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Laser Physics

Disorder physics in mixtures of fermionic atoms

K. Ziegler

Published Apr 1, 2006• 6 citations
Publisher

Abstract

A mixture of light and heavy fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. There is a complex interplay between light and heavy atoms which results in an Ising-like distribution of heavy atoms with a first-order transition from homogeneous to staggered order. A second-order transition is possible between an ordered and a disordered phase of heavy atoms. Depending on the phase of heavy atoms, light atoms are scattered around and can propagate, diffuse, and localize. Due to correlations in the disordered phase of heavy atoms, there can be a gap in the spectrum of light atoms, leading to a Mottlike incompressible state.

DOI
10.1134/s1054660x06040268

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A mixture of light and heavy fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. There is a complex interplay between light and heavy atoms which results in an Ising-like distribution of heavy atoms with a first-order transition from homogeneous to staggered order. A second-order transition is possible between an ordered and a disordered phase of heavy atoms. Depending on the phase of heavy atoms, light atoms are scattered around and can propagate, diffuse, and localize. Due to correlations in the disordered phase of heavy atoms, there can be a gap in the spectrum of light atoms, leading to a Mottlike incompressible state.
A mixture of spin-polarized light- and heavy-Fermionic atoms on a finite-size two-dimensional optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case where the heavy atoms are immobile in comparison to the light atoms, this system can be seen as a correlated binary alloy related to the Falicov-Kimball model. The heavy atoms represent a scattering environment for the light atoms. The distributions of the binary alloy are discussed in terms of strong- and weak-coupling expansions. We further present numerical results for the intermediate interaction regime and for the density of states of the light particles. The numerical approach is based on a combination of a Monte Carlo simulation and an exact diagonalization method. We find that the scattering by the correlated heavy atoms can open a gap in the spectrum of the light atoms, either for strong interaction or small temperatures.
A mixture of two fermionic species with different masses is studied in an optical lattice. The heavy fermions are subject only to thermal fluctuations, the light fermions also to quantum fluctuations. We derive the Ising-like distribution for the heavy atoms and study the localization properties of the light fermions numerically by a transfer-matrix method. In a two-dimensional system one-parameter scaling of the localization length is found with a transition from delocalized states at low temperatures to localized states at high temperature. The critical exponent of the localization length is ν≈0.88.
A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between the two atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs, and an exchange of fermionic spins. Low-energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.
Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.
We discuss mixtures of bosons and spin-polarized fermions in optical lattices in the limits of heavy and light fermions. The first case is mapped to a Bose-Hubbard system with binary disorder or a super-lattice potential. Boundaries between Mott-insulating and compressible phases are determined analytically within an extended strong-coupling expansion. DMRG calculations reveal furthermore a novel phase with Bose-glass character. In the opposite limit of ultra-light fermions an effective boson Hamiltonian is derived with an oscillatory long-range interactions leading to additional phases such as compressible density-waves. We show that CDW and Luttinger-liquid phase are separated by a Bose-glass phase.