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arXiv:0907.3989 · Physical Review A

Observation of shock waves in a large Bose-Einstein condensate

R. Meppelink, S. B. Koller, J. M. M. J. Vogels, P. van der Straten, Erik van Ooijen, N. R. Heckenberg, Halina H. Rubinsztein-Dunlop, Simon A. Haine, Matthew J. Davis

Published Oct 12, 2009• 63 citations
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Abstract

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.

DOI
10.1103/physreva.80.043606

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•Jun 1, 2005•0 citations
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.
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.
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.
Abstract The problem of wave breaking during its propagation in the Bose–Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form (–x)1/n. The evolution of the wave is described by the Gross–Pitaevskii equation so that a dispersive shock wave is formed as a result of breaking; this wave can be represented using the Gurevich–Pitaevskii approach as a modulated periodic solution to the Gross–Pitaevskii equation, and the evolution of the modulation parameters is described by the Whitham equations obtained by averaging the conservation laws over fast oscillations in the wave. The solution to the Whitham modulation equations is obtained in closed form for n = 2, 3, and the velocities of the dispersion shock wave edges for asymptotically long evolution times are determined for arbitrary integers n > 1. The problem considered here can be applied for describing the generation of dispersion shock waves observed in experiments with the Bose–Einstein condensate.
The Bose-Einstein condensate (BEC) formed by ultracold atomic gases provides an ideal platform for studying various quantum phenomena. In this platform, researchers have explored in depth the important equilibrium and steady phenomena including superfluidity, vortices, and solitons, and recently started to study nonequilibrium problems. In a classical system, nonequilibrium problems, such as explosion, usually occur together with shock waves, which is presented when the explosion speed is larger than the local sound speed. For BEC systems which possess quantum properties, how to produce and understand the shock waves becomes a hot research topic. In this work, we systematically discuss the possibility of quantum shock wave and its essential mechanism in a one-dimensional BEC initially containing dark solitons through quenching interactions. When the system is quenched to the limit of non-interaction, we analytically obtain the post-quench dynamics of initially immobile dark solitons, and find the existence of shock wave, which can be explained through the quantum interference effect. When the system is quenched to finite interaction, we find similar phenomena through numerically solving the Gross-Pitaevskii equation, and analyze different situations. When the system is quenched to a finite weaker interaction, the situation is similar to a non-interaction case; when the system is quenched to a stronger interaction, the shock wave is accompanied by the splitting of the initial soliton, and the two objects can synchronously change; specifically when the quenched ratio of strength is an integer squared, the shock wave disappears, and the soliton is split perfectly. We further explore the properties of the shock wave including its amplitude and speed, and obtain the full scenario as the quenched interaction varies. This work provides theoretical guidance for realizing and measuring shock wave in experiment.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.