  In this paper, we study the decoherence and entanglement properties for the
two site Bose-Hubbard model in the presence of a non-linear damping. We apply
the techniques of thermo field dynamics and then use Hartree-Fock approximation
to solve the corresponding master equation. The expectation values of the
approximated field operators appearing in the solution of master equation, are
computed self-consistently. We solve this master equation for a small time $t$
so that we get the analytical solution, thereby we compute the decoherence and
entanglement properties of the solution of the two-mode bosonic system.
