The dynamics of an open Bose-Hubbard dimer with effective asymmetric coupling

We investigate an open Bose-Hubbard dimer with a non-Hermitian term represents an asymmetric coupling between the two sites. By mapping to the collective angular moment model with the Schwinger representation and assuming coherent evolution, we apply the mean-field approximation and obtain a set of nonlinear Bloch equations for this non-Hermitian many-particle system. Its quantum-classical correspondence is established by reformulating the mean-field dynamics as generalized classical canonical evolution equations. We analyze the fixed point structures across different parameter regions, which shows the interplay of nonlinearity and non-Hermiticity changes the behavior of mean-field dynamics. Specifically, the self-trapping transition is modified in the weak non-Hermiticity region, while the property of fixed points is changed in the strong non-Hermiticity region. Finally, the full many-particle evolution is solved numerically and found to agree with the mean-field dynamics.