The driven-dissipative Bose-Hubbard dimer: phase diagram and chaos

TL;DR

This paper analyzes the phase diagram of a driven-dissipative Bose-Hubbard dimer, revealing conditions for symmetry breaking and demonstrating the emergence of deterministic chaos through bifurcation mechanisms.

Contribution

It provides a detailed phase diagram and bifurcation analysis of the driven-dissipative Bose-Hubbard dimer, highlighting the conditions for symmetry breaking and chaos.

Findings

Symmetry breaking requires negative tunneling parameter J<0.

The model exhibits deterministic dissipative chaos.

Chaos arises from a Shilnikov mechanism in bifurcation scenarios.

Abstract

We present the phase diagram of the mean-field driven-dissipative Bose-Hubbard dimer model. For a dimer with repulsive on-site interactions ($U>0$) and coherent driving we prove that $\mathbb{Z}_2$-symmetry breaking, via pitchfork bifurcations with sizable extensions of the asymmetric solutions, require a negative tunneling parameter ($J<0$). In addition, we show that the model exhibits deterministic dissipative chaos. The chaotic attractor emerges from a Shilnikov mechanism of a periodic orbit born in a Hopf bifurcation and, depending on its symmetry properties, it is either localized or not.