First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

Abstract

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures ($0.6<T/T_c<1.2$) and for systems with $10^4$ to $10^8$ particles. The second sound modes (which exist only below $T_c$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near $T_c$ recently observed at JILA in systems with $10^3$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

a shorten version, more discussions are given on the nature of the second sound. A long footnote on the recent work of Zaremba, Griffin, and Nikuni (cond-mat/9705134) is added, the spectrum of the (\ell=1, n_2=0) mode is included in fig.1

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