Simultaneous cooling of degenerate mechanical modes in unresolved sideband regime via optical and mechanical nonlinearities

We propose a scheme to simultaneously cool multiple degenerate mechanical modes in optomechanical systems beyond the resolved sideband regime. In general, one of the main obstacles for cooling degenerate mechanical modes is the so-called dark -mode effect. The Duffing nonlinearities (mechanical nonlinearities) can be used to overcome the dark -mode effect of degenerate mechanical modes. A second -order nonlinear medium (optical nonlinearity) is introduced to accomplish the ground -state cooling of degenerate mechanical modes beyond the resolved sideband regime. We find the dark mode of degenerate mechanical modes can be broken when the mechanical nonlinearities of different mechanical modes are not very close. Our scheme paves the way toward the implementation of simultaneous ground -state cooling of degenerate mechanical modes of optomechanical systems beyond the resolved sideband regime in experiments.