  We explore how to cool atomic collective excitations in an optically-driven
three-level atomic ensemble, which may be described by a model of coupled two
harmonic oscillators (HOs) with a time-dependent coupling. Moreover, the
coupled two-HO model is further generalized to address other cooling issues,
where the lower-frequency HO can be cooled whenever the cooling process
dominates over the heating one during the sideband transitions. Unusually, due
to the absence of the heating process, the optimal cooling of our first cooling
protocol for collective excitations in an atomic ensemble could break a usual
sideband cooling limit for general coupled two-HO models.
