Josephson spectroscopy of a dilute Bose-Einstein condensate in a double-well potential

TL;DR

This paper investigates the quantum tunneling and resonance phenomena of a Bose-Einstein condensate in a double-well potential using the Gross-Pitaevskii equation, highlighting the importance of higher energy states.

Contribution

It provides a detailed analysis of tunneling resonances and critical velocities, validating a two-state model and emphasizing the role of higher-lying states in realistic scenarios.

Findings

Identification of tunneling resonances linked to energy level crossings

Determination of critical velocities for resonance conditions

Validation of the two-state model with considerations of higher states

Abstract

The dynamics of a Bose-Einstein condensate in a double-well potential are analysed in terms of transitions between energy eigenstates. By solving the time-dependent and time-independent Gross-Pitaevskii equation in one dimension, we identify tunnelling resonances associated with level crossings, and determine the critical velocity that characterises the resonance. We test the validity of a non-linear two-state model, and show that for the experimentally interesting case, where the critical velocity is large, the influence of higher-lying states is important.