Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

TL;DR

This paper models a minimal superfluid circuit using a triangular Bose-Hubbard trimer, analyzing its complex dynamics and stability across different parameters with a semiclassical approach.

Contribution

It introduces a semiclassical analysis of the triangular Bose-Hubbard trimer, revealing regimes of superfluid stability and chaos beyond the traditional superfluid-insulator transition.

Findings

Identified regimes of superfluid stability and chaos in the parameter space.

Mapped the Peierls-Nabarro energy landscape for the system.

Characterized many-body eigenstate stability and chaoticity.

Abstract

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase-space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the Peierls-Nabarro energy landscape, we deduce the various regimes in the $(\Omega,u)$ parameter-space, where $u$ is the interaction, and $\Omega$ is the superfluid rotation-velocity. We thus characterize the superfluid-stability and chaoticity of the many-body eigenstates throughout the Hilbert space.