  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.
