Approaching a final temperature prediction of an ensemble of atoms undergoing cavity-assisted cooling in the superradiant regime

We present results that determine the final temperature of an ensemble of atoms being supercooled in an optical resonator in the parameter regime of superradiance. We verify that one can perform a classical treatment of the light field and still recover the important lasing and superradiant physics.~This treatment yields a set of equations that contain no spin correlations. As a consequence this work ultimately shows that the quantum spin-spin correlations between atoms can be safely neglected in computational models in certain parameter regimes. Such a treatment may significantly reduce the size of the Hilbert space and therefore computational complexity needed to compute the final temperature.