1
|
Skipp J, Laurie J, Nazarenko S. Hamiltonian derivation of the point vortex model from the two-dimensional nonlinear Schrödinger equation. Phys Rev E 2023; 107:025107. [PMID: 36932471 DOI: 10.1103/physreve.107.025107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 02/01/2023] [Indexed: 03/19/2023]
Abstract
We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex.
Collapse
Affiliation(s)
- Jonathan Skipp
- Department of Mathematics, College of Engineering and Physical Sciences, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom
| | - Jason Laurie
- Department of Mathematics, College of Engineering and Physical Sciences, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Parc Valrose, 06108 Nice, France
| |
Collapse
|
2
|
Kanai T, Guo W. True Mechanism of Spontaneous Order from Turbulence in Two-Dimensional Superfluid Manifolds. PHYSICAL REVIEW LETTERS 2021; 127:095301. [PMID: 34506186 DOI: 10.1103/physrevlett.127.095301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
In a 2D turbulent fluid containing pointlike vortices, Lars Onsager predicted that adding energy to the fluid can lead to the formation of persistent clusters of like-signed vortices, i.e., Onsager vortex (OV) clusters. In the evolution of 2D superfluid turbulence in a uniform disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV clusters with opposite signs can form without any energy input. This striking spontaneous order was explained as being due to a vortex evaporative-heating mechanism, i.e., annihilations of vortex-antivortex pairs which remove the lowest-energy vortices and thereby boost the mean energy per vortex. However, in our search for exotic OV states in a boundaryless 2D spherical BEC, we found that OV clusters never form despite the annihilations of vortex pairs. Our analysis reveals that contrary to the general belief, vortex-pair annihilation emits intense sound waves, which damp the motion of all vortices and hence suppress the formation of OV clusters. We also present unequivocal evidence showing that the true mechanism underlying the observed spontaneous OV state is the vortices exiting the BEC boundaries. Uncovering this mechanism paves the way for a comprehensive understanding of emergent vortex orders in 2D manifolds of superfluids driven far from equilibrium.
Collapse
Affiliation(s)
- Toshiaki Kanai
- National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, USA
- Department of Physics, Florida State University, Tallahassee, Florida 32306, 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
| |
Collapse
|
3
|
van Kan A, Alexakis A, Brachet ME. Intermittency of three-dimensional perturbations in a point-vortex model. Phys Rev E 2021; 103:053102. [PMID: 34134270 DOI: 10.1103/physreve.103.053102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.
Collapse
Affiliation(s)
- Adrian van Kan
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Marc-Etienne Brachet
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| |
Collapse
|
4
|
Doran R, Billam TP. Numerical method for the projected Gross-Pitaevskii equation in an infinite rotating two-dimensional Bose gas. Phys Rev E 2020; 102:033309. [PMID: 33075866 DOI: 10.1103/physreve.102.033309] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 08/17/2020] [Indexed: 11/07/2022]
Abstract
We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasiperiodic boundary conditions to investigate the behavior of the bulk superfluid in this system, in the absence of boundaries and edge effects. We also give the Landau gauge expression for the phase of a BEC subjected to these boundary conditions. Our spectral representation uses the eigenfunctions of the one-body Hamiltonian as basis functions. Since there is no known exact quadrature rule for these basis functions we approximately implement the projection associated with the energy cutoff, but we show that by choosing a suitably fine spatial grid the resulting error can be made negligible. We show how the convergence of this model is affected by simulation parameters such as the size of the spatial grid and the number of Landau levels. Adding dissipation, we use our method to find the lattice ground state for N vortices. We can then perturb the ground-state, to investigate the melting of the lattice.
Collapse
Affiliation(s)
- R Doran
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - T P Billam
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| |
Collapse
|
5
|
Müller NP, Brachet ME, Alexakis A, Mininni PD. Abrupt Transition between Three-Dimensional and Two-Dimensional Quantum Turbulence. PHYSICAL REVIEW LETTERS 2020; 124:134501. [PMID: 32302183 DOI: 10.1103/physrevlett.124.134501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Revised: 02/06/2020] [Accepted: 03/07/2020] [Indexed: 06/11/2023]
Abstract
We present numerical evidence of a critical-like transition in an out-of-equilibrium mean-field description of a quantum system. By numerically solving the Gross-Pitaevskii equation we show that quantum turbulence displays an abrupt change between three-dimensional (3D) and two-dimensional (2D) behavior. The transition is observed both in quasi-2D flows in cubic domains (controlled by the amplitude of a 3D perturbation to the flow), as well as in flows in thin domains (controlled by the domain aspect ratio) in a configuration that mimics systems realized in laboratory experiments. In one regime the system displays a transfer of the energy towards smaller scales, while in the other the system displays a transfer of the energy towards larger scales and a coherent self-organization of the quantized vortices.
