1
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Zhu Y, Semisalov B, Krstulovic G, Nazarenko S. Self-similar evolution of wave turbulence in Gross-Pitaevskii system. Phys Rev E 2023; 108:064207. [PMID: 38243462 DOI: 10.1103/physreve.108.064207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 11/22/2023] [Indexed: 01/21/2024]
Abstract
We study the universal nonstationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively. In both the GPE and the WKE simulations for the direct cascade, we observe the first-kind self-similarity that is fully determined by energy conservation. For the inverse cascade evolution, we verify the existence of a self-similar evolution of the second kind describing self-accelerating dynamics of the spectrum leading to blowup at the zero mode (condensate) at a finite time. We believe that the universal self-similar spectra found in the present paper are as important and relevant for understanding the BEC turbulence in past and future experiments as the commonly studied stationary Kolmogorov-Zakharov (KZ) spectra.
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Affiliation(s)
- Ying Zhu
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 17 rue Julien Lauprêtre 06200 Nice, France
| | - Boris Semisalov
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
- Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Avenue, 630090 Novosibirsk, Russia
- Federal Research Center for Information and Computational Technologies, 6 Academician Lavrentyev Avenue, 630090 Novosibirsk, Russia
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 17 rue Julien Lauprêtre 06200 Nice, France
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2
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Berti N, Baudin K, Fusaro A, Millot G, Picozzi A, Garnier J. Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers. PHYSICAL REVIEW LETTERS 2022; 129:063901. [PMID: 36018655 DOI: 10.1103/physrevlett.129.063901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.
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Affiliation(s)
- Nicolas Berti
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | - Kilian Baudin
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | | | - Guy Millot
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
- Institut Universitaire de France (IUF), 1 Rue Descartes, 75005 Paris, France
| | - Antonio Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | - Josselin Garnier
- CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
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3
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Gorce JB, Falcon E. Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence. PHYSICAL REVIEW LETTERS 2022; 129:054501. [PMID: 35960568 DOI: 10.1103/physrevlett.129.054501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 04/27/2022] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our Letter paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.
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Affiliation(s)
- Jean-Baptiste Gorce
- Université Paris Cité, CNRS, MSC Laboratory, UMR 7057, F-75013 Paris, France
| | - Eric Falcon
- Université Paris Cité, CNRS, MSC Laboratory, UMR 7057, F-75013 Paris, France
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4
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Zhu Y, Semisalov B, Krstulovic G, Nazarenko S. Testing wave turbulence theory for the Gross-Pitaevskii system. Phys Rev E 2022; 106:014205. [PMID: 35974496 DOI: 10.1103/physreve.106.014205] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the combination of a breakdown of the theoretical assumptions underlying the WKE as well as numerical issues. Furthermore, we study how the wave statistics evolves toward Gaussianity in a timescale of the order of the kinetic time. The excellent agreement between direct numerical simulations of the GPE and the WKE provides a solid foundation to the theory of weak wave turbulence.
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Affiliation(s)
- Ying Zhu
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| | - Boris Semisalov
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229 - F 06304 Nice Cedex 4, France
- Novosibirsk State University, 1 Pirogova street, 630090 Novosibirsk, Russia
- Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Avenue, 630090 Novosibirsk, Russia
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229 - F 06304 Nice Cedex 4, France
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
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5
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Podivilov EV, Mangini F, Sidelnikov OS, Ferraro M, Gervaziev M, Kharenko DS, Zitelli M, Fedoruk MP, Babin SA, Wabnitz S. Thermalization of Orbital Angular Momentum Beams in Multimode Optical Fibers. PHYSICAL REVIEW LETTERS 2022; 128:243901. [PMID: 35776459 DOI: 10.1103/physrevlett.128.243901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2021] [Revised: 04/20/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
We report on the thermalization of light carrying orbital angular momentum in multimode optical fibers, induced by nonlinear intermodal interactions. A generalized Rayleigh-Jeans distribution of asymptotic mode composition is obtained, based on the conservation of the angular momentum. We confirm our predictions by numerical simulations and experiments based on holographic mode decomposition of multimode beams. Our work establishes new constraints for the achievement of spatial beam self-cleaning, giving previously unforeseen insights into the underlying physical mechanisms.
