Quantum phases in an optical lattice

We present the zero-temperature phase diagram of bosonic atoms in an optical lattice, using two different mean-field approaches. The phase diagram consists of various insulating phases and a superfluid phase. We explore the nature of the insulating phase by calculating both the quasiparticle abn quasihole dispersion relation. We also determine the parameters of our single band Bose-Hubbard model in terms of the microscopic parameters of the atoms in the optical lattic