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Optics Express

Quantum phases of Bose-Fermi mixtures in optical lattices

H. Fehrmann, M. Baranov, Maciej Lewenstein, Luis Santos

Published Jan 1, 2004• 16 citations
Publisher

Abstract

We analyze the ground-state phase diagram of an ultracold Bose-Fermi mixture placed in an optical lattice. The quantum phases involve pairing of fermions and one or several bosons. Depending on the physical parameters these composites can form a Fermi liquid, a density wave, a superfluid or a domain insulator. We determine by means of a mean-field formalism the phase boundaries for finite tunneling, and analyze the experimental feasibility of these sort of phases.

DOI
10.1364/opex.12.000055

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We analyze the ground-state phase diagram of an ultracold Bose-Fermi mixture placed in an optical lattice. The quantum phases involve pairing of fermions and one or several bosons. Depending on the physical parameters these composites can form a Fermi liquid, a density wave, a superfluid or a domain insulator. We determine by means of a mean-field formalism the phase boundaries for finite tunneling, and analyze the experimental feasibility of these sort of phases.
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.
We study an atomic Bose-Fermi mixture with unpolarized fermions in an optical lattice. We obtain the Mott ground states of such a system in the limit of the deep optical lattice and discuss the effect of quantum fluctuations on these states. We also study the superfluid-insulator transitions of bosons and metal-insulator transition of fermions in such a mixture within a slave-rotor mean-field approximation, and obtain the corresponding phase diagram. We discuss experimental implications of our results.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
The ground-state phase diagram of Fermi-Fermi mixtures in optical lattices is analyzed as a function of interaction strength, population imbalance, filling fraction, and tunneling parameters. It is shown that population imbalanced Fermi-Fermi mixtures reduce to strongly interacting Bose-Fermi mixtures in the molecular limit, in sharp contrast to homogeneous or harmonically trapped systems, where the resulting Bose-Fermi mixture is weakly interacting. Furthermore, insulating phases are found in optical lattices of Fermi-Fermi mixtures in addition to the standard phase-separated or coexisting superfluid--excess-fermion phases found in homogeneous systems. The insulating states can be a molecular Bose-Mott insulator (BMI), a Fermi-Pauli insulator (FPI), a phase-separated BMI-FPI mixture, or a Bose-Fermi checkerboard.
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.