Quantum limit of laser cooling in dispersively and dissipatively coupled optomechanical systems

Mechanical oscillators can be cooled by coupling them to an optical or microwave cavity. Going beyond the standard quantum noise approach, we find an analytic expression for the steady-state phonon number in systems where the position of the mechanical oscillator modulates the cavity frequency as well as the cavity linewidth. We trace the origin for the quantum limit of cooling to fluctuations in the optical force both at and away from the mechanical frequency. Finally, we calculate the minimal phonon number for the different types of couplings. Our study elucidates how to beneficially combine dispersive and dissipative optomechanical couplings.