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We consider an optomechanical system composed by a trapped ion dispersivelycoupled to a single mode of a pumped optical cavity. We focus in a parameterrange for which the semiclassical description predicts two clearly distinctequilibrium configurations in the limits of small and large photon pumping,while a bistable regime is found for intermediate pumping. This semiclassicaldescription, however, is not valid in close proximity of the system transitionsor when the mean photon number is low. Here we provide a numerical analysis ofthe fully quantum state in the few-photon regime, exploring the features of theasymptotic state across the transition and analyzing possible markers ofsemiclassical bistability. We find an increase in the entropy of the system andof the entanglement in the transition region, but no clear signatures ofmetastability in the spectrum of the evolution.

A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime