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Cavity cooling of an atom works best on a cyclic optical transition in thestrong coupling regime near resonance, where small cavity photon numberssuffice for trapping and cooling. Due to the absence of closed transitions astraightforward application to molecules fails: optical pumping can lead theparticle into uncoupled states. An alternative operation in the faroff-resonant regime generates only very slow cooling due to the reducedfield-molecule coupling. We predict to overcome this by using a strongly drivenring-cavity operated in the sideband cooling regime. As in the optomechanicalsetups one takes advantage of a collectively enhanced field-molecule couplingstrength using a large photon number. A linearized analytical treatmentconfirmed by full numerical quantum simulations predicts fast cooling despitethe off-resonant small single molecule - single photon coupling. Even groundstate cooling can be obtained by tuning the cavity field close to theAnti-stokes sideband for sufficiently high trapping frequency. Numericalsimulations show quantum jumps of the molecules between the lowest two trappinglevels, which can be be directly and continuously monitored via scattered lightintensity detection.

Optomechanics with molecules in a strongly pumped ring cavity