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We analyse the dynamics leading to radiative cooling of an atomic ensembleconfined inside an optical cavity when the atomic dipolar transitions areincoherently pumped and can synchronize. Our study is performed in thesemiclassical regime and assumes that cavity decay is the largest rate in thesystem dynamics. We identify three regimes characterising the cooling. At firsthot atoms are individually cooled by the cavity friction forces. After thisstage, the atoms' center-of-mass motion is further cooled by the coupling tothe internal degrees of freedom while the dipoles synchronize. In the lateststage dipole-dipole correlations are stationary and the center-of-mass motionis determined by the interplay between friction and dispersive forces due tothe coupling with the collective dipole. We analyse this asymptotic regime bymeans of a mean-field model and show that the width of the momentumdistribution can be of the order of the photon recoil. Furthermore, theinternal excitations oscillate spatially with the cavity standing wave formingan antiferromagnetic-like order.

Semiclassical theory of synchronization-assisted cooling