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Affiliation(s)
- E V Podivilov
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - F Mangini
- Department of Information Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - O S Sidelnikov
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - M Ferraro
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - M Gervaziev
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - D S Kharenko
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - M Zitelli
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - M P Fedoruk
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - S A Babin
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - S Wabnitz
- Novosibirsk State University, Novosibirsk 630090, Russia
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
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6
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Świsłocki T, Gajda M, Brewczyk M, Deuar P. Spin distillation cooling of ultracold Bose gases. Sci Rep 2021; 11:6441. [PMID: 33742005 PMCID: PMC7979932 DOI: 10.1038/s41598-021-85298-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 02/23/2021] [Indexed: 12/03/2022] Open
Abstract
We study the spin distillation of spinor gases of bosonic atoms and find two different mechanisms in [Formula: see text]Cr and [Formula: see text]Na atoms, both of which can cool effectively. The first mechanism involves dipolar scattering into initially unoccupied spin states and cools only above a threshold magnetic field. The second proceeds via equilibrium relaxation of the thermal cloud into empty spin states, reducing its proportion in the initial component. It cools only below a threshold magnetic field. The technique was initially demonstrated experimentally for a chromium dipolar gas (Naylor et al. in Phys Rev Lett 115:243002, 2015), whereas here we develop the concept further and provide an in-depth understanding of the required physics and limitations involved. Through numerical simulations, we reveal the mechanisms involved and demonstrate that the spin distillation cycle can be repeated several times, each time resulting in a significant additional reduction of the thermal atom fraction. Threshold values of magnetic field and predictions for the achievable temperature are also identified.
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Affiliation(s)
- Tomasz Świsłocki
- Institute of Information Technology, Warsaw University of Life Sciences - SGGW, ul. Nowoursynowska 159, 02786, Warsaw, Poland.
| | - Mariusz Gajda
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warsaw, Poland
| | - Mirosław Brewczyk
- Wydział Fizyki, Uniwersytet w Białymstoku, ul. K. Ciołkowskiego 1L, 15245, Białystok, Poland
| | - Piotr Deuar
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warsaw, Poland
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7
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Baudin K, Fusaro A, Krupa K, Garnier J, Rica S, Millot G, Picozzi A. Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization. PHYSICAL REVIEW LETTERS 2020; 125:244101. [PMID: 33412051 DOI: 10.1103/physrevlett.125.244101] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 09/25/2020] [Accepted: 11/16/2020] [Indexed: 06/12/2023]
Abstract
Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.
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Affiliation(s)
- K Baudin
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
| | - A Fusaro
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
- CEA, DAM, DIF, F-91297 Arpajon Cedex, France
| | - K Krupa
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
- Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Poland
| | - J Garnier
- CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - S Rica
- Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén, 7910000, Santiago, Chile
| | - G Millot
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
- Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France
| | - A Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
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8
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Falcon E, Michel G, Prabhudesai G, Cazaubiel A, Berhanu M, Mordant N, Aumaître S, Bonnefoy F. Saturation of the Inverse Cascade in Surface Gravity-Wave Turbulence. PHYSICAL REVIEW LETTERS 2020; 125:134501. [PMID: 33034484 DOI: 10.1103/physrevlett.125.134501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the observation of surface gravity-wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity-wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-crested waves.
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Affiliation(s)
- E Falcon
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - G Michel
- Sorbonne Université, IJLRA, UMR 7190 CNRS, F-75 005 Paris, France
| | - G Prabhudesai
- Ecole Normale Supérieure, LPS, UMR 8550 CNRS, F-75 205 Paris, France
| | - A Cazaubiel
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - M Berhanu
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - N Mordant
- Université Grenoble Alpes, LEGI, UMR 5519 CNRS, F-38 000 Grenoble, France
| | - S Aumaître
- CEA-Saclay, Sphynx, DSM, URA 2464 CNRS, F-91 191 Gif-sur-Yvette, France
| | - F Bonnefoy
- Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
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9
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Fusaro A, Garnier J, Krupa K, Millot G, Picozzi A. Dramatic Acceleration of Wave Condensation Mediated by Disorder in Multimode Fibers. PHYSICAL REVIEW LETTERS 2019; 122:123902. [PMID: 30978031 DOI: 10.1103/physrevlett.122.123902] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Indexed: 06/09/2023]
Abstract
Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. However, achieving complete thermalization and condensation of incoherent waves through nonlinear optical propagation is known to require prohibitive large interaction lengths. Here, we derive a discrete kinetic equation describing the nonequilibrium evolution of the random wave in the presence of a structural disorder of the medium. Our theory reveals that a weak disorder accelerates the rate of thermalization and condensation by several order of magnitudes. Such a counterintuitive dramatic acceleration of condensation can provide a natural explanation for the recently discovered phenomenon of optical beam self-cleaning. Our experiments in multimode optical fibers report the observation of the transition from an incoherent thermal distribution to wave condensation, with a condensate fraction of up to 60% in the fundamental mode of the waveguide trapping potential.
