# A Wigner Function Approach to Coherence in a Talbot-Lau Interferometer

## TL;DR

This paper models a trapped interferometer using a Wigner function approach, revealing how residual harmonic traps affect coherence, visibility, and echo timing, and suggests optimization strategies to mitigate these effects.

## Contribution

It introduces a Wigner function-based model for a Talbot-Lau interferometer with residual trapping, highlighting the impact of residual potential on coherence and visibility.

## Key findings

- Residual potential limits interferometer visibility
- Echo time shifts due to residual trap
- Optimizing initial trap frequency improves coherence

## Abstract

Using a thermal gas, we model the signal of a trapped interferometer. This interferometer uses two short laser pulses, separated by time T, which act as a phase grating for the matter waves. Near time 2T, there is an echo in the cloud's density due to the Talbot-Lau effect. Our model uses the Wigner function approach and includes a weak residual harmonic trap. The analysis shows that the residual potential limits the interferometer's visibility, shifts the echo time of the interferometer, and alters its time dependence. Loss of visibility can be mitigated by optimizing the initial trap frequency just before the interferometer cycle begins.