  We perform a comparative study of the finite temperature behavior of
ultracold Bose atoms in optical lattices by the slave fermion and the slave
boson approaches to the Bose Hubbard model. The phase diagram of the system is
presented. Although both approaches are equivalent without approximations, the
mean field theory based on the slave fermion technique is quantitatively more
appropriate. Conceptually, the slave fermion approach automatically excludes
the double occupancy of two identical fermions on the same lattice site. By
comparing to known results in limiting cases, we find the slave fermion
approach better than the slave boson approach. For example, in the
non-interacting limit, the critical temperature of the superfluid-normal liquid
transition calculated by the slave fermion approach is closer to the well-known
ideal Bose gas result. At zero-temperature limit of the critical interaction
strength from the slave fermion approach is also closer to that from the direct
calculation using a zero-temperature mean field theory.
