Mixtures of ultra-cold atoms in 1D disordered potentials

TL;DR

This paper investigates the phase diagram of disordered 1D Bose-Fermi mixtures, identifying three distinct phases with different localization and superfluid properties, using advanced theoretical methods and discussing experimental signatures.

Contribution

The study extends previous work by constructing a detailed phase diagram of disordered 1D Bose-Fermi mixtures and analyzing the nature of each phase with novel theoretical approaches.

Findings

Identified three phases: delocalized Luttinger liquid, fully localized, and mixed localized-delocalized phase.

Found that bosonic and fermionic localization lengths can differ significantly in the localized phase.

Provided experimentally accessible signatures to distinguish the phases via momentum distribution and structure factor.

Abstract

We study interacting 1D two-component mixtures of cold atoms in a random potential, and extend the results reported earlier [{\it Phys. Rev. Lett.} {\bf 105}, 115301 (2010)]. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions (ii) a fully localized phase with both components pinned by disorder, and (iii) an intermediate phase where fermions are localized but bosons are superfluid. Within the variational approach, each phase corresponds to a different level of replica symmetry breaking. In the fully localized phase we find that the bosonic and fermionic localization lengths can largely differ. We also compute the momentum distribution as well as the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished.