Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis

TL;DR

This paper investigates a two-site Bose-Hubbard model with nonlinear tunneling, analyzing classical and quantum phases, phase transitions, and the structure of Bethe ansatz solutions to understand the system's quantum properties.

Contribution

It provides a combined classical and quantum analysis of the extended Bose-Hubbard model with atom-pair tunneling, identifying phase transitions and linking Bethe ansatz roots to physical phenomena.

Findings

Identified three quantum phases: self-trapping, phase-locking, and Josephson states.

Mapped the parameter space of quantum phase transitions driven by atom-pair tunneling.

Linked Bethe ansatz root structures to quantum phase transitions.

Abstract

The extended Bose-Hubbard model for a double-well potential with atom-pair tunneling is studied. Starting with a classical analysis we determine the existence of three different quantum phases: self-trapping, phase-locking and Josephson states. From this analysis we built the parameter space of quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunneling. Considering only the repulsive case, we confirm the phase transition by the measure of the energy gap between the ground state and the first excited state. We study the structure of the solutions of the Bethe ansatz equations for a small number of particles. An inspection of the roots for the ground state suggests a relationship to the physical properties of the system. By studying the energy gap we find that the profile of the roots of the Bethe ansatz equations is related to a quantum phase transition.