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arXiv:cond-mat/0511158 · Physical Review A

Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps

Gao Xianlong, Marco Polini, Reza Asgari, M. P. Tosi

Published Mar 15, 2006• 42 citations
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Abstract

Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas via a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to 100 atoms.

DOI
10.1103/physreva.73.033609

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Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas via a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to 100 atoms.
We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with a Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikov-type phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.
We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k F → 4k F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.
We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly from the weakly interacting regime to the strongly interacting regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable interspecies repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various interspecies interactions. It is shown that with the increase in interspecies interaction, the system exhibits composite-fermionization crossover.
Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe ansatz based local-density approximation for the correlation energy that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.
The low-energy excitations of a two-component repulsive Fermi gas confined to one dimension are linear dispersing spin- and charge-density waves whose respective propagation velocities depend on the strength and sign of their interaction. Quasi-1D fermions with attractive interaction realize the Luther-Emery liquid, which exhibits a rich array of phenomena, many of which are qualitatively different from those exhibited by their repulsive counterpart. We use a Feshbach resonance to access attractive interactions with 6^66Li atoms. We measured the spin and charge dynamic structure factors using Bragg spectroscopy and find that, contrary to repulsive interactions, the spin wave propagates faster than the charge density wave, thus producing an inversion of the classic spin-charge separation. We also find that a small spin polarization strongly suppresses the spin gap in the measured Bragg spectra. Evidence for pairing are a reduction in spin correlations with increasing attraction and RF spectra consistent with an atom/molecule mixture.