Direct measurement of Tan's contact in a one-dimensional Lieb-Liniger gas

TL;DR

This study reports the first direct measurement of Tan's contact in a one-dimensional Lieb-Liniger Bose gas using a novel expansion scheme that isolates interaction effects, confirming theoretical predictions and enabling detailed characterization of strongly correlated quantum gases.

Contribution

It introduces a two-stage expansion method for direct measurement of Tan's contact in a 1D Bose gas, overcoming previous experimental challenges.

Findings

Excellent agreement with quantum Monte Carlo predictions.

Results follow universal scaling laws for the Lieb-Liniger model.

Method enables characterization across various interaction regimes.

Abstract

The Tan contact has emerged as a pivotal quantity in characterizing many-body quantum systems, bridging microscopic short-range correlations to thermodynamic behavior. It is defined as the weight of universal $1/k^4$ fall off in momentum distribution tails, which can be measured directly in ultracold gases. So far, however, its direct measurement has been hindered in Bose gases due to interactions strongly affecting the expansion dynamics. Here, we present the first direct measurement of the Tan contact in a strongly-correlated Lieb-Liniger gas. Leveraging the one-dimensional geometry of our system, we implement a two-stage expansion scheme, yielding interaction-immune time-of-flight imaging. Our results show excellent agreement with theoretical predictions from quantum Monte Carlo calculations, which also provides independent thermometry of the experiment. By varying atom number, temperature, and interaction strength, we obtain results consistent with the universal scaling law predicted for the trapped Lieb-Liniger model. Our work paves the way for further characterization of the Lieb-Liniger gas across broad interaction regimes and holds promise for extension to other correlated quantum gases in confined geometries.