Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

Wang, Wenlong; Bisset, R. N.; Ticknor, Christopher; Carretero-González, R.; Frantzeskakis, D. J.; Collins, L. A.

doi:10.1103/physreva.95.043638

Cited by 30 publications

(23 citation statements)

References 65 publications

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“…These works are of considerable interest due to the intrinsically complex yet tractable nature of the vortex leapfrogging problem. In addition, recent works both at the level of analysis of experiments performed in liquid helium [14] and at that of exploring vortex rings in confined atomic Bose-Einstein condensates [8] (and also recent works such as [3,4,15]) render this phenomenology quite interesting to understand and generalize. In the context of superfluid helium experiments, there is an interest in exploring generalized leapfrogging of three, or more vortex rings [14].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian bifurcation perspective on two interacting vortex pairs: From symmetric to asymmetric leapfrogging, period doubling, and chaos

2018

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In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the 2d plane. The vortices are considered as effective particles and their interaction can be desribed in classical mechanics terms. We first construct a Poincaré section, for a typical value of the energy, in order to acquire a picture of the structure of the phase space of the system. We divide the phase space in different regions which correspond to qualitatively distinct motions and we demonstrate its different temporal evolution in the "real" vortex-space. Our main emphasis is on the leapfrogging periodic orbit, around which we identify a region that we term the "leapfrogging envelope" which involves mostly regular motions, such as higher order periodic and quasi-periodic solutions. We also identify the chaotic region of the phase plane surrounding the leapfrogging envelope as well as the so-called walkabout and braiding motions. Varying the energy as our control parameter, we construct a bifurcation tree of the main leapfrogging solution and its instabilities, as well as the instabilities of its daughter branches. We identify the symmetry-breaking instability of the leapfrogging solution (in line with earlier works), and also obtain the corresponding asymmetric branches of periodic solutions. We then characterize their own instabilities (including period doubling ones) and bifurcations in an effort to provide a more systematic perspective towards the types of motions available to this dynamical system.

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Section: Introductionmentioning

confidence: 99%

Hamiltonian bifurcation perspective on two interacting vortex pairs: From symmetric to asymmetric leapfrogging, period doubling, and chaos

2018

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“…The VR survival during its propagation in the superfluid bulk is thus determined by two competing effects: On the one hand, the VR tends to expand [70] to conserve its incompressible kinetic energy as it moves towards lowerdensity regions with decreasing transverse size. On the other hand, the radial trapping asymmetry (ω y = ω z ) leads to elliptical VR profiles with oscillating aspect ratio, corresponding to a m = 2 Kelvin wave excitation on a circular VR [71].…”

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confidence: 99%

“…As the VR approaches the edge of the condensate, it breaks up into two anti-parallel vortex lines [Fig. 4(b), final snapshot][22,70,74]. Critically, thermal fluctuations destabilize the VR, causing it to drift off-axis, and reach the transversal boundary asymmetrically [Fig.…”

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confidence: 99%

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction

et al. 2020

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We study the onset of dissipation in an atomic Josephson junction between Fermi superfluids in the molecular Bose-Einstein condensation limit of strong attraction. Our simulations identify the critical population imbalance and the maximum Josephson current delimiting dissipationless and dissipative transport, in quantitative agreement with recent experiments. We unambiguously link dissipation to vortex ring nucleation and dynamics, demonstrating that quantum phase slips are responsible for the observed resistive current. Our work directly connects microscopic features with macroscopic dissipative transport, providing a comprehensive description of vortex ring dynamics in three-dimensional inhomogeneous constricted superfluids at zero and finite temperatures. arXiv:1905.08893v2 [cond-mat.quant-gas]

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“…Some interesting examples include the vortex-linebright and the vortex-ring-bright structures [36]. Other dark soliton surfaces and vortical filaments are also interesting, and their systematic studies are useful towards formulating effective filament-level dynamical theories for pattern formation within Bose-Einstein condensates [29,38].…”

Section: Conclusion and Future Challengesmentioning

confidence: 99%

Ring dark solitons in three-dimensional Bose-Einstein condensates

2019

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In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semianalytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed. * Electronic address: wenlongcmp@gmail.com † Electronic address: kevrekid@math.umass.edu FIG. 1: Density contour and phase profile of a stationary ring dark soliton in a spherical harmonic trap of frequency ω = 1 at chemical potential µ = 16 (Eq. (1)). There is a ring of vanishing density separating two segments with phase difference of π shown as two different colours (red and green). Note the ring is not vertically straight, but bends. The state is generated from numerical computation. the incongruence between the cylindrical symmetry of the 2D pattern and the closer to spherical (or more accurately: ellipsoidal) nature of the 3D condensate. A cross section perpendicular to the axis is a 2D ring, and the radius is larger at the edges and smaller at the center. See Fig. 1 for a density and phase profile of the RDS.Despite its extensive analysis in the 2D case, including the recent corroboration of its modes of vibration and even its multi-component extension [18], the RDS has not been studied in detail in three dimensions. Instead, other structures, such as the planar dark soliton (PDS) [19,20] and the spherical dark soliton (SDS) [20,21] have been considered due to their symmetry. The latter have been dynamically recognized as generating spontaneously structures such as vortex rings and multi-ring generalizations thereof [19,22,23]. In that arXiv:1910.02272v1 [cond-mat.quant-gas]

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Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

Cited by 30 publications

References 65 publications

Hamiltonian bifurcation perspective on two interacting vortex pairs: From symmetric to asymmetric leapfrogging, period doubling, and chaos

Hamiltonian bifurcation perspective on two interacting vortex pairs: From symmetric to asymmetric leapfrogging, period doubling, and chaos

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction

Ring dark solitons in three-dimensional Bose-Einstein condensates

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