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Affiliation(s)
- Adrien Fusaro
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
| | - Josselin Garnier
- Centre de Mathematiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France
| | - Katarzyna Krupa
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
- Dipartimento di Ingegneria dell'Informazione, Università di Brescia, via Branze 38, 25123, Brescia, Italy
| | - Guy Millot
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
| | - Antonio Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France
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10
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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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11
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Veltmaat J, Niemeyer JC, Schwabe B. Formation and structure of ultralight bosonic dark matter halos. Int J Clin Exp Med 2018. [DOI: 10.1103/physrevd.98.043509] [Citation(s) in RCA: 96] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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Sich M, Chana JK, Egorov OA, Sigurdsson H, Shelykh IA, Skryabin DV, Walker PM, Clarke E, Royall B, Skolnick MS, Krizhanovskii DN. Transition from Propagating Polariton Solitons to a Standing Wave Condensate Induced by Interactions. PHYSICAL REVIEW LETTERS 2018; 120:167402. [PMID: 29756939 DOI: 10.1103/physrevlett.120.167402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Indexed: 06/08/2023]
Abstract
We explore phase transitions of polariton wave packets, first, to a soliton and then to a standing wave polariton condensate in a multimode microwire system, mediated by nonlinear polariton interactions. At low excitation density, we observe ballistic propagation of the multimode polariton wave packets arising from the interference between different transverse modes. With increasing excitation density, the wave packets transform into single-mode bright solitons due to effects of both intermodal and intramodal polariton-polariton scattering. Further increase of the excitation density increases thermalization speed, leading to relaxation of the polariton density from a solitonic spectrum distribution in momentum space down to low momenta, with the resultant formation of a nonequilibrium condensate manifested by a standing wave pattern across the whole sample.
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Affiliation(s)
- M Sich
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - J K Chana
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
- Base4 Innovation, Ltd., Cambridge CB3 0FA, United Kingdom
| | - O A Egorov
- Technische Physik der Universität Würzburg, Am Hubland 97074, Würzburg, Germany
| | - H Sigurdsson
- Science Institute, University of Iceland, Dunhagi-3, IS-107 Reykjavik, Iceland
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, IS-107 Reykjavik, Iceland
- Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia
| | - D V Skryabin
- Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - P M Walker
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - E Clarke
- EPSRC National Centre for III-V Technologies, The University of Sheffield, Sheffield S1 4DE, United Kingdom
| | - B Royall
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
| | - M S Skolnick
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
- Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia
| | - D N Krizhanovskii
- Department of Physics and Astronomy, The University of Sheffield, Sheffield S3 7RH, United Kingdom
- Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia
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13
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Castillo G, Falcón C. Generation of intermittent gravitocapillary waves via parametric forcing. Phys Rev E 2018; 97:043101. [PMID: 29758672 DOI: 10.1103/physreve.97.043101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2016] [Indexed: 06/08/2023]
Abstract
We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for a wide range of forcing parameters. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power laws as a function of the time lag, with exponents that are nonlinear functions of the order of the structure function. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves. Finally, some interpretations are proposed to explain the appearance of this intermittent spectrum.
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Affiliation(s)
- Gustavo Castillo
- Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile
| | - Claudio Falcón
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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14
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Šantić N, Fusaro A, Salem S, Garnier J, Picozzi A, Kaiser R. Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors. PHYSICAL REVIEW LETTERS 2018; 120:055301. [PMID: 29481198 DOI: 10.1103/physrevlett.120.055301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Indexed: 06/08/2023]
Abstract
The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.
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Affiliation(s)
- Neven Šantić
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
- Institute of Physics, Bijenička cesta 46, 10000 Zagreb, Croatia
| | - Adrien Fusaro
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, Dijon 21078, France
| | - Sabeur Salem
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
| | - Josselin Garnier
- Centre de Mathematiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France
| | - Antonio Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, Dijon 21078, France
| | - Robin Kaiser
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
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15
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Weill R, Bekker A, Levit B, Zhurahov M, Fischer B. Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers. OPTICS EXPRESS 2017; 25:18963-18973. [PMID: 29041087 DOI: 10.1364/oe.25.018963] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Accepted: 07/18/2017] [Indexed: 06/07/2023]
Abstract
We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.
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16
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Fukushima K. Evolution to the quark-gluon plasma. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:022301. [PMID: 27992382 DOI: 10.1088/1361-6633/80/2/022301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Theoretical studies on the early-time dynamics in the ultra-relativistic heavy-ion collisions are reviewed, including pedagogical introductions on the initial condition with small-[Formula: see text] gluons treated as a color glass condensate, the bottom-up thermalization scenario, plasma/glasma instabilities, basics of some formulations such as the kinetic equations and the classical statistical simulation. More detailed discussions follow to make an overview of recent developments on the fast isotropization, the onset of hydrodynamics, and the transient behavior of momentum spectral cascades.
