Relevance of Bose-Einstein Condensation to the Interference of Two Independent Bose Gases

TL;DR

This paper investigates how Bose-Einstein condensation influences interference patterns in two independent Bose gases, showing that condensation enhances the stability and visibility of interference fringes, with fluctuations diminishing below the critical temperature.

Contribution

It provides a quantitative relation between the fringe contrast and the purity of the gases, linking condensation to observable interference phenomena in a canonical ensemble framework.

Findings

Average fringe contrast equals the purity of each gas.

Fluctuations in interference vanish below the critical temperature.

Interference patterns are reliably observed in the condensed phase.

Abstract

Interference of two independently prepared ideal Bose gases is discussed, on the basis of the idea of measurement-induced interference: even if the number of each gas is individually fixed finite and the symmetry of the system is not broken, an interference pattern is observed on each single snapshot. The key role is played by the Hanbury Brown and Twiss effect, which leads to an oscillating pattern of the cloud of identical atoms. Then, how essential is the Bose-Einstein condensation to the interference? We describe the ideal Bose gases trapped respectively in two spatially separated 3D harmonic traps at a finite temperature as canonical ensembles with fixed numbers of atoms, and compute the full statistics of the snapshot profiles of the expanding and overlapping gases released from the traps. We obtain a simple formula, which shows that the average fringe spectrum (average fringe contrast) is given by the purity of each gas. The purity is known to be a good measure of condensation, and this result clarifies the relevance of the condensation to the interference. The fluctuation of the interference spectrum is also studied, and it is shown that the fluctuation is vanishingly small below the critical temperature, while it is nonvanishing above. This implies that interference pattern is certainly observed on every snapshot below the critical temperature. The fact that the number of atoms is fixed in the canonical ensemble is crucial to this vanishing fluctuation.