Tan's two-body contact across the superfluid transition of a planar Bose gas

TL;DR

This paper experimentally measures Tan's contact in a 2D Bose gas across the superfluid transition, linking it to thermodynamics and providing data in the critical region where theory is incomplete.

Contribution

First experimental realization of the thermodynamic definition of Tan's contact in a 2D Bose gas across the BKT transition, bridging theory and experiment.

Findings

Measurements agree with theoretical predictions in degenerate and normal regimes.

Provides data on Tan's contact in the critical region of the superfluid transition.

Highlights need for further theoretical work to explain observed behavior.

Abstract

Tan's contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e. the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of $^{87}$Rb atoms across the Berezinskii-Kosterlitz-Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.