Stable Hopf solitons in rotating Bose-Einstein condensates

Bidasyuk, Y. M.; Chumachenko, A. V.; Prikhodko, O. O.; Vilchinskiĭ, S. I.; Weyrauch, M.; Yakimenko, A. I.

doi:10.1103/physreva.92.053603

Cited by 20 publications

(23 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that such reconnection events, particularly interesting in their own right and especially relevant in turbulent dynamics (see, e.g., Refs. [35,36]), have also been observed in the presence of rotation [19].…”

Section: B Nonlinear Dynamicsmentioning

confidence: 74%

“…A stable hopfion state has so far only been predicted in somewhat complicated experimental * rnbisset@gmail.com † http://nlds.sdsu.edu configurations. These include, for instance, elaborate radially increasing nonlinear interactions [18] or a rotation of the trap [19]. Here we show that the hopfion can, in fact, be stable for large chemical potential ranges and simple trapping configurations, i.e., inside a parabolic trap.…”

Section: Introductionmentioning

confidence: 91%

“…[17]. Of increasing interest of late is the one-component counterpart to the Skyrmion, namely the so-called hopfion state [18,19]. This state consists of a VR and VL in the same component, with the axis of the VR coinciding with that of the VL.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

et al. 2015

View full text Add to dashboard Cite

Performing a systematic Bogoliubov-de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings, and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regimes, we not only identify the unstable mode, such as a quadrupolar or hexapolar mode, but we also observe the corresponding instability dynamics. Furthermore, deep in the Thomas-Fermi regime, we investigate the particlelike behavior of vortex rings and hopfions.

show abstract

Section: B Nonlinear Dynamicsmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 91%

See 1 more Smart Citation

Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

et al. 2015

View full text Add to dashboard Cite

show abstract

“…This model makes it possible to create very robust solitons of diverse types, including fundamental ones and solitary vortices [57,58], as well as sophisticated 3D states -notably, hopfions (vortex tori with inner twist, which feature two independent topological numbers). A challenging problem is finding still more general physically relevant conditions for the creation of complex 3D modes, such as the hopfions [60], skyrmions (which, similar to hopfions, carry two different topological charges) [61,62], monopoles [63], linked vortex rings, and others. In terms of the experiment, the entire area of multidimensional solitons remains a challenging one, as very few experimental results have been reported, thus far (the latest experimental findings are the creation of (2+1)D optical spatial solitons in media with competing focusing-defocusing cubic-quintic [64] and quintic-septimal [65] nonlinearities, as well as the making of a quasi-stable vortex solitons in an optical medium where nonlinear losses are essential [66]).…”

Section: Discussionmentioning

confidence: 99%

Multidimensional solitons: Well-established results and novel findings

Malomed

2016

Eur. Phys. J. Spec. Top.

125

View full text Add to dashboard Cite

A brief review is given of some well-known and some very recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to the instability induced by the occurrence of the critical and supercritical collapse, respectively, in the same 2D and 3D models that give rise to the solitons. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses one well-established topic, viz., the stabilization of the 3D and 2D states, with S = 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic which was developed very recently: the stabilization of 2D and 3D free-space solitons, which mix components with S = 0 and ±1 (semi-vortices and mixed modes), in a binary system with the spinorbit coupling (SOC) between its components. In both cases, the generic situations are drastically different in the 2D and 3D geometries. In the former case, the stabilization mechanism creates a stable ground state (GS, which was absent without it), whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow to create a GS, but metastable solitons can be constructed.

show abstract

“…In particular, the possibility of the creation of BEC skyrmions was predicted in a number of settings [10] and realized experimentally [11]. Also predicted were settings appropriate for the creation of atomic knots [12] and hopfions [13], and the experimental creation of monopoles was recently reported in Ref. [14].This topic is closely related to the general problem of the creation of 2D and 3D self-trapped modes in nonlinear media (often considered as solitons), which also finds many physically relevant ramifications [15], [16], especially in nonlinear optics and matter-wave dynamics in BECs.…”

mentioning

confidence: 99%

Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators

2016

View full text Add to dashboard Cite

The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.

show abstract

Stable Hopf solitons in rotating Bose-Einstein condensates

Cited by 20 publications

References 25 publications

Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

Multidimensional solitons: Well-established results and novel findings

Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators

Contact Info

Product

Resources

About