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arXiv:1401.7257 · Physical Review A

Isotropic vortex tangles in trapped atomic Bose-Einstein condensates via laser stirring

A. J. Allen, Nicholas G. Parker, Nick P. Proukakis, Carlo F. Barenghi

Published Feb 28, 2014• 13 citations
arXivHTMLPDF

Abstract

The generation of isotropic vortex configurations in trapped atomic Bose-Einstein condensates offers a platform to elucidate quantum turbulence on mesoscopic scales. We demonstrate that a laser-induced obstacle moving in a figure-8 path within the condensate provides a simple and effective means to generate an isotropic three-dimensional vortex tangle due to its minimal net transfer of angular momentum to the condensate. Our characterization of vortex structures and their isotropy is based on projected vortex lengths and velocity statistics obtained numerically via the Gross-Pitaevskii equation. Our methodology provides a possible experimental route for generating and characterizing vortex tangles and quantum turbulence in atomic Bose-Einstein condensates.

DOI
10.1103/physreva.89.025602

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The generation of isotropic vortex configurations in trapped atomic Bose-Einstein condensates offers a platform to elucidate quantum turbulence on mesoscopic scales. We demonstrate that a laser-induced obstacle moving in a figure-8 path within the condensate provides a simple and effective means to generate an isotropic three-dimensional vortex tangle due to its minimal net transfer of angular momentum to the condensate. Our characterization of vortex structures and their isotropy is based on projected vortex lengths and velocity statistics obtained numerically via the Gross-Pitaevskii equation. Our methodology provides a possible experimental route for generating and characterizing vortex tangles and quantum turbulence in atomic Bose-Einstein condensates.
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Binary Bose-Einstein condensates of two distinct atomic species are studied, with interesting effects being verified due to the imbalance of atomic masses. We study the formation of vortices and associated turbulence flows created by stirring two mass-imbalanced coupled Bose-Einstein condensates in the miscible regime. We consider the mixture in the laboratory frame, confined in a pancake-like harmonic trap slightly perturbed elliptically by a time-dependent periodic potential, which introduces turbulent dynamics with final stable patterns of vortices, induced by the periodicity of the perturbation. Derived rotational frequencies are shown to be associated with the observed vortex patterns in the asymptotic regime, with a correspondence between the stirring procedure and a direct time-independent approach being indicated. It was also confirmed that a larger pattern of vortices is supported by the higher mass condensed species at the same frequency. For the experimentally accessible mixtures $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$, we numerically solve the equations of motion and analyze the system dynamics using a range of measures including energy spectra. In the transient turbulent regime, spectral analysis shows evidence for the characteristic ${k}^{\ensuremath{-}5/3}$ Kolmogorov classical law associated with turbulence, modified by the universal ${k}^{\ensuremath{-}3}$ vortex core scaling in the ultraviolet regime.
We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed or induce clusters of like-signed vortices in two-dimensional (2D) Bose-Einstein condensates. We propose statistical measures of clustering based on Ripley's KKK function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.