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arXiv:1910.07749 · Journal of Physics B Atomic Molecular and Optical Physics

Controllable splitting dynamics of a doubly quantized vortex in a ring-shaped condensate

Bo Xiong, Tao Yang, Yu-Ju Lin, Daw-Wei Wang

Published Jan 27, 2020• 5 citations
arXivHTMLPDF

Abstract

Abstract We prepared a ring-shaped Bose–Einstein condensate with quantized circulation by imprinting a linear azimuthal phase. A doubly quantized vortex (DQV) can be generated and exist stably in the middle of the condensate cloud after the system is released into a rotationally symmetric harmonic trap. For an asymmetric trap with a small degree of anisotropy the generated DQV initially splits into two singly quantized vortices and revives again but eventually evolves into two unit vortices due to the dynamic instability. For the degree of anisotropy above a critical value, the DQV is extremely unstable and decays rapidly into two singlet vortices. The geometry-dependent lifetime of the DQV and vortex-induced excitations are also discussed intensively.

DOI
10.1088/1361-6455/ab707d

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Abstract We prepared a ring-shaped Bose–Einstein condensate with quantized circulation by imprinting a linear azimuthal phase. A doubly quantized vortex (DQV) can be generated and exist stably in the middle of the condensate cloud after the system is released into a rotationally symmetric harmonic trap. For an asymmetric trap with a small degree of anisotropy the generated DQV initially splits into two singly quantized vortices and revives again but eventually evolves into two unit vortices due to the dynamic instability. For the degree of anisotropy above a critical value, the DQV is extremely unstable and decays rapidly into two singlet vortices. The geometry-dependent lifetime of the DQV and vortex-induced excitations are also discussed intensively.
Abstract We study the splitting dynamics of a triply quantized vortex (TQV) confined in a ring-shaped Bose–Einstein condensate under a weakly elliptical harmonic trap. Using full 3D simulations in cylindrical coordinates, combined with a semi-analytical energy analysis, we show that the vortex preferentially splits along the long axis of the trap, a direction that minimizes the kinetic-energy cost relative to the initial TQV state. Systematic parameter scans reveal that initial quantum fluctuations increase the splitting time and suppress the transient three-core pattern observed in noise-free simulations, whereas stronger nonlinear interactions accelerate the splitting. When the trap is nearly isotropic, the unstable Bogoliubov modes are dominated by both azimuthal quantum number l q = 3 and l q = 2 ; this leads to a dynamical sequence where three daughter vortices first form a triangular arrangement, later evolving into a linear chain. For stronger anisotropy, geometric coupling selectively enhances the l q = 2 mode, making it the sole dominant channel and resulting directly in linear vortex alignment—a clear signature of geometry-induced mode competition explained through combined energy-based and Bogoliubov stability analysis. Our results provide a quantitative connection between confinement geometry and unstable mode selection, clarifying how symmetry breaking reorganizes the instability spectrum and thereby steers the splitting pathway and final vortex configuration. This mechanism-based understanding offers experimentally testable guidance for geometry-controlled vortex engineering.
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)].
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.
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.
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)].