Simultaneous cooling coupled nano-mechanical resonators in cavity optomechanics

Coupled mechanical resonators have recently attracted great attention for both practical applications and fundamental studies. As a preparation step, it is needed to cool the coupled mechanical resonators to their ground states. Here we propose a theoretical scheme to cool two coupled mechanical resonators by introducing an optomechanical interface. The final mean phonon numbers of the two mechanical resonators are calculated exactly and the results show that the ground-state cooling is achievable in the resolved-sideband regime and under the optimal driving. Moreover, we derived analytical expressions of the cooling limits by adiabatically eliminating the cavity field under the large-decay limit.