# Matter wave interference of dilute Bose gases in the critical regime

## TL;DR

This paper presents a theoretical study of matter wave interference in ultra-cold Bose gases near the critical point, linking interference visibility to correlation length and enabling experimental insights into phase transition behavior.

## Contribution

It introduces a simple relation between interference visibility and correlation length, providing a new method to analyze critical phenomena in ultra-cold Bose gases.

## Key findings

- Interference visibility correlates with the correlation length.
- The theory explains experimental observations of critical behavior.
- Method enables studying various ultra-cold gases through interference patterns.

## Abstract

Ultra-cold atomic gases provide new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science {\bf 315}, 1556 (2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.