Quantum Dynamics of Coupled Bosonic Wells within the Bose-Hubbard Picture

TL;DR

This paper explores the quantum dynamics of the two-site Bose-Hubbard model by connecting it to semiclassical equations, analyzing the energy spectrum, and interpreting classical symmetries using a variational and spin-based approach.

Contribution

It introduces a detailed quantum analysis of the two-site Bose-Hubbard model using a spin picture and dynamical algebra, linking quantum and classical descriptions.

Findings

Energy spectrum characterized through various approximations.

Classical symmetries interpreted quantum mechanically.

Quantum dynamics related to semiclassical nonlinear equations.

Abstract

We relate the quantum dynamics of the Bose-Hubbard model (BHM) to the semiclassical nonlinear equations that describe an array of interacting Bose condensates by implementing a standard variational procedure based on the coherent state method. We investigate the dynamics of the two-site BHM from the purely quantum viewpoint by recasting first the model within a spin picture and using then the related dynamical algebra. The latter allows us to study thoroughly the energy spectrum structure and to interpret quantally the classical symmetries of the two-site dynamics. The energy spectrum is also evaluated through various approximations relying on the coherent state approach.