  Simultaneous ground-state cooling of multiple degenerate mechanical modes is
a tough issue in optomechanical system due to the existence of the dark mode
effect. Here we propose a universal and scalable method to break the dark mode
effect of two degenerate mechanical modes by introducing the cross-Kerr (CK)
nonlinearity. At most four stable steady states can be achieved in our scheme
in the presence of the CK effect, different from the bistable behavior of the
standard optomechanical system. Under the constant input laser power, the
effective detuning and mechanical resonant frequency can be modulated by the CK
nonlinearity, which results in an optimal CK coupling strength for cooling.
Similarly, there will be an optimal input laser power for cooling when the CK
coupling strength stays fixed. Our scheme can be extended to break the dark
mode effect of multiple degenerate mechanical modes by introducing more than
one CK effects. To fulfill the requirement of the simultaneous ground-state
cooling of N multiple degenerate mechanical modes N-1 CK effects with different
strengths are needed. Our proposal provides new insights in dark mode control
and might pave the way to manipulating of multiple quantum states in
macroscopic system.
