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arXiv:1111.2706 · Physical Review A

Mixtures of ultracold atoms in one-dimensional disordered potentials

François Crépin, Gergely Zaránd, Pascal Simon

Published Feb 21, 2012• 6 citations
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Abstract

We study interacting one-dimensional two-component mixtures of cold atoms in a random potential, and extend the results reported earlier [Phys. Rev. Lett. 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 long-wavelength asymptotic behavior of the momentum distribution as well as that of the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished.

DOI
10.1103/physreva.85.023625

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We analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.
The interplay between disorder and interactions in quantum systems is a long-standing topic of condensed matter physics. We study the fate of a two-component one-dimensional mixture of cold atoms in the presence of a weak random potential. We show how disorder-induced localization of one species can influence the localization of the other species through interactions and identity three distinct phases: a delocalized phase described by a two-component Luttinger liquid, a hybrid phase where only one species is localized and a fully localized phase where both components of the mixture are localized. The latter phase is characterized by two nested localization length scales. We present the possible signatures of these phases in various observables such as the structure factors (related to Bragg scattering experiments) and the momentum distributions observed in time-of-flight experiments.
We have considered one-dimensional Bose-Fermi mixture with equal densities and unequal masses using numerical density matrix renormalization group. For the mass ratio of K-Rb mixture and attraction between bosons and fermions, we determined the phase diagram. For weak boson-boson interactions, there is a direct transition between two-component Luttinger liquid and collapsed phases as the boson-fermion attraction is increased. For strong enough boson-boson interactions, we find an intermediate ``paired'' phase, which is a single-component Luttinger liquid of composite particles. We investigated correlation functions of such a ``paired'' phase, studied the stability of ``paired'' phase to density imbalance, and discussed various experimental techniques which can be used to detect it.
We present a review of properties of ultracold atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. In the strong interacting limit and at very low temperatures, fermions form, together with bosons or bosonic holes, composite fermions. Composite fermions behave as a spinless interacting Fermi gas, and in the presence of local disorder they interact via random couplings and feel effective random local potential. This opens a wide variety of possibilities of realizing various kinds of ultracold quantum disordered systems. In this paper we review these possibilities, discuss the accessible quantum disordered phases, and methods for their detection. The discussed quantum phases include Fermi glasses, quantum spin glasses, ``dirty'' superfluids, disordered metallic phases, and phases involving quantum percolation.
We study the quantum phase diagrams of Bose-Fermi mixtures of ultracold atoms confined to one dimension in an optical lattice. For systems with incommensurate densities, various quantum phases, e.g., spin- or charge-density waves, pairing, phase separation, and the Wigner crystal, are found to be dominant in different parameter regimes within a bosonization approach. The structure of the phase diagram leads us to propose that the system is best understood as a Luttinger liquid of polarons (i.e., atoms of one species surrounded by screening clouds of the other species). Special fillings, half filling for fermions, and unit filling for bosons, and the resulting gapped phases are also discussed, as well as the properties of the polarons and the experimental realization of these phases.
One-dimensional Bose-Fermi mixture systems in a random potential are numerically investigated with focus on their superfluidity and localization properties. It is known that one-dimensional bosons and fermions behave differently in a weak random potential: Interacting bosons in a weak random potential exhibit superfluidity if the interactions are repulsive and not too strong, while interacting fermions with repulsive forces are localized in the presence of randomness. So the question is what happens if weakly interacting bosons and fermions are mixed in a random potential, which might be actually realized by the technique of trapping atoms on a random optical lattice. To answer this question we performed quantum Monte Carlo simulations of bosons and fermions on a one-dimensional lattice with random site energies. The result showed that when the boson-fermion interactions were attractive, both bosons and fermions tended to be localized. However when the boson- fermion interactions were repulsive and relatively weak, the superfluidity of bosons was enhanced and the fermions were delocalized.