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Affiliation(s)
- Kenji Fukushima
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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17
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Akhmediev N, Soto-Crespo JM, Devine N. Breather turbulence versus soliton turbulence: Rogue waves, probability density functions, and spectral features. Phys Rev E 2016; 94:022212. [PMID: 27627303 DOI: 10.1103/physreve.94.022212] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Indexed: 06/06/2023]
Abstract
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics.
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Affiliation(s)
- N Akhmediev
- Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia
| | - J M Soto-Crespo
- Instituto de Óptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain
| | - N Devine
- Optical Sciences Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia
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18
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Zhurahov M, Bekker A, Levit B, Weill R, Fischer B. CW laser light condensation. OPTICS EXPRESS 2016; 24:6553-6558. [PMID: 27136845 DOI: 10.1364/oe.24.006553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a first experimental demonstration of classical CW laser light condensation (LC) in the frequency (mode) domain that verifies its prediction (Fischer and Weill, Opt. Express20, 26704 (2012)). LC is based on weighting the modes in a noisy environment in a loss-gain measure compared to an energy (frequency) scale in Bose-Einstein condensation (BEC). It is characterized by a sharp transition from multi- to single-mode oscillation, occurring when the spectral-filtering (loss-trap) has near the lowest-loss mode ("ground-state") a power-law dependence with an exponent smaller than 1. An important meaning of the many-mode LC system stems from its relation to lasing and photon-BEC.
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19
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Rückriegel A, Kopietz P. Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets. PHYSICAL REVIEW LETTERS 2015; 115:157203. [PMID: 26550749 DOI: 10.1103/physrevlett.115.157203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2015] [Indexed: 06/05/2023]
Abstract
We show that the formation of a magnon condensate in thin ferromagnetic films can be explained within the framework of a classical stochastic non-Markovian Landau-Lifshitz-Gilbert equation where the properties of the random magnetic field and the dissipation are determined by the underlying phonon dynamics. We have numerically solved this equation for a tangentially magnetized yttrium-iron garnet film in the presence of a parallel parametric pumping field. We obtain a complete description of all stages of the nonequilibrium time evolution of the magnon gas which is in excellent agreement with experiments. Our calculation proves that the experimentally observed condensation of magnons in yttrium-iron garnet at room temperature is a purely classical phenomenon which should be called Rayleigh-Jeans rather than Bose-Einstein condensation.
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Affiliation(s)
- Andreas Rückriegel
- Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany
| | - Peter Kopietz
- Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany
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20
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Gallet B, Nazarenko S, Dubrulle B. Wave-turbulence description of interacting particles: Klein-Gordon model with a Mexican-hat potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012909. [PMID: 26274249 DOI: 10.1103/physreve.92.012909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Indexed: 06/04/2023]
Abstract
In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models, one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such waves. Wave turbulence deals with out-of-equilibrium ensembles of weakly nonlinear waves, and is therefore well suited to address this problem. As an example, we consider the complex Klein-Gordon equation with a Mexican-hat potential. This simple equation displays two kinds of excitations around the fundamental state: massive particles and massless Goldstone bosons. The former are waves with a nonzero frequency for vanishing wave number, whereas the latter obey an acoustic dispersion relation. Using wave-turbulence theory, we derive wave kinetic equations that govern the coupled evolution of the spectra of massive and massless waves. We first consider the thermodynamic solutions to these equations and study the wave condensation transition, which is the classical equivalent of Bose-Einstein condensation. We then focus on nonlocal interactions in wave-number space: we study the decay of an ensemble of massive particles into massless ones. Under rather general conditions, these massless particles accumulate at low wave number. We study the dynamics of waves coexisting with such a strong condensate, and we compute rigorously a nonlocal Kolmogorov-Zakharov solution, where particles are transferred nonlocally to the condensate, while energy cascades towards large wave numbers through local interactions. This nonlocal cascading state constitutes the intermediate asymptotics between the initial distribution of waves and the thermodynamic state reached in the long-time limit.
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Affiliation(s)
- Basile Gallet
- Laboratoire SPHYNX, Service de Physique de l'État Condensé, DSM, CEA Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
| | - Sergey Nazarenko
- Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
| | - Bérengère Dubrulle
- Laboratoire SPHYNX, Service de Physique de l'État Condensé, DSM, CEA Saclay, CNRS UMR 3680, 91191 Gif-sur-Yvette, France
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21
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Düring G, Josserand C, Rica S. Self-similar formation of an inverse cascade in vibrating elastic plates. Phys Rev E 2015; 91:052916. [PMID: 26066238 DOI: 10.1103/physreve.91.052916] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Indexed: 11/07/2022]
Abstract
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.
