Time-Dependent Variational Analysis of Josephson Oscillations in a Two-component Bose-Einstein Condensate

TL;DR

This paper investigates how Gaussian wave-packet dynamics influence Josephson oscillations in two coupled Bose-Einstein condensates using a time-dependent variational approach, highlighting differences when traps are displaced.

Contribution

It introduces a time-dependent variational method with Gaussian states to analyze Josephson oscillations, considering trap displacements and shape oscillations, which is a novel approach.

Findings

Models agree when traps are not displaced.

Displaced traps cause significant differences between models.

Full model captures trap displacement effects more accurately.

Abstract

The dynamics of Josephson-like oscillations between two coupled Bose-Einstein condensates is studied using the time-dependent variational method. We suppose that the quantum state of the condensates is a gaussian wave-packet which can translate and perform breathing shape oscillations. Under this hypotheses we study the influence of these degrees of freedom on the tunneling dynamics by comparing the full-model with one where these degrees of freedom are ``frozen'' at its equilibrium values. The result of our calculation shows that when the traps are not displaced the two models agree, whereas when they are, the models differ considerably, the former being now closer to its linear approximation.