Interference of an Array of Independent Bose-Einstein Condensates

TL;DR

This paper provides a detailed theoretical analysis of interference patterns in an array of independent Bose-Einstein condensates, explaining how fringes appear despite finite atom numbers and undefined phases, with analytical formulas for their statistical properties.

Contribution

It offers the first analytical derivation of the interference fringe statistics for independent condensates, clarifying the underlying processes and their relation to symmetry-breaking models.

Findings

Interference fringes are observed in each snapshot despite finite atom numbers.

Analytical formulas for average fringe amplitudes and fluctuations are derived.

The relationship with symmetry-breaking descriptions is clarified.

Abstract

Interference of an array of independent Bose-Einstein condensates, whose experiment has been performed recently, is theoretically studied in detail. Even if the number of the atoms in each gas is kept finite and the phases of the gases are not well defined, interference fringes are observed on each snapshot. The statistics of the snapshot interference patterns, i.e., the average fringe amplitudes and their fluctuations (covariance), are computed analytically, and concise formulas for their asymptotic values for long time of flight are derived. Processes contributing to these quantities are clarified and the relationship with the description on the basis of the symmetry-breaking scenario is revealed.