Interference between a large number of independent Bose-Einstein condensates

TL;DR

This paper theoretically analyzes the interference patterns formed by many independent Bose-Einstein condensates, revealing that correlations diminish with increasing number and average visibility decreases as the inverse square root of the number of condensates.

Contribution

It demonstrates that density correlations become negligible for large numbers of condensates and models the interference pattern behavior using a random-walk analogy.

Findings

Correlations vanish as N increases

Average visibility scales as N^{-1/2}

Interference patterns become less pronounced with more condensates

Abstract

We study theoretically the interference patterns produced by the overlap of an array of Bose-Einstein condensates that have no phase coherence among them. We show that density-density correlations at different quasimomenta, which play an important role in two-condensate interference, become negligible for large $N$, where $N$ is the number of overlapping condensates. In order to understand the physics of this phenomenon, it is sufficient to consider the periodicity of the lattice and the statistical probability distribution of a random-walk problem. The average visibility of such interference patterns decreases as $N^{-1/2}$ for large $N$.