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arXiv:cond-mat/9810317

Propagation of Sound in Two-Species Bose-Einstein Condensates

Dennis Lima, P. Borckmans, Guy Dewel

Published Oct 23, 1998• 0 citations
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Abstract

We investigate the propagation of zero sound in two-species interpenetrating Bose-Einstein condensates. In very elongated clouds, this propagation is shown to be essentially one-dimensional. We also present 1D numerical experiments that exhibit the existence of two different sound pulses with velocities consistent with the theoretical predictions.

DOI
10.48550/arxiv.cond-mat/9810317

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We investigate the propagation of zero sound in two-species interpenetrating Bose-Einstein condensates. In very elongated clouds, this propagation is shown to be essentially one-dimensional. We also present 1D numerical experiments that exhibit the existence of two different sound pulses with velocities consistent with the theoretical predictions.
We show that under rather general conditions the propagation of sound pulses along the long axis of a Bose-Einstein condensed cloud in a very anisotropic trap is essentially one dimensional. In the linear regime, we demonstrate that the square of the velocity of propagation is given by the square of the local sound velocity c2=nU0/m{c}^{2}{=nU}_{0}/mc2=nU0​/m averaged over the cross section of the cloud. We also carry out calculations in the nonlinear regime and determine how the speed of the pulse depends on its amplitude.
The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BEC's. A mathematical model based on the linearized coupled Gross-Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach.
We study the propagation of sound waves in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the velocity of the propagation of sound wave packets decreases with increasing optical lattice depth, as predicted by the Bogoliubov theory. The strong interplay between nonlinearities and the periodicity of the external potential generates phenomena that are not present in the uniform case. Shock waves, for instance, can propagate slower than sound waves, due to the negative curvature of the dispersion relation. Moreover, nonlinear corrections to the Bogoliubov theory appear to be important even with very small density perturbations, inducing a saturation of the amplitude of the sound signal.
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We study the propagation of a density wave in a magnetically trapped Bose-Einstein condensate at finite temperatures. The thermal cloud is in the hydrodynamic regime and the system is therefore described by the two-fluid model. A phase-contrast imaging technique is used to image the cloud of atoms and allows us to observe small density excitations. The propagation of the density wave in the condensate is used to determine the speed of sound as a function of the temperature. We find the speed of sound to be in good agreement with calculations based on the Landau two-fluid model.
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 3∕5\sqrt{3∕5}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.