Performance of a cooling method by quadratic coupling at high temperatures

Cooling mechanical resonators to a quantum regime at high temperatures is important in terms of exploring and applying their quantum effects unrestricted by low environmental temperatures. It has been suggested by M. Bhattacharya et al. [Phys. Rev. A 77, 033819 (2008)] that quadratic coupling could be used to help cool a membrane in membrane-in-the-middle optomechanical systems (MMOSs) at room temperature to a state with a mean phonon number smaller than 1. Its cooling effect is actually overestimated because of the unconsidered factor that it is limited by the small frequency difference between the quadratically coupled cavity mode and its neighboring mode, which imposes an upper bound on the input trapping laser power and therefore restricts its cooling effect. Based on the MMOS and by taking the above factors into consideration, we have concretely investigated the performance of this cooling method by a more rigorous calculation. Our calculation shows that the cooling effect is indeed ultimately limited by the input trapping laser power, but one can still cool a membrane close to a quantum regime at 77 K with parameters approaching experimental values.