We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics is a competition of the mechanical effects of the cavity and of the laser photons, which may mutually interfere. We focus on the good-cavity limit and identify novel cooling schemes, which are based on quantum interference effects and lead to efficient ground-state cooling in experimentally accessible parameter regimes.
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