Collective cooling of atoms in a ring cavity

Abstract

We study the cooling effect induced by a transversely pumped ring cavity on the motion of N linearly polarizable particles, all of which are trapped in the same cavity. We derive the friction tensor including cross friction terms and compare it to the friction coefficient of single-atom cavity cooling. We find that atoms that are not trapped by the cavity field are cooled independently with the same efficiency as a single untrapped atom. For atoms self-trapped in the cavity field, however, collective effects kick in. These result in an N-fold increase of the friction on the center-of-mass mode, however, all other modes of motion are practically not cooled by the cavity. This shows that cavity cooling works efficiently for many particles cooled collectively, and allows us to reach the regime where the particles are deeply trapped in harmonic wells. There it has to be complemented by other cooling methods, e.g. sideband cooling.