Collapse
Affiliation(s)
- Nicolás P Müller
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, & IFIBA, CONICET, Ciudad Universitaria, Buenos Aires 1428, Argentina
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France
| | - Marc-Etienne Brachet
- Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Pablo D Mininni
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, & IFIBA, CONICET, Ciudad Universitaria, Buenos Aires 1428, Argentina
| |
Collapse
|
6
|
Curtis CW, Carretero-González R, Polimeno M. Characterizing coherent structures in Bose-Einstein condensates through dynamic-mode decomposition. Phys Rev E 2019; 99:062215. [PMID: 31330623 DOI: 10.1103/physreve.99.062215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 11/07/2022]
Abstract
We use the dynamic mode decomposition (DMD) methodology to study weakly turbulent flows in two-dimensional Bose-Einstein condensates modeled by a Gross-Pitaevskii equation subject to band-limited stochastic forcing. The forcing is balanced by the removal of energy at both ends of the energy spectrum through phenomenological hypoviscosity and hyperviscosity terms. Using different combinations of these parameters, we simulate three different regimes corresponding to weak-wave turbulence, and high- and low-frequency saturation. By extracting and ranking the primary DMD modes carrying the bulk of the energy, we are able to characterize the different regimes. In particular, the proposed DMD mode projection is able to seamlessly extract the vortices present in the condensate. This is achieved despite the fact that we do not use any phase information of the condensate as it is usually not directly available in realistic atomic BEC scenarios. Being model independent, this DMD methodology should be portable to other models and experiments involving complex flows. The DMD implementation could be used to elucidate different types of turbulent regimes as well as identifying and pinpointing the existence of delicate and hidden coherent structures within complex flows.
Collapse
Affiliation(s)
- Christopher W Curtis
- Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA.,Computational Sciences Research Center, San Diego State University, San Diego, California 92182-7720, USA
| | - R Carretero-González
- Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA.,Computational Sciences Research Center, San Diego State University, San Diego, California 92182-7720, USA
| | - Matteo Polimeno
- Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA
| |
Collapse
|
7
|
Gauthier G, Reeves MT, Yu X, Bradley AS, Baker MA, Bell TA, Rubinsztein-Dunlop H, Davis MJ, Neely TW. Giant vortex clusters in a two-dimensional quantum fluid. Science 2019; 364:1264-1267. [DOI: 10.1126/science.aat5718] [Citation(s) in RCA: 86] [Impact Index Per Article: 17.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Accepted: 06/06/2019] [Indexed: 11/02/2022]
Abstract
Adding energy to a system through transient stirring usually leads to more disorder. In contrast, point-like vortices in a bounded two-dimensional fluid are predicted to reorder above a certain energy, forming persistent vortex clusters. In this study, we experimentally realize these vortex clusters in a planar superfluid: a 87Rb Bose-Einstein condensate confined to an elliptical geometry. We demonstrate that the clusters persist for long time periods, maintaining the superfluid system in a high-energy state far from global equilibrium. Our experiments explore a regime of vortex matter at negative absolute temperatures and have relevance for the dynamics of topological defects, two-dimensional turbulence, and systems such as helium films, nonlinear optical materials, fermion superfluids, and quark-gluon plasmas.
Collapse
Affiliation(s)
- Guillaume Gauthier
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Matthew T. Reeves
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Xiaoquan Yu
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - Ashton S. Bradley
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9016, New Zealand
| | - Mark A. Baker
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Thomas A. Bell
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Halina Rubinsztein-Dunlop
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Matthew J. Davis
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| | - Tyler W. Neely
- Australian Research Council Centre of Excellence for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St. Lucia, QLD 4072, Australia
| |
Collapse
|
8
|
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.
Collapse
|
9
|
Groszek AJ, Davis MJ, Paganin DM, Helmerson K, Simula TP. Vortex Thermometry for Turbulent Two-Dimensional Fluids. PHYSICAL REVIEW LETTERS 2018; 120:034504. [PMID: 29400494 DOI: 10.1103/physrevlett.120.034504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Indexed: 06/07/2023]
Abstract
We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.165302, and we find previously unidentified vortex power-law distributions that emerge from the dynamics.
