  We derive an effective Bose-Hubbard model that predicts a phase transition
from Bose-Einstein condensate to Mott insulator in two different systems
subject to applied periodic potentials: microcavity exciton-polaritons and
indirect excitons. Starting from a microscopic Hamiltonian of electrons and
holes, we derive an effective Bose-Hubbard model for both systems and evaluate
the on-site Coulomb interaction U and hopping transition amplitudes t.
Experimental parameters required for observing a phase transition between a
Bose-Einstein condensate and a Mott insulator are discussed. Our results
suggest that strong periodic potentials and polaritons with a very large
excitonic component are required for observing the phase transition. The form
of the indirect exciton interaction is derived including direct and exchange
components of the Coulomb interaction. For indirect excitons, the system
crosses over from a Bose-Hubbard model into a double layer Fermi-Hubbard model
as a function of increasing bilayer separation. The Fermi-Hubbard model
parameters are calculated, and the criteria for the location of this crossover
are derived. We conjecture that a crossover between a Bose Mott insulator to a
Fermi Mott insulator should occur with increasing bilayer separation.
