1
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Yui S, Tang Y, Guo W, Kobayashi H, Tsubota M. Universal Anomalous Diffusion of Quantized Vortices in Ultraquantum Turbulence. PHYSICAL REVIEW LETTERS 2022; 129:025301. [PMID: 35867430 DOI: 10.1103/physrevlett.129.025301] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2022] [Revised: 04/29/2022] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
In classical viscous fluids, turbulent eddies are known to be responsible for the rapid spreading of embedded particles. However, in inviscid quantum fluids where the turbulence is induced by a chaotic tangle of quantized vortices, dispersion of the particles can be achieved via a nonclassical mechanism, i.e., their binding to the evolving vortices. However, knowledge on how the vortices diffuse and spread in quantum-fluid turbulence is very limited, especially for the so-called ultraquantum turbulence (UQT) generated by a random tangle of vortices. Here we report a systematic numerical study of the apparent diffusion of vortices in UQT in superfluid helium-4 using the full Biot-Savart simulation. We reveal that the vortices in the superfluid exhibit a universal anomalous diffusion (superdiffusion) at small times, which transits to normal diffusion at large times. This behavior is found to be the result of a generic scaling property of the vortex velocity. Our simulation at finite temperatures also nicely reproduces recent experimental observations. The knowledge obtained from this study may form the base for understanding turbulent transport and universal vortex dynamics in various quantum fluids.
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Affiliation(s)
- Satoshi Yui
- Department of Physics, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, Osaka 558-8585, Japan
| | - Yuan Tang
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
- Mechanical Engineering Department, FAMU-FSU College of Engineering, Florida State University, Tallahassee, Florida 32310, USA
| | - Wei Guo
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
- Mechanical Engineering Department, FAMU-FSU College of Engineering, Florida State University, Tallahassee, Florida 32310, USA
| | - Hiromichi Kobayashi
- Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Kohoku-ku, Yokohama 223-8521, Japan
- Department of Physics, Keio University, 4-1-1 Hiyoshi, Kohoku-ku, Yokohama 223-8521, Japan
| | - Makoto Tsubota
- Department of Physics, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, Osaka 558-8585, Japan
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2
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Metz F, Polo J, Weber N, Busch T. Deep-learning-based quantum vortex detection in atomic Bose–Einstein condensates. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abea6a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Quantum vortices naturally emerge in rotating Bose–Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena, such as turbulence and chaos. However, the study of such phenomena requires the determination of the precise location of each vortex within a BEC, which becomes challenging when either only the density of the condensate is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine-learning-based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the phase profile of the condensate is also available. We anticipate that our vortex detector will be advantageous for both experimental and theoretical studies of the static and dynamic properties of vortex configurations in BECs.
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3
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Tang Y, Bao S, Guo W. Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence. Proc Natl Acad Sci U S A 2021; 118:e2021957118. [PMID: 33526696 PMCID: PMC8017924 DOI: 10.1073/pnas.2021957118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Generic scaling laws, such as Kolmogorov's 5/3 law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose-Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence, i.e., quantum turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid 4He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex-velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.
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Affiliation(s)
- Yuan Tang
- The Cryogenics Laboratory, National High Magnetic Field Laboratory, Tallahassee, FL 32310
- Mechanical Engineering Department, Florida State University, Tallahassee, FL 32310
| | - Shiran Bao
- The Cryogenics Laboratory, National High Magnetic Field Laboratory, Tallahassee, FL 32310
- Mechanical Engineering Department, Florida State University, Tallahassee, FL 32310
| | - Wei Guo
- The Cryogenics Laboratory, National High Magnetic Field Laboratory, Tallahassee, FL 32310;
- Mechanical Engineering Department, Florida State University, Tallahassee, FL 32310
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4
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Alperin SN, Grotelueschen AL, Siemens ME. Quantum Turbulent Structure in Light. PHYSICAL REVIEW LETTERS 2019; 122:044301. [PMID: 30768340 DOI: 10.1103/physrevlett.122.044301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Revised: 12/17/2018] [Indexed: 06/09/2023]
Abstract
The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures, a timelike axis appears to emerge with which we can define vortex velocities in a useful way: With both numerical simulations and optical experiments, we show that the statistics of these velocities match those of turbulent quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. These statistics are shown to be independent of system scale. These results raise deep questions about the general nature of quantum chaos and the role of nonlinearity in the structure of turbulence.
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Affiliation(s)
- Samuel N Alperin
- Department of Physics & Astronomy, University of Denver, Denver, Colorado 80210, USA
| | | | - Mark E Siemens
- Department of Physics & Astronomy, University of Denver, Denver, Colorado 80210, USA
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5
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Bland T, Stagg GW, Galantucci L, Baggaley AW, Parker NG. Quantum Ferrofluid Turbulence. PHYSICAL REVIEW LETTERS 2018; 121:174501. [PMID: 30411963 DOI: 10.1103/physrevlett.121.174501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 08/29/2018] [Indexed: 06/08/2023]
Abstract
We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly nonequilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low-density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of the vortex line length is enhanced, closely following a t^{-3/2} behavior. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.
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Affiliation(s)
- T Bland
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - G W Stagg
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - L Galantucci
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - A W Baggaley
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - N G Parker
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
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6
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Turbulence in a matter-wave supersolid. Sci Rep 2018; 8:12589. [PMID: 30135502 PMCID: PMC6105649 DOI: 10.1038/s41598-018-30852-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2018] [Accepted: 08/01/2018] [Indexed: 11/08/2022] Open
Abstract
Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a two-dimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC). When the coupling constant of the soft-core interaction is over a critical value, the superfluid (SF) system can transition into a hexagonal supersolid (SS) state. Based on the Gross-Pitaevskii equation approach, we have discovered a new characteristic k-13/3 scaling law for wave turbulence in the SS state, that coexists with the waveaction k-1/3 and energy k-1 cascades commonly existing in a SF BEC. The new k-13/3 scaling law implies that the SS system exhibits a negative, minus-one power energy dispersion (E ~ k-1) at the wavevector consistent with the radius of the SS droplet. For vortex turbulence, in addition to the presence of the Kolmogorov energy k-5/3 and Saffman enstrophy k-4 cascades, it is found that large amount of independent vortices and antivortices pinned to the interior of the oscillating SS results in a strong k-1 scaling at the wavevector consistent with the SS lattice constant.
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7
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Seo SW, Ko B, Kim JH, Shin Y. Observation of vortex-antivortex pairing in decaying 2D turbulence of a superfluid gas. Sci Rep 2017; 7:4587. [PMID: 28676634 PMCID: PMC5496920 DOI: 10.1038/s41598-017-04122-9] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Accepted: 05/09/2017] [Indexed: 11/10/2022] Open
Abstract
In a two-dimensional (2D) classical fluid, a large-scale flow structure emerges out of turbulence, which is known as the inverse energy cascade where energy flows from small to large length scales. An interesting question is whether this phenomenon can occur in a superfluid, which is inviscid and irrotational by nature. Atomic Bose-Einstein condensates (BECs) of highly oblate geometry provide an experimental venue for studying 2D superfluid turbulence, but their full investigation has been hindered due to a lack of the circulation sign information of individual quantum vortices in a turbulent sample. Here, we demonstrate a vortex sign detection method by using Bragg scattering, and we investigate decaying turbulence in a highly oblate BEC at low temperatures, with our lowest being ~0.5T c , where T c is the superfluid critical temperature. We observe that weak spatial pairing between vortices and antivortices develops in the turbulent BEC, which corresponds to the vortex-dipole gas regime predicted for high dissipation. Our results provide a direct quantitative marker for the survey of various 2D turbulence regimes in the BEC system.
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Affiliation(s)
- Sang Won Seo
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea
| | - Bumsuk Ko
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea
| | - Joon Hyun Kim
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea.,Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea
| | - Y Shin
- Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, 08826, Korea. .,Center for Correlated Electron Systems, Institute for Basic Science, Seoul, 08826, Korea.
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8
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Abstract
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates.
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9
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Krstulovic G. Grid superfluid turbulence and intermittency at very low temperature. Phys Rev E 2016; 93:063104. [PMID: 27415355 DOI: 10.1103/physreve.93.063104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Indexed: 06/06/2023]
Abstract
Low-temperature grid-generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states. Results are later confronted with the (quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality of the statistics. For this flow, the statistics are found to be intermittent and a Kolmogorov constant close to the one of classical fluid is found for the second-order structure function.
