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

Abstract

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.

Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics

“…It is well-known that 3D generalizations of RDS exist but are also dynamically unstable [57]. Hence, it is perhaps of more interest to examine the interactions of vortex rings with vortex lines [68] and to analyze the relevant particle/filament picture for which we are not aware of any theoretical results. In the same spirit as our multi-ring structures herein, one can also explore multi-vortex-ring entities and lattices thereof in 3D BECs, which are also of interest in their own right [69].…”

Topological transformation and free-space transport of photonic hopfions

“… – 21 They are also known as Faddeev–Hopf knots 22 , 23 and can be elegantly mapped to a Hopf fibration and characterized by a Hopf index 24 , 25 . Hopfions have fundamental importance in many physical systems in high-energy physics, 26 chiral and frustrated magnets, 27 – 32 quantum fields, 33 , 34 condensed matter physics, 35 – 38 cosmology, 39 , 40 fluid dynamics, 41 liquid crystals, 42 , 43 and very recently, were realized in free-space photonics 44 . Due to their rich 3D spin texture, hopfions can potentially provide many opportunities in investigations and applications of topological structures.…”

Identification of vortices in quantum fluids: Finite element algorithms and programs

“…Different types of vortices have been observed in experiments or numerical simulations of BEC: Abrikosov triangular vortex lattices (Engels et al, 2003), bent vortex lines of "U" or "S" shapes (Rosenbusch et al, 2002a;Aftalion and Danaila, 2003), giant vortices (Bretin et al, 2004;Aftalion and Danaila, 2004;Danaila, 2005) or more exotic shapes of vortices (double rings, hopfions, stars, etc.) (Bisset et al, 2015;Crasovan et al, 2004). Experimental images of quantized vortices in BEC are typically obtained by switching-off the magnetic trap and imaging (after a time of flight) the absorption of a resonant laser beam propagating along the z-axis.…”