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arXiv:cond-mat/0505725 · Journal of Physics B Atomic Molecular and Optical Physics

Thermally induced instability of a doubly quantized vortex in a Bose–Einstein condensate

Krzysztof Gawryluk, Mirosław Brewczyk, Kazimierz Rza̧żewski

Published May 2, 2006• 25 citations
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Abstract

We study the instability of a doubly quantized vortex topologically imprinted on 23 Na condensate, as reported in recent experiment (Shin et al 2004 Phys. Rev. Lett. 93 160406). We have performed numerical simulations using three-dimensional Gross–Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even very small thermal fluctuations, corresponding to 10–15% of thermal atoms, cause the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex is a monotonic function of the interaction strength.

DOI
10.1088/0953-4075/39/11/l01

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We study the instability of a doubly quantized vortex topologically imprinted on 23 Na condensate, as reported in recent experiment (Shin et al 2004 Phys. Rev. Lett. 93 160406). We have performed numerical simulations using three-dimensional Gross–Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even very small thermal fluctuations, corresponding to 10–15% of thermal atoms, cause the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex is a monotonic function of the interaction strength.
The recent experiment by Shin et al. [Phys. Rev. Lett. 93, 160406 (2004)] on the decay of a doubly quantized vortex is analyzed by numerically solving the Gross-Pitaevskii equation. Our results demonstrate that the vortex decay is mainly a consequence of dynamical instability. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate.
The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23Na{}^{23}\mathrm{Na}23Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards division into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al., Phys. Rev. Lett. 89, 190403 (2002)].
Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin, Phys. Rev. Lett. 93, 160406 (2004)10.1103/PhysRevLett.93.160406]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental setup. We show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments.
The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.