Numerical Simulation on Tunnel Splitting of Bose-Einstein Condensate in Multi-Well Potentials

TL;DR

This paper numerically investigates the tunnel splitting of Bose-Einstein condensates in multi-well potentials, comparing results with analytical methods to validate the accuracy of the simulations.

Contribution

It provides a numerical approach to calculate tunnel splitting in BECs and validates it against analytical instanton results.

Findings

Numerical results agree well with analytical predictions.

Ground state tunnel splitting is accurately evaluated.

Method applicable to symmetric double-well and periodic potentials.

Abstract

The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel splitting is evaluated in terms of the even and odd wave functions corresponding to the global ground and excited states respectively. We show that the numerical result is in good agreement with the analytic level splitting obtained by means of the periodic instanton method.