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Affiliation(s)
- Gustavo Düring
- Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
| | - Christophe Josserand
- Sorbonne Universités, CNRS & UPMC Univ Paris 06, UMR 7190, Institut d'Alembert, F-75005, Paris, France
| | - Sergio Rica
- Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén, Santiago, Chile
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22
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Rubio AM, Julien K, Knobloch E, Weiss JB. Upscale energy transfer in three-dimensional rapidly rotating turbulent convection. PHYSICAL REVIEW LETTERS 2014; 112:144501. [PMID: 24765971 DOI: 10.1103/physrevlett.112.144501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Indexed: 06/03/2023]
Abstract
Rotating Rayleigh-Bénard convection exhibits, in the limit of rapid rotation, a turbulent state known as geostrophic turbulence. This state is present for sufficiently large Rayleigh numbers representing the thermal forcing of the system, and is characterized by a leading order balance between the Coriolis force and pressure gradient. This turbulent state is itself unstable to the generation of depth-independent or barotropic vortex structures of ever larger scale through a process known as spectral condensation. This process involves an inverse cascade mechanism with a positive feedback loop whereby large-scale barotropic vortices organize small scale convective eddies. In turn, these eddies provide a dynamically evolving energy source for the large-scale barotropic component. Kinetic energy spectra for the barotropic dynamics are consistent with a k-3 downscale enstrophy cascade and an upscale cascade that steepens to k-3 as the box-scale condensate forms. At the same time the flow maintains a baroclinic convective component with an inertial range consistent with a k-5/3 spectrum. The condensation process resembles a similar process in two dimensions but is fully three-dimensional.
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Affiliation(s)
- Antonio M Rubio
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Keith Julien
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Jeffrey B Weiss
- Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado 80309, USA
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23
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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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24
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Sob'yanin DN. Bose-Einstein condensation of light: general theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022132. [PMID: 24032800 DOI: 10.1103/physreve.88.022132] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2013] [Indexed: 06/02/2023]
Abstract
A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.
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Affiliation(s)
- Denis Nikolaevich Sob'yanin
- Tamm Department of Theoretical Physics, Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospekt 53, Moscow, 119991 Russia
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25
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Fatome J, Pitois S, Morin P, Assémat E, Sugny D, Picozzi A, Jauslin HR, Millot G, Kozlov VV, Wabnitz S. A universal optical all-fiber Omnipolarizer. Sci Rep 2012; 2:938. [PMID: 23226836 PMCID: PMC3515841 DOI: 10.1038/srep00938] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Accepted: 11/19/2012] [Indexed: 11/09/2022] Open
Abstract
Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device - the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes - as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity.
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Affiliation(s)
- J Fatome
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Université de Bourgogne, 9 Av. Alain Savary, BP 47870, 21078 Dijon, France.
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26
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Picozzi A, Garnier J. Incoherent soliton turbulence in nonlocal nonlinear media. PHYSICAL REVIEW LETTERS 2011; 107:233901. [PMID: 22182089 DOI: 10.1103/physrevlett.107.233901] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2011] [Indexed: 05/31/2023]
Abstract
The long-term behavior of a modulationally unstable nonintegrable system is known to be characterized by the soliton turbulence self-organization process: It is thermodynamically advantageous for the system to generate a large-scale coherent soliton in order to reach the ("most disordered") equilibrium state. We show that this universal process of self-organization breaks down in the presence of a highly nonlocal nonlinear response. A wave turbulence approach based on a Vlasov-like kinetic equation reveals the existence of an incoherent soliton turbulence process: It is advantageous for the system to self-organize into a large-scale, spatially localized, incoherent soliton structure.
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Affiliation(s)
- Antonio Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS-Université de Bourgogne, 21078 Dijon, France
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27
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Suret P, Picozzi A, Randoux S. Wave turbulence in integrable systems: nonlinear propagation of incoherent optical waves in single-mode fibers. OPTICS EXPRESS 2011; 19:17852-17863. [PMID: 21935152 DOI: 10.1364/oe.19.017852] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation.
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Affiliation(s)
- Pierre Suret
- Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, Université Lille 1, Sciences et Technologies, Villeneuve d'Ascq, France.
