Coupled-mode theory for Bose-Einstein condensates

TL;DR

This paper develops a coupled-mode theoretical framework for Bose-Einstein condensates in double-well potentials, capturing complex dynamics like Josephson oscillations and self-trapping, validated through numerical simulations.

Contribution

It introduces a novel coupled-mode approach to analyze BEC dynamics in double-well traps, extending nonlinear optics concepts to quantum gases.

Findings

Derived coupled-mode equations for BECs in double-well potentials.

Described nonlinear Josephson effects for various well separations.

Confirmed macroscopic self-trapping through numerical simulations.

Abstract

We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by numerical simulations.