10,707 research outputs found
Time-Dependent Density-Functional Theory for Superfluids
A density-functional theory is established for inhomogeneous superfluids at
finite temperature, subject to time-dependent external fields in isothermal
conditions. After outlining parallelisms between a neutral superfluid and a
charged superconductor, Hohenberg-Kohn-Sham-type theorems are proved for
gauge-invariant densities and a set of Bogolubov-Popov equations including
exchange and correlation is set up. Earlier results applying in the linear
response regime are recovered.Comment: 12 pages. Europhysics Letters, in pres
Collective excitations of a periodic Bose condensate in the Wannier representation
We study the dispersion relation of the excitations of a dilute Bose-Einstein
condensate confined in a periodic optical potential and its Bloch oscillations
in an accelerated frame. The problem is reduced to one-dimensionality through a
renormalization of the s-wave scattering length and the solution of the
Bogolubov - de Gennes equations is formulated in terms of the appropriate
Wannier functions. Some exact properties of a periodic one-dimensional
condensate are easily demonstrated: (i) the lowest band at positive energy
refers to phase modulations of the condensate and has a linear dispersion
relation near the Brillouin zone centre; (ii) the higher bands arise from the
superposition of localized excitations with definite phase relationships; and
(iii) the wavenumber-dependent current under a constant force in the
semiclassical transport regime vanishes at the zone boundaries. Early results
by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron
energy bands are used to specify the conditions under which the Wannier
functions may be approximated by on-site tight-binding orbitals of harmonic-
oscillator form. In this approximation the connections between the low-lying
excitations in a lattice and those in a harmonic well are easily visualized.
Analytic results are obtained in the tight-binding scheme and are illustrated
with simple numerical calculations for the dispersion relation and
semiclassical transport in the lowest energy band, at values of the system
parameters which are relevant to experiment.Comment: 20 pages, 2 figures, 22 reference
Boson-fermion mixtures inside an elongated cigar-shaped trap
We present mean-field calculations of the equilibrium state in a gaseous
mixture of bosonic and spin-polarized fermionic atoms with repulsive or
attractive interspecies interactions, confined inside a cigar-shaped trap under
conditions such that the radial thickness of the two atomic clouds is
approaching the magnitude of the s-wave scattering lengths. In this regime the
kinetic pressure of the fermionic component is dominant. Full demixing under
repulsive boson-fermion interactions can occur only when the number of fermions
in the trap is below a threshold, and collapse under attractive interactions is
suppressed within the range of validity of the mean-field model. Specific
numerical illustrations are given for values of system parameters obtaining in
7Li-6Li clouds.Comment: 12 pages, 6 figure
Sound propagation in elongated superfluid fermion clouds
We use hydrodynamic equations to study sound propagation in a superfluid
Fermi gas inside a strongly elongated cigar-shaped trap, with main attention to
the transition from the BCS to the unitary regime. We treat first the role of
the radial density profile in the quasi-onedimensional limit and then evaluate
numerically the effect of the axial confinement in a configuration in which a
hole is present in the gas density at the center of the trap. We find that in a
strongly elongated trap the speed of sound in both the BCS and the unitary
regime differs by a factor sqrt{3/5} from that in a homogeneous
three-dimensional superfluid. The predictions of the theory could be tested by
measurements of sound-wave propagation in a set-up such as that exploited by
M.R. Andrews et al. [Phys. Rev. Lett. 79, 553 (1997)] for an atomic
Bose-Einstein condensate
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