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28
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Krstulovic G, Brachet M. Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066311. [PMID: 21797481 DOI: 10.1103/physreve.83.066311] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2010] [Revised: 02/12/2011] [Indexed: 05/31/2023]
Abstract
The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand-canonical distributions. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact (low-temperature) results obtained by steepest descent on the (grand-canonical) partition function. A standard finite-temperature second-order λ transition is exhibited. A mechanism of GPE thermalization through a direct cascade of energy is found using initial conditions with mass and energy distributed at large scales. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are shown to disappear as a prelude to final thermalization and their annihilation is related to the contraction of vortex rings due to mutual friction. Increasing the amount of dispersion at the truncation wave number is shown to slow thermalization and vortex annihilation. A bottleneck that produces spontaneous effective self-truncation with partial thermalization is characterized in the limit of large dispersive effects. Metastable counterflow states, with nonzero values of momentum, are generated using the SGLE algorithm. Spontaneous nucleation of the vortex ring is observed and the corresponding Arrhenius law is characterized. Dynamical counterflow effects on vortex evolution are investigated using two exact solutions of the GPE: traveling vortex rings and a motionless crystal-like lattice of vortex lines. Longitudinal effects are produced and measured on the crystal lattice. A dilatation of vortex rings is obtained for counterflows larger than their translational velocity. The vortex ring translational velocity has a dependence on temperature that is an order of magnitude above that of the crystal lattice, an effect that is related to the presence of finite-amplitude Kelvin waves. This anomalous vortex ring velocity is quantitatively reproduced by assuming equipartition of energy of the Kelvin waves. Orders of magnitude are given for the predicted effects in weakly interacting Bose-Einstein condensates and superfluid ^{4}He.
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Affiliation(s)
- Giorgio Krstulovic
- Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, associé au CNRS et aux Universités Paris VI et VII, 24 Rue Lhomond, F-75231 Paris, France
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29
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Krstulovic G, Brachet M. Dispersive bottleneck delaying thermalization of turbulent bose-einstein condensates. PHYSICAL REVIEW LETTERS 2011; 106:115303. [PMID: 21469873 DOI: 10.1103/physrevlett.106.115303] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2010] [Revised: 01/10/2011] [Indexed: 05/30/2023]
Abstract
A new mechanism of thermalization involving a direct energy cascade is obtained in the truncated Gross-Pitaevskii dynamics. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are found to disappear as a prelude to final thermalization. A bottleneck that produces spontaneous effective self-truncation and delays thermalization is characterized when large dispersive effects are present at the truncation wave number. Order of magnitude estimates indicate that self-truncation takes place in turbulent Bose-Einstein condensates. This effect should also be present in classical hydrodynamics and models of turbulence.
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Affiliation(s)
- Giorgio Krstulovic
- Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, associé au CNRS et aux Universités Paris VI et VII, 24 Rue Lhomond, 75231 Paris, France
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30
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Weill R, Levit B, Bekker A, Gat O, Fischer B. Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser. OPTICS EXPRESS 2010; 18:16520-16525. [PMID: 20721041 DOI: 10.1364/oe.18.016520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We have recently predicted (R. Weill, B. Fischer and O. Gat, Phys. Rev. Lett.104, 173901, 2010) condensation of light in actively mode locked lasers when the laser power increases, or the noise, that takes the role of temperature, decreases. The condensate is characterized by strong light pulses due to the dominance of the lowest eigenmode ("ground state") power. Here, we experimentally demonstrate, for the first time, light mode condensation transition in an actively mode-locked fiber laser. Following the theoretical prediction, the condensation is obtained for modulations that have a power law dependence on time with exponents smaller than 2. The laser light system is strictly one dimensional, a special opportunity in experimental physics. We also discuss experimental schemes for condensation in two- and three-dimensional laser systems.
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Affiliation(s)
- Rafi Weill
- 1Max-Planck Institute for Polymer Research, Mainz 55128, Germany
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31
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Weill R, Fischer B, Gat O. Light-mode condensation in actively-mode-locked lasers. PHYSICAL REVIEW LETTERS 2010; 104:173901. [PMID: 20482109 DOI: 10.1103/physrevlett.104.173901] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2009] [Indexed: 05/29/2023]
Abstract
We show that the formation of pulses in actively mode-locked lasers exhibits in certain conditions a transition of the laser mode system to a light pulse state that is similar to Bose-Einstein condensation (BEC). The study is done in the framework of statistical light-mode dynamics with a mapping between the distribution of the laser eigenmodes to the equilibrium statistical physics of noninteracting bosons in an external potential. The light-mode BEC transition occurs for a mode-locking modulation that has a power law dependence on time with an exponent smaller than 2.
