Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions

TL;DR

This paper provides an exact solution for 1D spin-polarized fermions with resonant p-wave interactions, revealing how effective range effects and shape resonances influence the system's properties and excitation spectrum.

Contribution

It introduces an exact Bethe Ansatz solution that incorporates effective range effects, highlighting novel spectral features and experimental signatures.

Findings

Effective range significantly alters system properties.

Unusual excitation spectrum with inverted branches and roton-like minima.

Breathing mode frequency signals effective range effects.

Abstract

Using the asymptotic Bethe Ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and hole-like branches at small momenta, and roton-like minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.