  A recurrence relation ansatz between annihilation operators applied to the
hopping interaction term of the Jaynes-Cummings-Hubbard model (JCHM) reduces
the JCHM to that of the ordinary Jaynes-Cummings model (JCM), albeit, with a
boson energy depending on the hopping strength. This allows us to calculate the
phase diagram for the Mott-to-superfluid phase transition and the critical
hopping strength as a function of the detuning.
