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arXiv:cond-mat/0701411 · Physical Review A

Self-induced density modulations in the free expansion of Bose-Einstein condensates

Luca Salasnich, Nicola Manini, Federico Bonelli, Michael Korbman, Alberto Parola

Published Apr 19, 2007• 15 citations
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Abstract

We simulate numerically the free expansion of a repulsive Bose-Einstein condensate with an initially Gaussian density profile. We find a self-similar expansion only for weak interatomic repulsion. In contrast, for strong repulsion we observe the spontaneous formation of a shock wave at the surface followed by a significant depletion inside the cloud. In the expansion, contrary to the case of a classical viscous gas, the quantum fluid can generate radial rarefaction density waves with several minima and maxima. These intriguing nonlinear effects, never observed in free-expansion experiments with ultracold alkali-metal atoms, can be detected with the available setups.

DOI
10.1103/physreva.75.043616

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We simulate numerically the free expansion of a repulsive Bose-Einstein condensate with an initially Gaussian density profile. We find a self-similar expansion only for weak interatomic repulsion. In contrast, for strong repulsion we observe the spontaneous formation of a shock wave at the surface followed by a significant depletion inside the cloud. In the expansion, contrary to the case of a classical viscous gas, the quantum fluid can generate radial rarefaction density waves with several minima and maxima. These intriguing nonlinear effects, never observed in free-expansion experiments with ultracold alkali-metal atoms, can be detected with the available setups.
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.
The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.
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.
We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behavior when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyze in detail caustic formation in a quasi-one-dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two-dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for noninteracting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images [Chen et al., Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.