P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps

TL;DR

This paper explores how p-wave contacts in dilute quantum gases confined in quasi-one-dimensional and quasi-two-dimensional traps are interconnected through a universal relation, revealing the interplay between dimensional crossover and universal contact relations.

Contribution

It derives a universal relation connecting p-wave contacts across different length scales in confined quantum gases, highlighting the role of geometry in universal relations.

Findings

Universal relation between p-wave contacts in different dimensions

Dependence of the relation on transverse confinement geometry

Illustration of dimensional crossover effects on contacts

Abstract

The length scale separation in dilute quantum gases in quasi-one-dimensional or quasi-two-dimensional traps has spatially divided the system into two distinct regimes. Whereas universal relations defined in strict one or two dimensions apply in a scale that is much larger than the characteristic length of the transverse confinements, physical observables in the short distances are inevitably governed by three-dimensional contacts. Here, we show that p-wave contacts defined in different length scales are intrinsically connected by a universal relation, which depends on a simple geometric factor of the transverse confinements. While this universal relation is derived for one of the p-wave contacts, it establishes a concrete example of how dimensional crossover interplays with contacts and universal relations for arbitrary partial wave scatterings.