  We propose a scheme which can realize an extended two-component Bose-Hubbard
model using polaritons confined in an array of optical cavities. In addition to
the density-dependent interactions, this model also contains nonlinear coupling
terms between the two components of the polariton. Using a mean-field
calculation, we obtain the phase diagram which shows how these terms affect the
transition between the Mott insulator and the superfluid phase. In addition, we
employ both a perturbation approach and an exact diagonalization method to gain
more insights into the phase diagram.
