Density expectation value of two independent interacting Bose-Einstein condensates

TL;DR

This paper calculates the density expectation value of two initially independent Bose-Einstein condensates after overlapping, showing that exchange symmetry and interactions lead to observable interference patterns consistent with experiments.

Contribution

It introduces a model considering exchange symmetry and interactions to explain interference in independent condensates, aligning theory with experimental observations.

Findings

Nonzero interference term arises from exchange symmetry and interactions.

Calculated density matches experimental interference patterns.

Independence of condensates becomes coherence after overlapping.

Abstract

After removing the double-well potential trapping two initially independent Bose condensates, the density expectation value is calculated when both the exchange symmetry of identical bosons and interatomic interaction are considered. After the overlapping, it is shown that there is a nonzero interference term in the density expectation value. This nonzero interference term physically arises from the exchange symmetry of identical bosons and interatomic interaction which make two initially independent condensates become coherent after the overlapping. It is found that the calculated density expectation value with this model agrees with the interference pattern observed in the experiment by Andrews et al (Science 275, 637 (1997)).