Quantum dynamics of a four-well Bose-Hubbard model with two different tunneling rates

TL;DR

This paper investigates the quantum dynamics of a four-well Bose-Hubbard model with two different tunneling rates, revealing complex behaviors and thermalization properties beyond mean-field predictions, with potential for experimental realization.

Contribution

It provides a detailed quantum analysis of a four-well Bose-Hubbard model with unequal tunneling rates, highlighting behaviors not captured by mean-field models and demonstrating thermalization.

Findings

System exhibits dynamics different from mean-field predictions.

System equilibrates to a maximum entropy state.

Model is feasible for experimental implementation.

Abstract

We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intra-system coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [\pra {\bf 81}, 043616 (2010) ]. We examine the quantum dynamics of this model for a range of different initial conditions, in terms of both the number distribution among the wells and the quantum statistics. We find that the time evolution is different to that predicted by a mean-field model and that this system exhibits a wide range of interesting behaviours. We find that the system equilibriates to a maximum entropy state and is thus a useful model for quantum thermalisation. As our model may be realised to a good approximation in the laboratory, it becomes a candidate for experimental investigation.