Localization of a Bose-Fermi mixture in a bichromatic optical lattice

TL;DR

This paper investigates the localization phenomena in a Bose-Fermi mixture within a bichromatic optical lattice, revealing symbiotic and Anderson localization states, their phase diagram, and stability under perturbations.

Contribution

It demonstrates the existence and stability of symbiotic and Anderson localized states in a Bose-Fermi mixture using coupled mean-field equations.

Findings

Existence of symbiotic localized states confirmed.

Observation of Anderson localization of the Bose component.

Phase diagram showing localization regions.

Abstract

We study the localization of a cigar-shaped super-fluid Bose-Fermi mixture in a quasi-periodic bichromatic optical lattice (OL) for inter-species attraction and intra-species repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.