Exactly solvable case of a one-dimensional Bose-Fermi mixture

TL;DR

This paper provides an exact solution for a one-dimensional Bose-Fermi mixture with equal masses and repulsive interactions, analyzing its stability, density profiles, and correlation functions across different interaction regimes.

Contribution

It introduces an exact Bethe-ansatz solution for the ground state of a 1D Bose-Fermi mixture with equal masses and interactions, and explores its stability and properties.

Findings

The mixture is always stable against demixing.

Density profiles and collective modes are calculated using the exact solution.

Correlation functions are derived in the strongly interacting regime.

Abstract

We consider a one dimensional interacting bose-fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between bose-fermi and bose-bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime we use exact wavefunctions to calculate correlation functions for bosons and fermions under periodic boundary conditions.