Quantum vortex reconnections

Zuccher, Simone; Caliari, Marco; Baggaley, Andrew W.; Barenghi, Carlo F.

doi:10.1063/1.4772198

Cited by 123 publications

(162 citation statements)

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“…This prototype of turbulence-a tangle of quantized vortex line-can be excited at small length scales by injecting ions or vortex rings (26), or at larger length scales using vibrating objects (15,28), or by suddenly halting the rotation and destabilizing an existing vortex lattice (25). Besides the residual friction potentially caused by thermal excitations, dissipation of kinetic energy is possible due to acoustic emission from short and rapidly rotating Kelvin waves (55) and from vortex reconnections (31). The length scale required for efficient acoustic emission is much shorter than the typical curvature at the quantum length scale ℓ ≈ L −1=2 , but can be achieved by a Kelvin wave cascade-which is the energy transfer to increasingly smaller scales arising from the nonlinear interaction of Kelvin waves (56,57); this mechanism is discussed by Barenghi et al (10)).…”

Section: Types and Regimes Of Quantum Turbulencementioning

confidence: 99%

Introduction to quantum turbulence

Barenghi

Skrbek

Sreenivasan

2014

Proc. Natl. Acad. Sci. U.S.A.

284

264

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The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.Turbulence is a spatially and temporally complex state of fluid motion. Five centuries ago, Leonardo da Vinci noticed that water falling into a pond creates eddies of motion. Today, turbulence still provides physicists, applied mathematicians, and engineers with a continuing challenge. Leonardo realized that the motion of water shapes the landscape. Today's researchers appreciate that many physical processes, from the generation of the Galactic magnetic field to the efficiency of jet engines, depend on turbulence.The articles in this collection are devoted to a special form of turbulence known as quantum turbulence (1-3), which appears in quantum fluids. Quantum fluids differ from ordinary fluids in three respects: (i) they exhibit two-fluid behavior at nonzero temperature or in the presence of impurities, (ii) they can flow freely, without the dissipative effect of viscous forces, and (iii) their local rotation is constrained to discrete vortex lines of known strength (unlike the eddies in ordinary fluids, which are continuous and can have arbitrary size, shape, and strength). Superfluidity and quantized vorticity are extraordinary manifestations of quantum mechanics at macroscopiclength scales.Recent experiments have highlighted quantitative connections, as well as fundamental differences, between turbulence in quantum fluids and turbulence in ordinary fluids (classical turbulence). The relation between the two forms of turbulence is indeed a common theme in the articles collected here. Because different scientific communities (lowtemperature physics, condensed-matter physics, fluid dynamics, and atomic physics) have contributed to progress in quantum turbulence, † the aim of this article is to introduce the main ideas in a coherent way. Quantum FluidsIn this series of articles, we shall be concerned almost exclusively with superfluid 4 He, the B-phase of superfluid 3 He, and, to a lesser extent, with ultracold atomic gases. These systems exist as fluids at temperatures on the order of a Kelvin, milliKelvin, and microKelvin, respectively.‡ Their constituents are either bosons (such as 4 He atoms with zero spin) or fermions (such as 3 He atoms with spin 1/2). This difference is fundamental: the former obey Bose-Einstein statistics and the latter Fermi-Dirac quantum statistics.Let us consider an...

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Section: Types and Regimes Of Quantum Turbulencementioning

confidence: 99%

Introduction to quantum turbulence

Barenghi

Skrbek

Sreenivasan

2014

Proc. Natl. Acad. Sci. U.S.A.

284

264

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“…Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence. Although helicity is perfectly conserved in barotropic ideal fluids, in real fluids [13,14] and in superfluids [15,16] vortex reconnection events, which alter the topology of the flow, can take place. It is unclear how well helicity is preserved under reconnection.…”

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confidence: 99%

Helicity, topology, and Kelvin waves in reconnecting quantum knots

Leoni

Mininni

Brachet³

2016

Phys. Rev. A

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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 and solar physics, in fluid dynamics, in atmospheric sciences, and in 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 vortex lines can be downright impossible to apply in complex and turbulent scenarios. We present a new definition of helicity which overcomes these problems. With it, we show that only certain reconnection events conserve helicity. In other cases helicity can change abruptly during reconnection. Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence. Although helicity is perfectly conserved in barotropic ideal fluids, in real fluids [13,14] and in superfluids [15,16] vortex reconnection events, which alter the topology of the flow, can take place. It is unclear how well helicity is preserved under reconnection. As a few examples, experiments of vortex knots in water have shown that center line helicity remains constant throughout reconnection events [17], while theoretical arguments indicate that writhe (one component of the helicity) should be conserved in anti-parallel reconnection events [18], a fact later confirmed in numerical simulations of a few specific quantum vortex knots [19]. However, numerical studies of Burgers-type vortices indicate that helicity is not conserved [20]. While experiments studying helicity in quantum flows have not been done yet, the recent experimental creation of quantum knots in a Bose-Einstein condensate in the laboratory [21] is a significant step in that direction.Recently, quantum flows have been used as a testbed for many of these ideas [17,19], as vorticity in a quantum flow is concentrated along vortex lines with quantized circulation, and as these vortex lines can reconnect without dissipation. However, the lack of a fluid-like definition of helicity for a quantum flow requires complex topological measurements of the linking and knottedness of vortex lines [17], or artificial filtering of the fields [19] to prevent spurious values of helicity resulting from the singularity near quantum vortices. Moreover, helicity in quantum flows has an interest per se, as reconnection events in superfluid turbulence can excite Kelvin waves [22]. These are helical perturbations that travel along the vortex lines first predicted for classical vortices by Lord Kelvin (see [23]). Kelvin waves are believed to be responsible for the generation of an energy cascade [24,25] leading to Kelvin wave turbulence [26]. Possible links between helicity and the development of Kelvin wave turbulence have remain obscure as a result of the difficulties i...

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“…We extract the position of the vortex core by finding the grid points where the density is a local minimum and about which the phase changes by 2π [41]. The time-dependence of this quantity (before and after the reconnection) was experimentally observed in superfluid 4 He, and predicted theoretically for superfluids based on the GPE (T = 0) [37] and for ordinary viscous fluids based on the classical Navier-Stokes equation [42]. To enable comparison of δ(t) between the homogeneous and trapped systems, we must convert between harmonic trap units (based on the harmonic oscillator length and frequency) and natural units (based on the healing length and the chemical potential).…”

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confidence: 99%

Vortex reconnections in atomic condensates at finite temperature

et al. 2014

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The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length/time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the ZarembaNikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further show reconnections to be insensitive to the inhomogeneity in the background density. In this paper we present results of an investigation of vortex reconnections in finite-temperature trapped Bose-Einstein condensates. We model the problem in the context of the Zaremba-Nikuni-Griffin (ZNG) formalism [26,27], where the Gross-Pitaevskii equation (GPE) is generalized by the inclusion of the thermal cloud mean field, and a dissipative or source term which is associated with a collision term in a semiclassical Boltzmann equation for the thermal cloud. The main feature of this model is that the condensate and thermal cloud interact with each other self-consistently; for a strongly nonlinear dynamical event like a vortex reconnection, a simpler and less accurate approach may give misleading answers.The governing ZNG equations areandIn this formalism φ = φ(r, t) is the condensate wavefunction, f = f (r, p, t) is the phase-space distribution function of thermal atoms, V ext = mω 2 r 2 /2 is the harmonic potential which confines the atoms (assumed, for simplicity, to be spherically-symmetric), ω is the trapping frequency, m the atomic mass, and g = 4πh 2 a s /m, with a s being the s-wave scattering length. Equation (1) generalises the GPE for a T = 0 condensate by the addition of the thermal cloud mean-field potential 2gñ and the dissipation/source term −iR(r, t). The condensate density is n c (r, t) = |φ(r, t)| 2 and the thermal cloud density is recovered from f (r, p, t) via an integration over all momenta,ñ(r, t) = (2πh) −3 dpf (p, r, t). The mean-field potential acting on the thermal cloud is U eff = V ext (r) + 2g[n c (r, t) +ñ(r, t)]. The quantities C 22 [f ] and C 12 [φ, f ] are collision integrals defined in arXiv:1404.4557v2 [cond-mat.quant-gas]

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Quantum vortex reconnections

Cited by 123 publications

References 50 publications

Introduction to quantum turbulence

Introduction to quantum turbulence

Helicity, topology, and Kelvin waves in reconnecting quantum knots

Vortex reconnections in atomic condensates at finite temperature

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