Exact nonlinear Bloch-state solutions for Bose-Einstein condensates in a periodic array of quantum wells

TL;DR

This paper derives exact solutions for Bose-Einstein condensates in a periodic quantum well array, enabling detailed analysis of their physical properties and offering a more tractable model than sinusoidal or Kronig-Penney potentials.

Contribution

It provides the first set of exact closed-form Bloch-state solutions for BECs in a quantum well lattice, facilitating analytical study of their properties.

Findings

Analytical expressions for Bloch band structure.

Dependence of effective mass and sound speed on potential depth.

Quantum well array is more analytically tractable than sinusoidal potential.

Abstract

A set of exact closed-form Bloch-state solutions to the stationary Gross-Pitaevskii equation are obtained for a Bose-Einstein condensate in a one-dimensional periodic array of quantum wells, i.e. a square-well periodic potential. We use these exact solutions to comprehensively study the Bloch band, the compressibility, effective mass and the speed of sound as functions of both the potential depth and interatomic interaction. According to our study, a periodic array of quantum wells is more analytically tractable than the sinusoidal potential and allows an easier experimental realization than the Kr\"onig-Penney potential, therefore providing a useful theoretical model for understanding Bose-Einstein condensates in a periodic potential.