Unitary $p$-wave Fermi gas in one dimension

TL;DR

This paper investigates the universal thermodynamic properties of a one-dimensional, two-component ultracold Fermi gas near a $p$-wave Feshbach resonance, revealing universal behavior at the unitarity limit and analyzing its equation of state and spectral functions.

Contribution

It introduces the concept of a one-dimensional unitary $p$-wave Fermi gas and derives its universal thermodynamics, contrasting it with higher-dimensional cases and exploring spectral properties.

Findings

Universal thermodynamics at the unitarity limit in 1D $p$-wave Fermi gases.

Derived the universal equation of state using many-body $T$-matrix and virial expansion.

Conjectured the invariance of the Bertsch parameter across dimensions for this system.

Abstract

We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the $p$-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, $p$-wave scattering length and effective range. At the unitarity limit where the $p$-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact $s$-wave interaction in three dimensions. It is in contrast to a Fermi gas with the $p$-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary $p$-wave Fermi gas within the many-body $T$-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary $p$-wave Fermi gas.