We derive an equation for the cooling dynamics of the quantum motion of an atom trapped by an external potential inside an optical resonator. This equation has broad validity and allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. Our result shows that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency. DOI: 10.1103/PhysRevLett.95.143001 PACS numbers: 32.80.Pj, 32.80.Lg, 42.50.Pq Cavity cooling is a recent expression, which stresses the role of the mechanical effects of a resonator on the atomic and molecular center-of-mass dynamics. Indeed, the coupling between resonator and atom gives rise to complex dynamics, one aspect of which is the substantial modification of the atom spectroscopic properties [1]. This property allows one to change the atom scattering cross section, thereby affecting, and eventually tailoring, the mechanical dynamics of the atomic center of mass [2]. Moreover, the motion of the atom changes the medium density, thereby affecting the resonator field itself. Several recent experiments have reported relevant features of these complex dynamics [3][4][5][6][7][8]. Experimental demonstrations of atom cooling in resonators [3][4][5][6][7] have shown, among others, that cavities are a promising tool for preparing and controlling cold atomic samples of scalable dimensions, which may find relevant applications, for instance, in quantum information processing [9].In this Letter, we present a study of the quantum dynamics of the center-of-mass motion of an atomic dipole, which couples to a resonator and to a laser field driving it from the side. The system is sketched in Fig. 1. Differently from recent theoretical works on cavity cooling of atomic clouds [10], here the center of mass is confined by a tight trap, in a configuration that may correspond to the experimental situations reported, for instance, in [4,11,12]. Starting from a master equation for the quantum variables of the dipole, cavity, and center of mass, we derive a closed equation for the center-of-mass dynamics. This equation generalizes previous theoretical studies [13,14] and allows us to identify novel parameter regimes, where cooling can be efficient. Moreover, its form permits us to identify the individual scattering contributions, thereby gaining insight into the role of the various physical parameters. We show that quantum correlations between atom and resonator may lead to the suppression of scattering transitions, thereby enhancing the cooling efficiency.The starting point is the master equation for an atom of mass M whose dipole transition between the ground and excited states jgi and jei couples (quasi)resonantly to a laser and the mode of an optical resonator with wave vector k L and k c , respectively (jk L j jk c j k). In the reference frame of the laser, the...