Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement

We examine theoretically the driven-dissipative Bose-Hubbard dimer in the optical bistable regime. Various approximation schemes based on a Gutzwiller mean-field decoupling are applied and compared. Depending on the system parameters, we show that a decoupling with respect to the real space or to the reciprocal space can be more accurate. The Gutzwiller decoupling is applied both at the level of the density matrix and for the wave function during a quantum trajectory simulation. The latter is shown to be a more accurate approximation. A Gaussian approximation for the nonhomogeneous antibonding mode is also explored. We also show that entanglement in this system is witnessed by squeezing in reciprocal space.