we term it as phonon assist-coherent population oscillation by combining the phonon-phonon coupling in the system. This studies may have potential applications in optical telecommunications and information processing.