Influence of the Kerr effect in a Mott insulator on the superfluid transition from the point of view of the Jaynes–Cummings–Hubbard model

We have studied analytically the Jaynes–Cummings–Hubbard model for a one-dimensional optical lattice with the account of the Kerr-type nonlinearity under the fermionic approximation. We have found that an increase in the number of photons or in the detuning parameter favors the superfluid phase. We have also found that the nonlinear Kerr effect favors the Mott insulator phase, which is in agreement with experimental observations.