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arXiv:cond-mat/0512010 · Physical Review A

Sound velocity and dimensional crossover in a superfluid Fermi gas in an optical lattice

T. K. Koponen, J.-P. Martikainen, J. J. Kinnunen, Päivi Törmä

Published Mar 24, 2006• 27 citations
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Abstract

We study the sound velocity in cubic and noncubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothed by interactions and eventually vanishes when interactions are strong enough. For noncubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the one- and two-dimensional limits.

DOI
10.1103/physreva.73.033620

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We study the sound velocity in cubic and noncubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothed by interactions and eventually vanishes when interactions are strong enough. For noncubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the one- and two-dimensional limits.
A system of equal mixture of 6Li^6Li6Li atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.
Abstract A system of equal mixture of 6Li atomic Fermi gas of two hyperfine states loaded into a cubic three‐dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon‐like mode and the speed of sound in the long‐wavelength limit are obtained by solving the Bethe‐Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.
The sound waves, the stability of Bloch waves, the Bloch oscillation, and the self-trapping phenomenon in interacting two-component Fermi gases throughout the BEC-BCS crossover in one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) optical lattices are discussed in detail. Within the hydrodynamical theory and by using the perturbative and tight-binding approximation, sound speed in both weak and tight 1D, 2D, 3D optical lattices, and the criteria for occurrences of instability of Bloch waves and self-trapping of Fermi gases along the whole BEC-BCS crossover in tight 1D, 2D, 3D optical lattices are obtained analytically. The results show that the sound speed, the criteria for occurrences of instability of Bloch waves and self-trapping, and the destruction of Bloch oscillation are modified dramatically by the lattice parameters (lattice dimension and lattice strength), the atom density or atom number, and the atom interaction.
We point out that the velocity of propagation of sound wavepackets in a Bose-Einstein condensate filling a three-dimensional cubic optical lattice undergoes a maximum with increasing lattice depth. For a realistic choice of parameters, the maximum sound velocity in a lattice condensate can exceed the sound velocity in a homogeneous condensate with the same average density by 30%. The maximum falls into the superfluid regime, and should be observable under currently achievable laboratory conditions.
We study the Bogoliubov spectrum of an elongated Fermi superfluid confined in an one-dimensional superfluid along the Bose-Einstein-condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover. We derive analytic expressions for the sound velocity, effective mass and the Bogoliubov excitation spectrum of the axial quasiparticles long the crossover based on the hydrodynamic theory. Our investigation reveal interesting signatures of BEC-BCS crossover in an optical lattice which deserve experimental investigation.
We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov--de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.