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Free expansion of a quasi-2D Bose-Einstein condensate with quantized vortices

Sang Won Seo, Jae-yoon Choi, Yong-il Shin

Published May 21, 2013• 0 citations
OpenAlex

Abstract

We observe that a density-depleted vortex core evolves into concentric density ripples in a freely expanding quasi-two-dimensional Bose-Einstein condensate. The atomic density of the expanding condensate rapidly reduces due to the fast expansion along the tightly confining axial direction, and thus the transverse expansion of the condensate is not significantly affected by the atom-atom interactions. We find that the observed density profiles of the vortex cores are in good quantitative agreement with numerical simulations assuming no interactions. We analyze the defocused images of the vortex cores, where defocussing is caused by the free fall of the condensate during the expansion time. In the defocused images, the vortex core becomes magnified and appears to be filled after a certain expansion time which depends on the vortex charge number.

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We observe that a density-depleted vortex core evolves into concentric density ripples in a freely expanding quasi-two-dimensional Bose-Einstein condensate. The atomic density of the expanding condensate rapidly reduces due to the fast expansion along the tightly confining axial direction, and thus the transverse expansion of the condensate is not significantly affected by the atom-atom interactions. We find that the observed density profiles of the vortex cores are in good quantitative agreement with numerical simulations assuming no interactions. We analyze the defocused images of the vortex cores, where defocussing is caused by the free fall of the condensate during the expansion time. In the defocused images, the vortex core becomes magnified and appears to be filled after a certain expansion time which depends on the vortex charge number.
We observe that a density-depleted vortex core evolves into concentric density ripples in a freely-expanding quasi-two-dimensional Bose-Einstein condensate. The atomic density of the expanding condensate rapidly reduces due to the fast expansion along the tightly confined axial direction; thus, the transverse expansion of the condensate is not significantly affected by atom-atom interactions. We find that the observed density profiles of the vortex cores are in good quantitative agreement with numerical simulations assuming no interactions. We analyze the defocused images of the vortex cores, where defocussing is caused by the free fall of the condensate during the expansion time. In the defocused images, the vortex core becomes magnified and appears to be filled after a certain expansion time that depends on the vortex charge number.
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 study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding the axial confinement fixed we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core implies that the timing of its observation should be chosen appropriately.
In this work, we analyze the free expansion of Bose-Einstein condensates containing multicharged vortices. The atomic cloud is initially confined in a three-dimensional asymmetric harmonic trap. We apply both approximate variational solutions and numerical simulations of the Gross-Pitaevskii equation. The data obtained provide a way to establish the presence as well as the multiplicity of vortices based only on the properties of the expanded cloud which can be obtained via time-of-flight measurements. In addition, several features such as the evolution of the vortex core size and the asymptotic velocity during free expansion were studied considering the atomic cloud as being released from different harmonic trap configurations.
We measure the in-plane distribution of thermally activated vortices in a trapped quasi-2D Bose gas, where we enhance the visibility of density-depleted vortex cores by radially compressing the sample before releasing the trap. The pairing of vortices is revealed by the two-vortex spatial correlation function obtained from the vortex distribution. The vortex density decreases gradually as temperature is lowered, and below a certain temperature, a vortex-free region emerges in the center of the sample. This shows the crossover from a Berezinskii-Kosterlitz-Thouless phase containing vortex-pair excitations to a vortex-free Bose-Einstein condensate in a finite-size 2D system.
We measure the power spectrum of density fluctuations emerging in a freely expanding quasi-two-dimensional (2D) degenerate Bose gas, and we investigate the scaling behavior of the spectrum for the expansion time. The power spectrum shows an oscillatory shape for long expansion times, where the spectral peak positions are observed to be shifted to lower spatial frequencies than the theoretical prediction for a noninteracting expansion case. We find the spectral peak positions in good agreement with the recent numerical simulation presented by Mazets [Phys. Rev. A 86, 055603 (2012)], where the atom-atom interactions are taken into account. We present a mean-field description of the interaction effect in the expansion dynamics and quantitatively account for the observed spectral peak shifts. The spectral shift is intrinsic to the free expansion of a quasi-2D Bose gas due to finite axial confinement. Finally, we investigate the defocusing effect in the power spectrum measurement.