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Physical Review A

Shock waves in a Bose-Einstein condensate

Igor K. Kulikov, Michail A. Zak

Published Jun 18, 2003• 18 citations
Publisher

Abstract

A theoretical possibility of shock wave formation in a high-density Bose-Einstein condensate with strong repulsive interaction is reported. A mechanism of transformation of sound waves into shock waves is described. The speed of shock waves as well as relationships between jumps of velocity and density at the front of the surface of discontinuity are derived. The theory is illustrated by the analytical solution for shock wave propagation in a dense condensate cloud.

DOI
10.1103/physreva.67.063605

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A theoretical possibility of shock wave formation in a high-density Bose-Einstein condensate with strong repulsive interaction is reported. A mechanism of transformation of sound waves into shock waves is described. The speed of shock waves as well as relationships between jumps of velocity and density at the front of the surface of discontinuity are derived. The theory is illustrated by the analytical solution for shock wave propagation in a dense condensate cloud.
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We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a Bose-Einstein condensate.
The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as dispersive shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.
We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive blue-detuned light barrier, intersecting the Bose-Einstein condensate, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the wave front splits into two parts and clear fringes appear. The experiment is modeled using an effective one-dimensional Gross-Pitaevskii-like equation and gives excellent quantitative agreement with the experiment, even though matter waves with wavelengths two orders of magnitude smaller than the healing length are present. In these experiments, no significant heating or particle loss is observed.
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.