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We have studied the Jaynes-Cummings-Hubbard model for a chain with the Kerreffect (nonlinear optical effect) through fermionic approximation. We haveobserved that the Kerr effec does not cause major changes in the energyspectrum. However, the phase transition properties from Mott insulator tosuperfluid undergoes significant changes due to the Kerr effect.

The influence of the Kerr effect in Mott insulator to superfluid transition from the point of view of the Jaynes-Cummings-Hubbard model