Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength

Eva-Maria Graefe, Chiara Liverani

A generalised mean-field approximation for non-Hermitian many-particle systems has been introduced recently for a Bose-Hubbard dimer with complex on-site energies. Here we apply this approximation to a Bose-Hubbard dimer with a complex particle interaction term, modelling losses due to interactions in a two mode Bose-Einstein condensate. We derive the mean-field equations of motion leading to nonlinear dissipative Bloch dynamics, related to a nontrivial complex generalisation of the nonlinear Schrodinger equation. It is shown that depending on the parameter values there can be up to six stationary states. Further, for small values of the interaction strength the dynamics shows limit cycles.
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

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