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Affiliation(s)
- Rafi Weill
- Department of Electrical Engineering, Technion-IIT, Haifa 32000, Israel
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Suret P, Randoux S, Jauslin HR, Picozzi A. Anomalous thermalization of nonlinear wave systems. PHYSICAL REVIEW LETTERS 2010; 104:054101. [PMID: 20366765 DOI: 10.1103/physrevlett.104.054101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2009] [Indexed: 05/29/2023]
Abstract
We report theoretically and experimentally in an optical system a process of anomalous thermalization of one-dimensional nonlinear Hamiltonian waves. It is characterized by an irreversible evolution of the waves towards a specific equilibrium state of a fundamental different nature than the expected thermodynamic equilibrium state. A kinetic approach of the problem reveals that this phenomenon is due to the existence of a local invariant in frequency space. A novel family of equilibrium distributions is discovered, which is found in quantitative agreement with the numerical simulations.
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Affiliation(s)
- Pierre Suret
- Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Université de Lille, France
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Escobedo M, Valle MA. Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:061122. [PMID: 19658488 DOI: 10.1103/physreve.79.061122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2009] [Indexed: 05/28/2023]
Abstract
We study the four-wave kinetic equation of weak turbulence linearized around the Rayleigh-Jeans spectrum when the collision integral is associated with short-range interactions between nonrelativistic bosonic quasiparticles. The technique used for the analysis of the stability is based on the properties of the Mellin transform of the kernel in the integral equation. We find that any perturbation of the Rayleigh-Jeans distribution evolves toward low-momentum scales in such a form that when t-->infinity, all the particles occupy a sphere of radius arbitrary small.
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Affiliation(s)
- Miguel Escobedo
- Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain
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Barviau B, Kibler B, Kudlinski A, Mussot A, Millot G, Picozzi A. Experimental signature of optical wave thermalization through supercontinuum generation in photonic crystal fiber. OPTICS EXPRESS 2009; 17:7392-7406. [PMID: 19399118 DOI: 10.1364/oe.17.007392] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report an experimental, numerical and theoretical study of the incoherent regime of supercontinuum generation in a two zero-dispersion wavelengths fiber. By using a simple experimental setup, we show that the phenomenon of spectral broadening inherent to supercontinuum generation can be described as a thermalization process, which is characterized by an irreversible evolution of the optical field towards a thermal equilibrium state. In particular, the thermodynamic equilibrium spectrum predicted by the kinetic wave theory is characterized by a double peak structure, which has been found in quantitative agreement with the numerical simulations without adjustable parameters. We also confirm that stimulated Raman scattering leads to the generation of an incoherent structure in the normal dispersion regime which is reminiscent of a spectral incoherent soliton.
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Affiliation(s)
- Benoît Barviau
- Institut Carnot de Bourgogne, UMR 5029 CNRS-Université de Bourgogne, Dijon, France
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Barviau B, Kibler B, Coen S, Picozzi A. Toward a thermodynamic description of supercontinuum generation. OPTICS LETTERS 2008; 33:2833-2835. [PMID: 19037442 DOI: 10.1364/ol.33.002833] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We consider the incoherent nonlinear regime of the supercontinuum generation process in optical fibers. We show that, under certain conditions, the phenomenon of spectral broadening inherent to the supercontinuum generation may be described by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the supercontinuum generation process may be regarded as a thermalization process, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy.
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Affiliation(s)
- Benoît Barviau
- Institut Carnot de Bourgogne, UMR 5209 CNRS-Université de Bourgogne, 21000 Dijon, France.
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Picozzi A. Spontaneous polarization induced by natural thermalization of incoherent light. OPTICS EXPRESS 2008; 16:17171-17185. [PMID: 18957998 DOI: 10.1364/oe.16.017171] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We analyze theoretically the polarization properties of a partially coherent optical field that propagates in a nonlinear Kerr medium. We consider the standard model of two resonantly coupled nonlinear Schrödinger equations, which account for a wave-vector mismatch between the orthogonal polarization components. We show that such a phase-mismatch is responsible for the existence of a spontaneous repolarization process of the partially incoherent optical field during its nonlinear propagation. The repolarization process is characterized by an irreversible evolution of the unpolarized beam towards a highly polarized state, without any loss of energy. This unexpected result contrasts with the commonly accepted idea that an optical field undergoes a depolarization process under nonlinear evolution. The repolarization effect can be described in details by simple thermodynamic arguments based on the kinetic wave theory: It is shown to result from the natural tendency of the optical field to approach its thermal equilibrium state. The theory then reveals that it is thermodynamically advantageous for the optical field to evolve towards a highly polarized state, because this permits the optical field to reach the ???most disordered state???, i.e., the state of maximum (nonequilibrium) entropy. The theory is in quantitative agreement with the numerical simulations, without adjustable parameters. The physics underlying the reversible property of the repolarization process is briefly discussed in analogy with the celebrated Joule???s experiment of free expansion of a gas. Besides its fundamental interest, the repolarization effect may be exploited to achieve complete polarization of unpolarized incoherent light without loss of energy.
