Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry

TL;DR

This paper provides an analytical correction formula for relative phase measurements in 1D Bose gases interferometry, accounting for longitudinal expansion effects, thereby improving the accuracy of quantum simulations.

Contribution

It introduces a new analytical correction for phase readout that considers longitudinal dynamics, enhancing the reliability of interferometric measurements in cold-atom experiments.

Findings

Analytical correction formula for phase readout

Assessment of error propagation in physical quantity estimation

Guidance for improving phase extraction methods

Abstract

Spatially resolved relative phase measurement of two adjacent 1D Bose gases is enabled by matter-wave interference upon free expansion. However, longitudinal dynamics is typically ignored in the analysis of experimental data. We provide an analytical formula showing a correction to the readout of the relative phase due to longitudinal expansion and mixing with the common phase. We numerically assess the error propagation to the estimation of the gases' physical quantities such as correlation functions and temperature. Our work characterizes the reliability and robustness of interferometric measurements, directing us to the improvement of existing phase extraction methods necessary to observe new physical phenomena in cold-atomic quantum simulators.