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Physical Review A

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

Tarun Kanti Ghosh, Kazushige Machida

Published Nov 9, 2006• 2 citations
Publisher

Abstract

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
DOI
10.1103/physreva.74.057602

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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.