  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.
