Density profile of interacting Fermions in a one-dimensional optical trap

TL;DR

This paper investigates the density distribution of interacting fermions in a one-dimensional optical trap, revealing universal oscillation behaviors and a crossover to a spin-incoherent regime, supported by analytical and Bethe ansatz methods.

Contribution

It introduces an analytical formula based on bosonization for density oscillations across all interaction strengths and analyzes the universal scaling of the fermion cloud shape.

Findings

Universal density oscillations with scaling behavior

Wavelength change indicates crossover to spin-incoherent regime

Universal scaling form describes the fermion cloud shape

Abstract

The density distribution of the one-dimensional Hubbard model in a harmonic trapping potential is investigated in order to study the effect of the confining trap. Strong superimposed oscillations are always present on top of a uniform density cloud, which show universal scaling behavior as a function of increasing interactions. An analytical formula is proposed on the basis of bosonization, which describes the density oscillations for all interaction strengths. The wavelength of the dominant oscillation changes with interaction, which indicates the crossover to a spin-incoherent regime. Using the Bethe ansatz the shape of the uniform fermion cloud is analyzed in detail, which can be described by a universal scaling form.