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Affiliation(s)
- Giorgio Krstulovic
- Laboratoire J.L. Lagrange, UMR7293, Université de la Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
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10
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Villois A, Proment D, Krstulovic G. Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation. Phys Rev E 2016; 93:061103. [PMID: 27415198 DOI: 10.1103/physreve.93.061103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 06/06/2023]
Abstract
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently developed accurate and robust tracking algorithm, all quantized vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in helium II is observed. The topology of the tangle is then investigated showing that linked rings may appear during the evolution. The tracking also allows for determining the statistics of small-scale quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.
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Affiliation(s)
- Alberto Villois
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - Davide Proment
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - Giorgio Krstulovic
- Laboratoire J.L. Lagrange, UMR7293, Université de la Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, Boîte Postale 4229, 06304 Nice Cedex 4, France
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11
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Skaugen A, Angheluta L. Velocity statistics for nonuniform configurations of point vortices. Phys Rev E 2016; 93:042137. [PMID: 27176284 DOI: 10.1103/physreve.93.042137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2016] [Indexed: 06/05/2023]
Abstract
Within the point-vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-sign vortices scattered within a disk according to a fractal distribution of distances to the origin ∼r^{-α}. We show that the different random configurations of vortices induce velocity fluctuations that are broadly distributed and follow a power-law tail distribution P(V)∼V^{α-2} with a scaling exponent determined by the α exponent of the spatial distribution. We also show that the range of the power-law scaling regime in the velocity distribution is set by the mean density of vortices and the exponent α of the vortex density distribution.
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Affiliation(s)
- Audun Skaugen
- Department of Physics, University of Oslo, P.O. 1048 Blindern, 0316 Oslo, Norway
| | - Luiza Angheluta
- Department of Physics, University of Oslo, P.O. 1048 Blindern, 0316 Oslo, Norway
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12
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Skaugen A, Angheluta L. Vortex clustering and universal scaling laws in two-dimensional quantum turbulence. Phys Rev E 2016; 93:032106. [PMID: 27078291 DOI: 10.1103/physreve.93.032106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Indexed: 06/05/2023]
Abstract
We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal -5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a -5/3 exponent.
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Affiliation(s)
- Audun Skaugen
- Department of Physics, University of Oslo, P.O. 1048 Blindern, 0316 Oslo, Norway
| | - Luiza Angheluta
- Department of Physics, University of Oslo, P.O. 1048 Blindern, 0316 Oslo, Norway
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13
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Allen AJ, Parker NG, Proukakis NP, Barenghi CF. Quantum turbulence in atomic Bose-Einstein condensates. ACTA ACUST UNITED AC 2014. [DOI: 10.1088/1742-6596/544/1/012023] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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14
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Billam TP, Reeves MT, Anderson BP, Bradley AS. Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence. PHYSICAL REVIEW LETTERS 2014; 112:145301. [PMID: 24765984 DOI: 10.1103/physrevlett.112.145301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Indexed: 06/03/2023]
Abstract
Despite the prominence of Onsager's point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.
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Affiliation(s)
- T P Billam
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - M T Reeves
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - B P Anderson
- College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - A S Bradley
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
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15
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Fisher SN, Jackson MJ, Sergeev YA, Tsepelin V. Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3He-B. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4659-66. [PMID: 24704872 PMCID: PMC3970857 DOI: 10.1073/pnas.1312543110] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Andreev reflection of quasiparticle excitations provides a sensitive and passive probe of flow in superfluid (3)He-B. It is particularly useful for studying complex flows generated by vortex rings and vortex tangles (quantum turbulence). We describe the reflection process and discuss the results of numerical simulations of Andreev reflection from vortex rings and from quantum turbulence. We present measurements of vortices generated by a vibrating grid resonator at very low temperatures. The Andreev reflection is measured using an array of vibrating wire sensors. At low grid velocities, ballistic vortex rings are produced. At higher grid velocities, the rings collide and reconnect to produce quantum turbulence. We discuss spatial correlations of the fluctuating vortex signals measured by the different sensor wires. These reveal detailed information about the formation of quantum turbulence and about the underlying vortex dynamics.
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Affiliation(s)
- Shaun Neil Fisher
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Martin James Jackson
- Faculty of Mathematics and Physics, Charles University in Prague, 121 16 Prague, Czech Republic
| | - Yuri A. Sergeev
- School of Mechanical and Systems Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom; and
- Joint Quantum Centre Durham–Newcastle, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Viktor Tsepelin
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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16
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Berloff NG, Brachet M, Proukakis NP. Modeling quantum fluid dynamics at nonzero temperatures. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4675-82. [PMID: 24704874 PMCID: PMC3970864 DOI: 10.1073/pnas.1312549111] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.
