Theory of Optically-Driven Sideband Cooling for Atomic Collective Excitations and Its Generalization

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.