Vortex knots in a Bose-Einstein condensate

Proment, Davide; Onorato, Miguel; Barenghi, Carlo F.

doi:10.1103/physreve.85.036306

Cited by 96 publications

(111 citation statements)

References 34 publications

Supporting

Mentioning

108

Contrasting

Order By: Relevance

“…As the topological dynamics are intrinsically geometric, our system provides a unique opportunity for experimentally probing many aspects of inherently dynamical knotted excitations that are difficult or impossible to observe directly in other physical systems. We note, for example, that the general reconnection sequence is similar to that seen in recent simulations of knotted vortices in Bose-Einstein condensates based on the nonlinear Schrödinger equation 22 . Furthermore, knots and links have been conjectured to appear in classical and superfluid turbulence, where their ephemeral structure makes them challenging to resolve.…”

mentioning

confidence: 54%

“…More recently, these solutions were shown to be unstable to linear perturbations 28 ; however, when the LIA is no longer valid, the interplay of global and local induction complicates the situation considerably and the evolution of vortex knots remains a matter of theoretical debate both in the inviscid and viscid cases 21,22 . Simulations of knotted vortices with large cores, based on Navier-Stokes dynamics, suggest that they are short lived 29 ; however, numerical integration of Biot-Savart vortex evolution suggests that finite core size may enhance stability 21 .…”

mentioning

confidence: 99%

“…The topological evolution of vortex knots observed in our system offers an experimental window into knotted excitations that are thought to occur in a wide range of continuous phases, such as plasmas 11 , Bose-Einstein condensates 22 , superfluids and other nonlinear fields 2,3 . As the topological dynamics are intrinsically geometric, our system provides a unique opportunity for experimentally probing many aspects of inherently dynamical knotted excitations that are difficult or impossible to observe directly in other physical systems.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Creation and dynamics of knotted vortices

2013

View full text Add to dashboard Cite

Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have been the subject of considerable theoretical study, their creation in the laboratory has remained an outstanding experimental goal. Here we report the creation of isolated trefoil vortex knots and pairs of linked vortex rings in water using a new method of accelerating specially shaped hydrofoils. Using a high-speed scanning tomography apparatus, we measure their three-dimensional topological and geometrical evolution in detail. In both cases we observe that the linked vortices stretch themselves and then deform-as dictated by their geometrically determined energy-towards a series of local vortex reconnections. This work establishes the existence and dynamics of knotted vortices in real fluids.

show abstract

mentioning

confidence: 54%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Creation and dynamics of knotted vortices

2013

View full text Add to dashboard Cite

show abstract

“…The three dimensional analogue of our branch with (+2, −2) or (+3, −3) vortices would then be travelling waves with two or three parallel vortex rings at small distance one from another. This should probably be related to travelling vortex knots in Bose condensates as studied in [35] when the poloidal radius is rather small. Appendix A.…”

Section: Resultsmentioning

confidence: 96%

Multiple branches of travelling waves for the Gross–Pitaevskii equation

Chiron¹,

Scheid

2018

Nonlinearity

View full text Add to dashboard Cite

Explicit solitary waves are known to exist for the Kadomtsev-Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross-Pitaevskii (GP) equation, which in some long wave regime converges to the KP-I equation. Numerical simulations have already shown that a branch of travelling waves of GP converges to a ground state of KP-I, expected to be the lump. In this work, we perform numerical simulations showing that other explicit solitary waves solutions to the KP-I equation give rise to new branches of travelling waves of GP corresponding to excited states.

show abstract

“…This constraint gives rise to a conserved quantity known as helicity 6,7 , o ering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of 'cutand-splice' operations known as reconnections 3,4,[8][9][10][11] . Despite the potentially fundamental role of these reconnections in understanding helicity-and the stability of knotted fields more generally-their e ect is known only for a handful of simple knots…”

mentioning

confidence: 99%

How superfluid vortex knots untie

2016

View full text Add to dashboard Cite

Knots and links often occur in physical systems, including shaken strands of rope 1 and DNA (ref. 2), as well as the more subtle structure of vortices in fluids 3 and magnetic fields in plasmas 4 . Theories of fluid flows without dissipation predict these tangled structures persist 5 , constraining the evolution of the flow much like a knot tied in a shoelace. This constraint gives rise to a conserved quantity known as helicity 6,7 , o ering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of 'cutand-splice' operations known as reconnections 3,4,8-11 . Despite the potentially fundamental role of these reconnections in understanding helicity-and the stability of knotted fields more generally-their e ect is known only for a handful of simple knots 12 . Here we study the evolution of 322 elemental knots and links in the Gross-Pitaevskii model for a superfluid, and find that they universally untie. We observe that the centreline helicity is partially preserved even as the knots untie, a remnant of the perfect helicity conservation predicted for idealized fluids. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal two-dimensional knot diagrams, and tend to concentrate in states which are twisted in only one direction. These results have direct analogies to previous studies of simple knots in several systems, including DNA recombination 2 and classical fluids 3,12 . This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.Tying a knot has long been a metaphor for creating stability, and for good reason: untangling even a common knotted string requires either scissors or a complicated series of moves. This persistence has important consequences for filamentous physical structures such as DNA, the behaviour of which is altered by knots and links 9,13 . An analogous effect can be seen in physical fields, for example, magnetic fields in plasmas or vortices in fluid flow; in both cases knots never untie in idealized models, giving rise to new conserved quantities 6,14 . At the same time, there are numerous examples in which forcing real (non-ideal) physical systems causes them to become knotted: vortices in classical or superfluid turbulence 15,16 , magnetic fields in the solar corona 4 , and defects in condensed matter phases 10 . This presents a conundrum: why doesn't everything get stuck in a tangled web, much like headphone cords in a pocket 1 ?In all of these systems, 'reconnection events' allow fields to untangle by cutting and splicing together nearby lines/structures ( Fig. 1a; refs 3,4,8-11). As a result, the balance of knottedness, and its fundamental role as a constraint on the evolution of physical systems, depends critically on understanding if and how these mechanisms cause knots to untie.Previous studies of the evolution of knotted fields have been restricted ...

show abstract

Vortex knots in a Bose-Einstein condensate

Cited by 96 publications

References 34 publications

Creation and dynamics of knotted vortices

Creation and dynamics of knotted vortices

Multiple branches of travelling waves for the Gross–Pitaevskii equation

How superfluid vortex knots untie

Contact Info

Product

Resources

About