Quantum Oscillations between weakly coupled Bose-Einstein Condensates: Evolution in a Non-degenerate Double Well

TL;DR

This paper explores quantum oscillations between two weakly coupled Bose-Einstein condensates with energy differences, using a nonlinear Gross-Pitaevskii framework, revealing new observable effects due to energy and phase differences.

Contribution

It introduces a new set of Jacobian elliptic function solutions to describe the oscillations in a boson Josephson junction with energy imbalance.

Findings

Derived explicit oscillation period formulas.

Predicted novel effects from energy and phase interplay.

Provided solutions applicable to asymmetric double wells.

Abstract

We discuss coherent atomic oscillations between two weakly coupled Bose-Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross-Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.