Employing coupled cavities to increase the cooling rate of a levitated nanosphere in the resolved sideband regime

In this paper we investigate cooling of a levitated nanosphere in a system of coupled cavities in the resolved sideband regime. Thanks to the presence of an extra resonance in the coupled cavity cooling system, the coupling strength can be maximized at the optimum detuning. In this fashion, the intra-cavity photon number is increased and thereby the cooling rate is enhanced and the strong coupling regime is achieved without resorting to increased driving laser power. The underlying physics of the increased cooling efficiency in the here-proposed system of coupled cavities in the resolved sideband regime and that of the already reported system of coupled cavities in the unresolved sideband regime are significantly different from each other. Since the spectral density of the displacement of the particle can no longer be accurately approximated by the conventional Lorentzian lineshape in the strong coupling regime, a double Lorentzian lineshape is employed to accurately approximate the spectral density of the displacement of the particle and to provide analytical formulations for the cooling rate. The analytical expression given for the cooling rate is validated by numerical simulations.