  Regular arrays of electromagnetic resonators, in turn coupled coherently to
individual quantum two-level systems, exhibit a quantum phase transition of
polaritons from a superfluid phase to a Mott-insulating phase. The critical
behavior of such a Jaynes-Cummings lattice thus resembles the physics of the
Bose-Hubbard model. We explore this analogy by elaborating on the mean-field
theory of the phase transition, and by presenting several useful mappings which
pinpoint both similarities and differences of the two models. We show that a
field-theory approach can be applied to prove the existence of multicritical
curves analogous to the multicritical points of the Bose-Hubbard model, and we
provide analytical expressions for the position of these curves.
