$s$-wave Contacts of Quantum Gases in Quasi-one and Quasi-two Dimensions

TL;DR

This paper establishes an exact relation between three-dimensional and low-dimensional contacts in quantum gases confined in highly anisotropic traps, enabling the use of universal thermodynamic relations across different length scales.

Contribution

It introduces a precise relation linking 3D and low-dimensional contacts, facilitating the description of quasi-one- or two-dimensional quantum gases using strict 1D or 2D thermodynamic relations.

Findings

Derived an exact relation between 3D and low-dimensional contacts.

Connected physical quantities across different length scales.

Enabled characterization of quasi-1D and quasi-2D traps using universal thermodynamics.

Abstract

In quasi-one- or quasi-two-dimensional traps with strong transverse confinements, quantum gases behave like strictly one- or two-dimensional systems at large length scales. However, at short distance, the two-body scattering intrinsically has three-dimensional characteristics such that an exact description of any universal thermodynamic relation requires three-dimensional contacts, no matter how strong the confinement is. A fundamental question arises as to whether one- or two-dimensional contacts, which were originally defined for strictly one or two dimensions, are capable of describing quantum gases in quasi-one- or quasi-two-dimensional traps. Here, we point out an exact relation between the three- and low-dimensional contacts in these highly anisotropic traps. Such relation allows us to directly connect physical quantities at different length scales, and to characterise the quasi-one- or quasi-two-dimensional traps using universal thermodynamic relations that were derived for strict one or two dimensions.