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arXiv:cond-mat/0603508 · Physical Review A

Comment on “Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover”

P. Capuzzi, Patrizia Vignolo, F. Federici, Monica Tosi

Published Nov 9, 2006• 22 citations

Abstract

The work by T. K. Ghosh and K. Machida [Phys. Rev. A 73, 013613 (2006) and cond-mat/0510160] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi et al. [Phys. Rev. A 73, 021603(R) (2006) and cond-mat/0509323]. In this Comment, we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS and unitary limits and in the BEC regime are also shown.

DOI: 10.1103/physreva.74.057601

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Reply to “Comment on ‘Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover’”

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We are providing a Reply to the preceding Comment.Received 19 June 2006DOI:https://doi.org/10.1103/PhysRevA.74.057602©2006 American Physical Society

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Bogoliubov spectrum of a cigar shaped Fermi superfluid in an optical lattice at the BEC-BCS crossover

Bhattacherjee, A.B.

We study the Bogoliubov spectrum of an elongated Fermi superfluid confined in an onedimensional 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.

•Jan 1, 2007•1 citation

The work by T. K. Ghosh and K. Machida [Phys. Rev. A 73, 013613 (2006) and cond-mat/0510160] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi et al. [Phys. Rev. A 73, 021603(R) (2006) and cond-mat/0509323]. In this Comment, we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS and unitary limits and in the BEC regime are also shown.

We study properties of excited states of an elongated Fermi superfluid along the Bose-Einstein-condensate--BCS crossover including the unitarity limit. Analytic expressions for the sound velocity in an inhomogeneous as well as homogeneous Fermi superfluid along the crossover are obtained on the basis of the hydrodynamic theory. The complete excitation spectrum of axial quasiparticles with various discrete radial nodes is presented. We discuss the feasibility of measuring the sound velocity and the multibranch Bogoliubov spectrum experimentally.

We use hydrodynamic equations to study sound propagation in a superfluid Fermi gas at zero temperature inside a strongly elongated cigar-shaped trap, with main attention to the transition from the BCS to the unitary regime. First, we treat the role of the radial density profile in the limit of a cylindrical geometry 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 setup such as that exploited by Andrews et al. [Phys. Rev. Lett. 79, 553 (1997)] for an atomic Bose-Einstein condensate.

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 Bogoliubov spectrum of an elongated Fermi superfluid confined in an onedimensional 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.