We consider the reconnection of two untwisted, linked quantised vortex rings in a Bose-Einstein condensate. We show that the reconnection is capable of transferring helicity, from the links present in the initial configuration, to a twisting of the resulting vortex ring, and hence a rotation of the phase plane along the vortex ring. As velocities in a quantum fluid are the gradient of the phase, a twisting of the phase along the vortices leads to an axial flow along the vortices. Hence one would expect that the dynamics of quantum turbulence are strongly influence by the helicity of the initial conditions or the system forcing. Our results also provide an important link between quantised vortex reconnections and reconnections in classical and magnetised fluids.
We consider the reconnection of two untwisted, linked quantised vortex rings in a Bose-Einstein condensate. We show that the reconnection is capable of transferring helicity, from the links present in the initial configuration, to a twisting of the resulting vortex ring, and hence a rotation of the phase plane along the vortex ring. As velocities in a quantum fluid are the gradient of the phase, a twisting of the phase along the vortices leads to an axial flow along the vortices. Hence one would expect that the dynamics of quantum turbulence are strongly influence by the helicity of the initial conditions or the system forcing. Our results also provide an important link between quantised vortex reconnections and reconnections in classical and magnetised fluids.
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes, and ribbons. As such, it has found myriads of applications in astrophysics, fluid dynamics, atmospheric sciences, and biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of centerline vorticity can be downright impossible to apply in complex and turbulent scenarios. We present a definition of helicity which overcomes these problems and which gives the expected result in the large-scale limit. With it, we show that certain reconnection events can excite Kelvin waves and other complex motions of the centerline vorticity, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum fluids. This process also results in the depletion of helicity in a fully turbulent quantum flow, in a way reminiscent of the decay of helicity in classical fluids.
Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids,redistributing energy and helicity among the length scales and inducing fine-scale turbulent mixing. Unlike ordinary fluids, where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, conceptually easier to study. Here we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose--Einstein Condensate. In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds and ejections can also occur as a consequence of the non-homogeneous, confined nature of the system.
Vortex reconnections and interactions play a fundamental role in the dynamics of fluids and turbulent flows, both in the classical and quantum regime. Studying vortices in a clean system like ultracold gases can therefore help, as a bottom-up approach, to understand the physics in a wider context, including superfluid helium, polariton condensates, fluid dynamics and turbulence, neutron stars and cosmological models. So far vortex-vortex interaction was studied in Bose-Einstein condensates either in rotating systems with the observation of regular Abrikosov lattices or in flat condensates across the Berezinskii-Kosterlitz-Thouless transition. In both cases the geometrical constraints allowed to study just a planar interaction among aligned or anti-aligned vortices. The present study instead is carried out in an axisymmetric cigar-shaped Bose-Einstein condensate. Vortices in prolate structures are also known as solitonic vortices. This geometry is especially suitable for investigating vortex interactions. Indeed vortices are oriented perpendicularly to the condensate axis to minimize their length, hence energy, and, because of the cylindrical symmetry, the orientation of a vortex in the radial plane has no constraints. These facts permit interactions to occur with different incoming relative angles between the vortex lines and with different relative velocities. The strong confinement, acting along the radial axis, enhances also interesting effects due to the boundaries.
Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose-Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a [Formula: see text] scaling arising from the mutual interaction of the reconnecting strands and a [Formula: see text] scaling when extrinsic factors drive the individual vortices.
We statistically study of vortex reconnection in quantum fluids by evolving different realizations of vortex Hopf links using the Gross--Pitaevskii model. Despite the time-reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time-irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently in Proment and Krstulovic (2020), we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids.
By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged throughout the process. The gradual transfer from writhe (due to initial linking) to twist helicity, followed by a continuous relaxation of twist across scales during the evolution is shown to be a generic mechanism that consistently takes place on each individual component.