Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions

TL;DR

This paper investigates Tan's contact in a one-dimensional Bose gas under harmonic confinement, deriving strong-coupling expansions and a conjectural approach to estimate contact at arbitrary interactions, relevant for ultracold atom experiments.

Contribution

It introduces a strong-coupling expansion for Tan's contact using Bethe-Ansatz and local-density approximation, and proposes a conjectural method for arbitrary interactions.

Findings

Derived strong-coupling expansion for Tan's contact.

Proposed a conjectural expression for arbitrary interaction strength.

Results align with experimental conditions for ultracold gases.

Abstract

We study Tan's contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases.