Universal One-dimensional Atomic Gases Near Odd-wave Resonance

TL;DR

This paper investigates the universal properties of one-dimensional spin-polarized fermions near odd-wave resonance, deriving exact solutions and universal relations based on renormalized contact interactions.

Contribution

It introduces a renormalization approach for odd-wave interactions in 1D and derives universal relations for fermions near odd-wave resonance.

Findings

High-momentum distribution follows a $C/k^2$ behavior.

Universal relations for odd-wave contact are established.

The work reveals a new universal 1D fermionic system with large odd-wave scattering length.

Abstract

We show the renormalization of contact interaction for odd-wave scattering in one-dimension(1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap, and further explore the universal properties of spin-polarized fermions near odd-wave resonance using the operator product expansion method. It is found that the high-momentum distribution behaves as $C/k^2$, with $C$ the odd-wave contact. Various universal relations are derived. Our work suggests a new universal system emergent in 1D with large odd-wave scattering length.