Density waves in quasi-one-dimensional atomic gas mixture of boson and two-component fermion

TL;DR

This paper investigates density-wave states in a quasi-one-dimensional boson-fermion mixture, revealing how interatomic interactions induce various density-wave patterns and coexistence with Bose-Einstein condensation.

Contribution

It introduces a self-consistent mean-field method to analyze density-wave states in boson-fermion mixtures with two-component fermions, highlighting the role of inter-fermion interactions.

Findings

Density-waves appear in the ground state due to Peierls instability.

In-phase and out-phase density-waves depend on inter-fermion interaction strength.

Bose-Einstein condensate coexists with in-phase density-waves, but not with out-phase.

Abstract

We study the density-wave states of quasi-one-dimensional atomic gas mixture of one- and two-component boson and fermion using the mean-field approximation. Owing to the Peierls instability in the quasi-one-dimensional fermion system, the ground state of the system shows the fermion density wave and the periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in these components, and the phase difference between them distinguishes two types of ground states, the in-phase and the out-phase density-waves. In this paper, a self-consistent method in the mean-field approximation is presented to treat the density-wave states in boson-fermion mixture with two-component fermions. From the analysis of the effective potential and the interaction energies calculated by this method, the density-waves are shown to appear in the ground state, which are in-phase or out-phase depending on the strength of the inter-fermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density-wave of fermions, but, in the case of the out-phase one, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants.