Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer

TL;DR

This paper explores the relationship between many-particle quantum dynamics and mean-field approximations in a non-Hermitian Bose-Hubbard dimer, revealing how non-Hermiticity and nonlinearity affect system behavior and stability.

Contribution

It provides a detailed mean-field approximation for a non-Hermitian Bose-Hubbard dimer and analyzes the resulting dynamics, including a generalized canonical form and the effects of non-Hermiticity.

Findings

Non-Hermiticity promotes self-trapping transition.

Damping of self-trapping oscillations observed.

Rich many-particle dynamics including breakdown and revival.

Abstract

We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field approximation for this non-Hermitian many-particle system yielding an alternative complex nonlinear Schr\"odinger equation was introduced. Here we give details of this mean-field approximation and show that the resulting dynamics can be expressed in a generalized canonical form that includes a metric gradient flow. The interplay of nonlinearity and non-Hermiticity introduces a qualitatively new behavior to the mean-field dynamics: The presence of the non-Hermiticity promotes the self-trapping transition, while damping the self-trapping oscillations, and the nonlinearity introduces a strong sensitivity to the initial conditions in the decay of the normalization. Here we present a complete characterization of the mean-field dynamics and the fixed point structure. We also investigate the full many-particle dynamics, which shows a rich variety of breakdown and revival as well as tunneling phenomena on top of the mean-field structure.