  The superfluid to Mott insulator transition in cavity polariton arrays is
analyzed using the variational cluster approach, taking into account quantum
fluctuations exactly on finite length scales. Phase diagrams in one and two
dimensions exhibit important non-mean-field features. Single-particle
excitation spectra in the Mott phase are dominated by particle and hole bands
separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows
for changing the nature of the bosonic particles from quasi-localized excitons
to polaritons to weakly interacting photons. The Mott state with density one
exists up to temperatures $T/g\gtrsim0.03$, implying experimentally accessible
temperatures for realistic cavity couplings $g$.
