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