The three-site Bose-Hubbard model subject to atom losses: the boson-pair dissipation channel and failure of the mean-field approach

TL;DR

This study derives reduced master equations for a three-site Bose-Hubbard model with atom losses, revealing that boson-pair dissipation channels are missed by mean-field approaches, highlighting the need for beyond-mean-field analysis in dissipative many-site systems.

Contribution

The paper introduces a quantum derivation of dissipation channels in the three-site Bose-Hubbard model, showing the limitations of mean-field approximation in capturing boson-pair dissipation.

Findings

Boson-pair dissipation is not captured by mean-field models.

A matching condition determines the dominant dissipation channel.

Beyond-mean-field analysis is necessary for accurate dissipative dynamics.

Abstract

We employ the perturbation series expansion for derivation of the reduced master equations for the three-site Bose-Hubbard model subject to strong atom losses from the central site. The model describes a condensate trapped in a triple-well potential subject to externally controlled removal of atoms. We find that the $\pi$-phase state of the coherent superposition between the side wells decays via two dissipation channels, the single-boson channel (similar to the externally applied dissipation) and the boson-pair channel. The quantum derivation is compared to the classical adiabatic elimination within the mean-field approximation. We find that the boson-pair dissipation channel is not captured by the mean-field model, whereas the single-boson channel is described by it. Moreover, there is a matching condition between the zero-point energy bias of the side wells and the nonlinear interaction parameter which separates the regions where either the single-boson or the boson-pair dissipation channel dominate. Our results indicate that the $M$-site Bose-Hubbard models, for $M>2$, subject to atom losses may require an analysis which goes beyond the usual mean-field approximation for correct description of their dissipative features. This is an important result in view of the recent experimental works on the single site addressability of condensates trapped in optical lattices.