The influence of the Kerr effect in Mott insulator to superfluid   transition from the point of view of the Jaynes-Cummings-Hubbard model
  We have studied the Jaynes-Cummings-Hubbard model for a chain with the Kerr effect (nonlinear optical effect) through fermionic approximation. We have observed that the Kerr effec does not cause major changes in the energy spectrum. However, the phase transition properties from Mott insulator to superfluid undergoes significant changes due to the Kerr effect. 
C. B. Gomes, F. A. G. Almeida and A. M. C. Souza
quant-ph