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Affiliation(s)
- Natalia G. Berloff
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Cambridge-Skoltech Quantum Fluids Laboratory, Skolkovo Institute of Science and Technology ul. Novaya, Skolkovo 143025, Russian Federation
| | - Marc Brachet
- Centre National de la Recherche Scientifique, Laboratoire de Physique Statistique, Université Pierre-et-Marie-Curie Paris 06, Université Paris Diderot, Ecole Normale Supérieure, 75231 Paris Cedex 05, France; and
| | - Nick P. Proukakis
- Joint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
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17
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Fonda E, Meichle DP, Ouellette NT, Hormoz S, Lathrop DP. Direct observation of Kelvin waves excited by quantized vortex reconnection. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4707-10. [PMID: 24704878 PMCID: PMC3970858 DOI: 10.1073/pnas.1312536110] [Citation(s) in RCA: 115] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid (4)He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system.
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Affiliation(s)
- Enrico Fonda
- Institute for Research in Electronics and Applied Physics and
- Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, 34127 Trieste, Italy
- Department of Physics, New York University, New York, NY 10003
| | - David P. Meichle
- Institute for Research in Electronics and Applied Physics and
- Department of Physics, University of Maryland, College Park, MD 20742
| | - Nicholas T. Ouellette
- Institute for Research in Electronics and Applied Physics and
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520; and
| | - Sahand Hormoz
- Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106
| | - Daniel P. Lathrop
- Institute for Research in Electronics and Applied Physics and
- Department of Physics, University of Maryland, College Park, MD 20742
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18
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White AC, Anderson BP, Bagnato VS. Vortices and turbulence in trapped atomic condensates. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4719-26. [PMID: 24704880 PMCID: PMC3970853 DOI: 10.1073/pnas.1312737110] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
After more than a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices, and superfluidity and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates.
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Affiliation(s)
- Angela C. White
- Joint Quantum Centre (JQC), Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Brian P. Anderson
- College of Optical Sciences, University of Arizona, Tucson, AZ 85721; and
| | - Vanderlei S. Bagnato
- Instituto de Física de São Carlos, Universidade de São Paulo 13560-970 São Carlos, Sao Paulo, Brazil
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Barenghi CF, Skrbek L, Sreenivasan KR. Introduction to quantum turbulence. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4647-52. [PMID: 24704870 PMCID: PMC3970860 DOI: 10.1073/pnas.1400033111] [Citation(s) in RCA: 194] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
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.
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Affiliation(s)
- Carlo F. Barenghi
- Joint Quantum Centre Durham-Newcastle and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Ladislav Skrbek
- Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic; and
| | - Katepalli R. Sreenivasan
- Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
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Abstract
Cryogenic flow visualization techniques have been proved in recent years to be a very powerful experimental method to study superfluid turbulence. Micron-sized solid particles and metastable helium molecules are specifically being used to investigate in detail the dynamics of quantum flows. These studies belong to a well-established, interdisciplinary line of inquiry that focuses on the deeper understanding of turbulence, one of the open problem of modern physics, relevant to many research fields, ranging from fluid mechanics to cosmology. Progress made to date is discussed, to highlight its relevance to a wider scientific community, and future directions are outlined. The latter include, e.g., detailed studies of normal-fluid turbulence, dissipative mechanisms, and unsteady/oscillatory flows.
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Baggaley AW, Barenghi CF. Acceleration statistics in thermally driven superfluid turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:033006. [PMID: 24730936 DOI: 10.1103/physreve.89.033006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Indexed: 06/03/2023]
Abstract
New methods of flow visualization near absolute zero have opened the way to directly compare quantum turbulence (in superfluid helium) to classical turbulence (in ordinary fluids such as air or water) and explore analogies and differences. We present results of numerical simulations in which we examine the statistics of the superfluid acceleration in thermal counterflow. We find that, unlike the velocity, the acceleration obeys scaling laws similar to classical turbulence, in agreement with a recent quantum turbulence experiment of La Mantia et al.