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Affiliation(s)
- Antonio Picozzi
- Institut Carnot de Bourgogne, UMR 5209 CNRS-Université de Bourgogne, Dijon Cedex, France.
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Conti C, Leonetti M, Fratalocchi A, Angelani L, Ruocco G. Condensation in disordered lasers: theory, 3D+1 simulations, and experiments. PHYSICAL REVIEW LETTERS 2008; 101:143901. [PMID: 18851528 DOI: 10.1103/physrevlett.101.143901] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2008] [Indexed: 05/26/2023]
Abstract
The complex processes underlying the generation of a coherent emission from the multiple scattering of photons and wave localization in the presence of structural disorder are still mostly unexplored. Here we show that a single nonlinear Schrödinger equation, playing the role of the Schwalow-Townes law for standard lasers, quantitatively reproduces experimental results and three-dimensional time-domain parallel simulations of a colloidal laser system.
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Affiliation(s)
- C Conti
- Research Center Soft INFM-CNR, c/o Università di Roma "Sapienza," I-00185, Roma, Italy
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Picozzi A, Pitois S, Millot G. Spectral incoherent solitons: a localized soliton behavior in the frequency domain. PHYSICAL REVIEW LETTERS 2008; 101:093901. [PMID: 18851612 DOI: 10.1103/physrevlett.101.093901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2008] [Indexed: 05/26/2023]
Abstract
We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.
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Affiliation(s)
- Antonio Picozzi
- Institut Carnot de Bourgogne, CNRS, Université de Bourgogne, Dijon, France
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Berloff NG, Youd AJ. Dissipative dynamics of superfluid vortices at nonzero temperatures. PHYSICAL REVIEW LETTERS 2007; 99:145301. [PMID: 17930681 DOI: 10.1103/physrevlett.99.145301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2007] [Revised: 06/21/2007] [Indexed: 05/25/2023]
Abstract
We consider the evolution and dissipation of vortex rings in a condensate at nonzero temperatures in the context of the classical field approximation, based on the defocusing nonlinear Schrödinger equation. The temperature in such a system is fully determined by the total number density and the number density of the condensate. The collisions with noncondensed particles reduce the radius of a vortex ring until it completely disappears. We obtain a universal decay law for a vortex line length and relate it to mutual friction coefficients in the fundamental equation of vortex motion in superfluids.
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Affiliation(s)
- Natalia G Berloff
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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Picozzi A. Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. OPTICS EXPRESS 2007; 15:9063-9083. [PMID: 19547246 DOI: 10.1364/oe.15.009063] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
<p> <a href="http://oe.osa.org/virtual_issue.cfm?vid=36">Focus Serial: Frontiers of Nonlinear Optics</a> </p> This concise review is aimed at providing an introduction to the kinetic theory of partially coherent optical waves propagating in nonlinear media. The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the novel dynamical features inherent to partially coherent nonlinear optical waves. However, such theories leave unanswered the following important question: Which is the long term (spatiotemporal) evolution of a partially incoherent optical field propagating in a nonlinear medium? In complete analogy with kinetic gas theory, one may expect that the incoherent field may evolve, owing to nonlinearity, towards a thermodynamic equilibrium state. Weak-turbulence theory is shown to describe the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Precisely, the theory describes an irreversible evolution of the spectrum of the field towards a thermodynamic equilibrium state. The irreversible behavior is expressed through the H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann's H-theorem of kinetic gas theory. It is shown that thermal wave relaxation to equilibrium may be characterized by the existence of a genuine condensation process, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. In spite of the formal reversibility of optical wave propagation, the condensation process occurs by means of an irreversible evolution of the field towards a homogeneous plane-wave (condensate) with small-scale fluctuations superimposed (uncondensed particles), which store the information necessary for the reversible propagation. As a remarkable result, an increase of entropy ("disorder") in the optical field requires the generation of a coherent structure (plane-wave). We show that, beyond the standard thermodynamic limit, wave condensation also occurs in two spatial dimensions. The numerical simulations are in quantitative agreement with the kinetic wave theory, without any adjustable parameter.
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Pitois S, Lagrange S, Jauslin HR, Picozzi A. Velocity locking of incoherent nonlinear wave packets. PHYSICAL REVIEW LETTERS 2006; 97:033902. [PMID: 16907501 DOI: 10.1103/physrevlett.97.033902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2006] [Indexed: 05/11/2023]
Abstract
We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.
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Affiliation(s)
- Stéphane Pitois
- CNRS-LPUB, Laboratoire de Physique de l'Université de Bourgogne, Dijon, France
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