Collapse
Affiliation(s)
- Andrew J Groszek
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Matthew J Davis
- School of Mathematics and Physics, University of Queensland, Queensland 4072, Australia
| | - David M Paganin
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Kristian Helmerson
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Tapio P Simula
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| |
Collapse
|
10
|
Reeves MT, Billam TP, Yu X, Bradley AS. Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence. PHYSICAL REVIEW LETTERS 2017; 119:184502. [PMID: 29219534 DOI: 10.1103/physrevlett.119.184502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Indexed: 06/07/2023]
Abstract
We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying two-dimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a single length scale, the dynamics are found to be well characterized by a superfluid Reynolds number Re_{s} that depends only on the number of vortices and the initial kinetic energy scale. Under free evolution the vortices exhibit features of a classical enstrophy cascade, including a k^{-3} power-law kinetic energy spectrum, and constant enstrophy flux associated with inertial transport to small scales. Clear signatures of the cascade emerge for N≳500 vortices. Simulating up to very large Reynolds numbers (N=32 768 vortices), additional features of the classical theory are observed: the Kraichnan-Batchelor constant is found to converge to C^{'}≈1.6, and the width of the k^{-3} range scales as Re_{s}^{1/2}.
Collapse
Affiliation(s)
- Matthew T Reeves
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, QLD 4072, Australia
| | - Thomas P Billam
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Xiaoquan Yu
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand
| | - Ashton S Bradley
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand
| |
Collapse
|
11
|
Yu X, Bradley AS. Emergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions. PHYSICAL REVIEW LETTERS 2017; 119:185301. [PMID: 29219559 DOI: 10.1103/physrevlett.119.185301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 06/07/2023]
Abstract
We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Euler's equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement with numerical simulations of the point-vortex model.
Collapse
Affiliation(s)
- Xiaoquan Yu
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9054, New Zealand
| | - Ashton S Bradley
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9054, New Zealand
| |
Collapse
|
12
|
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.
Collapse
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.
| |
Collapse
|
13
|
Martin AM, Marchant NG, O'Dell DHJ, Parker NG. Vortices and vortex lattices in quantum ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:103004. [PMID: 28145899 DOI: 10.1088/1361-648x/aa53a6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
Collapse
Affiliation(s)
- A M Martin
- School of Physics, University of Melbourne, Victoria 3010, Australia
| | | | | | | |
Collapse
|
14
|
Reeves MT, Billam TP, Anderson BP, Bradley AS. Identifying a Superfluid Reynolds Number via Dynamical Similarity. PHYSICAL REVIEW LETTERS 2015; 114:155302. [PMID: 25933320 DOI: 10.1103/physrevlett.114.155302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2014] [Indexed: 06/04/2023]
Abstract
The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, Re(s), that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at Re(s)≈0.7, irrespective of obstacle width.
Collapse
Affiliation(s)
- M T Reeves
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - T P Billam
- Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom
| | - 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
| |
Collapse
|
15
|
Simula T, Davis MJ, Helmerson K. Emergence of order from turbulence in an isolated planar superfluid. PHYSICAL REVIEW LETTERS 2014; 113:165302. [PMID: 25361262 DOI: 10.1103/physrevlett.113.165302] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2014] [Indexed: 06/04/2023]
Abstract
We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation the remaining vortices self-organize into two macroscopic coherent "Onsager vortex" clusters that are stable indefinitely--despite the absence of driving or external dissipation in the dynamics. We demonstrate that this occurs due to a novel physical mechanism--the evaporative heating of the vortices--that results in a negative-temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a nonthermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.
Collapse
Affiliation(s)
- Tapio Simula
- School of Physics, Monash University, Victoria 3800, Australia
| | - Matthew J Davis
- School of Mathematics and Physics, University of Queensland, Queensland 4072, Australia
| | | |
Collapse
|
16
|
Powis AT, Sammut SJ, Simula TP. Vortex gyroscope imaging of planar superfluids. PHYSICAL REVIEW LETTERS 2014; 113:165303. [PMID: 25361263 DOI: 10.1103/physrevlett.113.165303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2014] [Indexed: 06/04/2023]
Abstract
We propose a robust imaging technique that makes it possible to distinguish vortices from antivortices in quasi-two-dimensional Bose-Einstein condensates from a single image of the density of the atoms. Tilting the planar condensate prior to standard absorption imaging excites a generalized gyroscopic mode of the condensate, revealing the sign and location of each vortex. This technique is anticipated to enable experimental measurement of the incompressible kinetic energy spectrum of the condensate and the observation of a negative-temperature phase transition of the vortex gas, driven by two-dimensional superfluid turbulence.
Collapse
Affiliation(s)
- A T Powis
- School of Physics, Monash University, Victoria 3800, Australia
| | - S J Sammut
- School of Physics, Monash University, Victoria 3800, Australia
| | - T P Simula
- School of Physics, Monash University, Victoria 3800, Australia
| |
Collapse
|