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arXiv:cond-mat/0508042 · Physical Review A

Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures

V. Ahufinger, Laurent Sanchez-Palencia, Adrian Kantian, Anna Sanpera, Maciej Lewenstein

Published Dec 21, 2005• 68 citations
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Abstract

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.

DOI
10.1103/physreva.72.063616

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Abstract. We investigate theoretically the low-temperature physics of ultracold Fermi-Bose mixtures in optical lattices. We show that composite Fermions form under specific conditions in the srongly correlated regime. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled. We finally investigate the quantum phase diagram of the composites and show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes. PACS numbers: 03.75.Kk,03.75.Lm,05.30.Jp,64.60.CnStrongly correlated Fermi-Bose mixtures in disordered optical lattices 2 1. Introduction to disordered quantum systems 1.1. From condensed matter physics to ultracold atomic gases Quantum disordered systems is a very active research field in condensed matter physics (CM) initiated by the work by P.W. Anderson [1] who first pointed out that quenched disorder can dramatically change the properties of a quantum system compared to
A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.
This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as with Bose glass. It then turns to various experimental realizations of disorder in ultracold atomic gases. The chapter focuses on disordered Bose-Einstein condensates and the phenomenon of Anderson localization in speckle or quasi-periodic, quasi-random potential. It moves on to disordered ultracold fermionic systems, and disordered ultracold Bose–Fermi (B–F) and Bose–Bose (B–B) mixtures. Finally, the chapter examines spin glasses (providing a brief presentation of the mean field theory of Parisi, and the droplet model) and disorder induced order.
Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.