Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer

TL;DR

This paper develops a mean-field approximation for a non-Hermitian Bose-Hubbard dimer with decay, analyzing its nonlinear dynamics and fixed points, and comparing results with full many-particle evolution.

Contribution

It introduces a mean-field approach for a non-Hermitian many-particle system and analyzes the resulting nonlinear dynamics and fixed points.

Findings

Mean-field dynamics agree with full many-particle evolution.

Decay modifies the self-trapping transition.

Fixed point structures show characteristic changes due to non-Hermiticity.

Abstract

We investigate an $N$-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular the fixed point structures showing characteristic modifications of the self-trapping transition, are analyzed. The mean-field dynamics is found to be in reasonable agreement with the full many-particle evolution.