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Affiliation(s)
- Andrew W Baggaley
- School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, United Kingdom
| | - Carlo F Barenghi
- Joint Quantum Centre Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
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Varga E, Barenghi CF, Sergeev YA, Skrbek L. Two-dimensional simulation of vortex points and tracer particles in counterflowing He-II. EPJ WEB OF CONFERENCES 2014. [DOI: 10.1051/epjconf/20146702124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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La Mantia M, Duda D, Rotter M, Skrbek L. Lagrangian velocity distributions in thermal counterflow of superfluid 4He. EPJ WEB OF CONFERENCES 2013. [DOI: 10.1051/epjconf/20134501005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Reeves MT, Billam TP, Anderson BP, Bradley AS. Inverse energy cascade in forced two-dimensional quantum turbulence. PHYSICAL REVIEW LETTERS 2013; 110:104501. [PMID: 23521262 DOI: 10.1103/physrevlett.110.104501] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2012] [Indexed: 06/01/2023]
Abstract
We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a stationary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of same-circulation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids.
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Affiliation(s)
- Matthew T Reeves
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
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Krstulovic G. Kelvin-wave cascade and dissipation in low-temperature superfluid vortices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:055301. [PMID: 23214835 DOI: 10.1103/physreve.86.055301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2012] [Revised: 09/26/2012] [Indexed: 06/01/2023]
Abstract
We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked. This procedure directly allows us to obtain the Kevin-wave occupation-number spectrum. Numerical data obtained from long time integration and ensemble average over initial conditions support the spectrum proposed in L'vov and Nazarenko [JETP Lett. 91, 428 (2010)]. Kelvin-wave modes in the inertial range are found to be Gaussian as expected by weak-turbulence predictions. Finally the dissipative range of the Kelvin-wave spectrum is studied. Strong non-Gaussian fluctuations are observed in this range.
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Affiliation(s)
- Giorgio Krstulovic
- Laboratoire Lagrange, UMR7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
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Angheluta L, Jeraldo P, Goldenfeld N. Anisotropic velocity statistics of topological defects under shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011153. [PMID: 22400558 DOI: 10.1103/physreve.85.011153] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2011] [Indexed: 05/31/2023]
Abstract
We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and nonrelaxational evolution assisted by an external shear flow. We propose a numerically efficient tracking method for finding the position and velocity of defects and apply it to vortices in a uniform field and dislocations in anisotropic stripe patterns. During relaxational dynamics, the distribution function of the velocity fluctuations is characterized by a dynamical scaling with a scaling function that has a robust algebraic tail with an inverse cube power law. This is characteristic of defects of codimension 2, e.g., point defects in two dimensions and filaments in three dimensions, regardless of whether the motion is isotropic (as for vortices) or highly anisotropic (as for dislocations). However, the anisotropic dislocation motion leads to anisotropic statistical properties when the interaction between defects and their motion is influenced by the presence of an external shear flow transverse to the stripe orientation.
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Affiliation(s)
- Luiza Angheluta
- Physics of Geological Processes, Department of Physics, University of Oslo, 0316 Oslo, Norway
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Baggaley AW, Barenghi CF. Quantum turbulent velocity statistics and quasiclassical limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:067301. [PMID: 22304221 DOI: 10.1103/physreve.84.067301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2011] [Revised: 11/16/2011] [Indexed: 05/31/2023]
Abstract
Two research groups have measured turbulent velocity statistics in superfluid helium using different techniques. The results were in conflict: one experiment revealed Gaussian distributions (as observed in ordinary turbulence), the other experiment determined power laws. To solve the apparent puzzle, we numerically model quantum turbulence as a tangle of vortex filaments, and conclude that there is no contradiction between the two experiments. The transition from Gaussian to power law arises from the different length scales which are probed using the two techniques. We find that the average distance between the quantum vortices marks the separation between quantum and quasiclassical length scales.
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Affiliation(s)
- A W Baggaley
- School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
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Takeuchi H, Ishino S, Tsubota M. Binary quantum turbulence arising from countersuperflow instability in two-component Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2010; 105:205301. [PMID: 21231243 DOI: 10.1103/physrevlett.105.205301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2010] [Revised: 10/06/2010] [Indexed: 05/30/2023]
Abstract
We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the countersuperflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.
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Affiliation(s)
- Hiromitsu Takeuchi
- Department of Physics, Osaka City University, Sumiyoshi-ku, Osaka 558-8585, Japan
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