Simultaneous cooling of two mechanical oscillators in dissipatively coupled optomechanical systems

We propose a scheme to simultaneously cool two mechanical oscillators in a dissipatively coupled optomechanical system. Calculating the mean phonon numbers of the two mechanical oscillators in steady state, we find that there are two cooling regions. Both mechanical oscillators can be cooled efficiently in the two cooling regions. We also find that when the coupling strength between the two mechanical oscillators is large, the second mechanical oscillator can be cooled to a temperature lower than the first mechanical oscillator. This feature can be understood as the entanglement between two phononic supermodes of the two mechanical oscillators. When the coupling strength is small, the second mechanical oscillator can also be cooled, but cannot reach a temperature lower than the first mechanical oscillator, as the thermal fluctuations of reservoir cannot be ignored. The quantum cooling limits of the two mechanical oscillators are discussed for both the strong and weak couplings between the two mechanical oscillators.