Crossover from interaction to driven regimes in quantum vortex reconnections

Abstract

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 quantised vortex lines, which are conceptually easier to study. New experimental techniques now allow visualisation 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 exhibit two distinct fundamental regimes: a δ ∼ t 1/2 scaling arising from the mutual interaction of the reconnecting strands and a δ ∼ t scaling when extrinsic factors drive the individual vortices. RECONNECTIONS IN CLASSICAL AND QUANTUM SYSTEMSarXiv:1812.00473v2 [cond-mat.quant-gas]

Matching theory to characterize sound emission during vortex reconnection in quantum fluids

“…Even if the scaling δ ∝ |t − t r | 1/2 is universal [25], the (dimensionless) pre-factors A ± are not: importantly, one usually finds that A + A − , that is filaments approach slower than they separate. Figure 1 reports a collection of (A + , A − ) values obtained in the literature for reconnections of very different nature following: the decay of Hopf links (red circles) [1]; interactions between vortex lines and rings in homogeneous and trapped superfluids (triangles) [27] and regular and random configurations of vortex filaments (all other symbols) [25]. These results are a clear evidence of the irreversible dynamics of the reconnection process in quantum fluids.…”

“…Following this seminal work, many numerical and theoretical studies were undertaken in the following decades. Many of those works focused on characterizing their rate of approach and separation, on the macroscopic angle between two reconnecting vortex filaments [6,[22][23][24][25][26][27][28], on the sound emission following a reconnection event [24,29], and on the evolution of the length of the filament and superfluid helicity throughout the Gray left and right triangles correspond to reconnections of free and trapped vortices respectively, from Galantucci et al [35].…”

“…Summarizing, in order to compute the differences before and after the reconnection in the incompressible energy and momentum of the superfluid, we use the theoretical description R ± 1,2 for the filaments given in Eqs. (27)(28)(29)(30). Namely, we use such parametrization when the distance is…”

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction

“…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]. This wobbling motion induces dissipation of the VR incompressible kinetic energy via the emission of phonon-like excitations, reducing the VR radius [72,73]: When R VR ∼ ξ, the VR loses its circulation and annihilates in a rarefaction pulse [22]. This picture remains qualitatively correct for the probed T 0.4 T c (red symbols in Figs.…”

Nanoscale Real-Time Detection of Quantum Vortices at Millikelvin Temperatures

“…4 is too scattered to indicate its functional form, we can use our range of lifetimes to make some rough estimates of the length scales involved. Optical measurements in superfluid helium 16,17 and simulations of quantum vortex behaviour 18 show that the timescale, t, for vortex-vortex interactions displays a square root relationship with the vortex spacing δ as δ = A √ κ t αγ , where κ is the circulation quantum and A a constant of order 1, depending on the geometry of the approaching vortices 17 . This expression and our range of lifetimes of 3 to 100 ms (as in Fig.…”