  Here we analyse cavity-mediated laser cooling for an experimental setup with
an external trap which strongly confines the motion of a particle in the
direction of the cavity axis. It is shown that the stationary state phonon
number exhibits three sharp minima as a function of the atom-cavity detuning
due to a direct atom-phonon-photon coupling term in the system Hamiltonian.
These resonances have the same origin as the Mollow triplet in the resonance
fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi
frequency-dependent atom-cavity detuning yields the lowest stationary state
phonon number for a wide range of experimental parameters.
