Yang-Yang thermodynamics of Bose-Fermi Mixture

TL;DR

This paper provides a theoretical analysis of a one-dimensional Bose-Fermi mixture at finite temperature using thermodynamic Bethe ansatz, offering exact solutions for density distributions that can aid experimental data interpretation.

Contribution

It combines Yang-Yang thermodynamics with local-density approximation to accurately calculate density profiles in a 1D Bose-Fermi mixture, surpassing mean-field methods.

Findings

Exact density distributions for bosons and fermions are obtained.

The approach can serve as a benchmark for experimental data fitting.

The method accounts for discrete and continuous excited states.

Abstract

We investigate theoretically the behavior of a one-dimensional interacting Bose-Fermi mixture with equal masses and equal repulsive interactions between atoms at finite temperature in the scheme of thermodynamic Bethe ansatz. Combining the Yang-Yang thermodynamic formalism with local-density approximation in a harmonic trap, we calculate the density distribution of bosons and fermions numerically by treating the radially and axially excited states as discrete and continuous ones, respectively. Our result from exactly solvable solutions may be used as a touchstone for one-dimensional interacting Bose-Fermi mixture for experimental data fitting where mean-field theoretical approaches fail.