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

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

2005-11-07

arxiv.org/abs/cond-mat/0511158v1

Phys. Rev. A 73, 033609 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

13 pages, 9 figures, submitted

Scientific paper

10.1103/PhysRevA.73.033609

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 {\it 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 a hundred atoms.

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