1
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Paredes A, Michinel H. Self-trapping of vortex crystals via competing nonlinearities. Phys Rev E 2024; 109:024216. [PMID: 38491634 DOI: 10.1103/physreve.109.024216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 01/18/2024] [Indexed: 03/18/2024]
Abstract
We investigate the existence of self-trapped nonlinear waves with multiple phase singularities. Working with the cubic-quintic nonlinear Schrödinger equation, we focus on configurations with an antivortex surrounded by a triangular arrangement of vortices within a hosting soliton. We find stationary patterns that can be interpreted as stable self-trapped vortex crystals, constituting the first example of a configuration of this sort with space-independent potentials. Their stability is linked to their norm, transitioning from unstable to stable as their size increases, with an intermediate region where the structure is marginally unstable, undergoing a remarkable and puzzling self-reconstruction during its evolution.
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Affiliation(s)
- Angel Paredes
- Instituto de Física e Ciencias Aeroespaciais (IFCAE), Universidade de Vigo. Campus de As Lagoas, E-32004 Ourense, Spain
| | - Humberto Michinel
- Instituto de Física e Ciencias Aeroespaciais (IFCAE), Universidade de Vigo. Campus de As Lagoas, E-32004 Ourense, Spain
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2
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Congy T, Azam P, Kaiser R, Pavloff N. Topological Constraints on the Dynamics of Vortex Formation in a Two-Dimensional Quantum Fluid. PHYSICAL REVIEW LETTERS 2024; 132:033804. [PMID: 38307046 DOI: 10.1103/physrevlett.132.033804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 11/27/2023] [Indexed: 02/04/2024]
Abstract
We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer than the mere conservation of vorticity impose an elaborate dynamical behavior to the formation and annihilation of vortex-antivortex pairs. We identify two such mechanisms, both described by the same fold-Hopf bifurcation. One of them is particularly efficient although it is not observed in the context of liquid helium films or stationary systems because it relies on the compressible nature of the fluid of light we consider and on the nonstationarity of its flow.
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Affiliation(s)
- T Congy
- Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
| | - P Azam
- Institut de Physique de Nice, Université Côte d'Azur, CNRS, F-06560 Valbonne, France
| | - R Kaiser
- Institut de Physique de Nice, Université Côte d'Azur, CNRS, F-06560 Valbonne, France
| | - N Pavloff
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
- Institut Universitaire de France (IUF)
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3
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Drori L, Das BC, Zohar TD, Winer G, Poem E, Poddubny A, Firstenberg O. Quantum vortices of strongly interacting photons. Science 2023; 381:193-198. [PMID: 37440622 DOI: 10.1126/science.adh5315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Accepted: 06/07/2023] [Indexed: 07/15/2023]
Abstract
Vortices are topologically nontrivial defects that generally originate from nonlinear field dynamics. All-optical generation of photonic vortices-phase singularities of the electromagnetic field-requires sufficiently strong nonlinearity that is typically achieved in the classical optics regime. We report on the realization of quantum vortices of photons that result from a strong photon-photon interaction in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for copropagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function. For three photons, the formation of vortex lines and a central vortex ring confirms the existence of a genuine three-photon interaction. The wave function topology, governed by two- and three-photon bound states, imposes a conditional phase shift of π per photon, a potential resource for deterministic quantum logic operations.
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Affiliation(s)
- Lee Drori
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Bankim Chandra Das
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Tomer Danino Zohar
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Gal Winer
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Eilon Poem
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Alexander Poddubny
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ofer Firstenberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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4
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Kamchatnov AM. Contour dynamics of two-dimensional dark solitons. Phys Rev E 2022; 105:044204. [PMID: 35590675 DOI: 10.1103/physreve.105.044204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 03/22/2022] [Indexed: 06/15/2023]
Abstract
Equations for contour dynamics of trough-shaped dark solitons are obtained for the general form of the nonlinearity function. Their self-similar solution which describes the nonlinear stage of the bending instability of dark solitons is studied in detail.
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Affiliation(s)
- A M Kamchatnov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
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5
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Marcucci G, Hu X, Cala P, Man W, Pierangeli D, Conti C, Chen Z. Anisotropic Optical Shock Waves in Isotropic Media with Giant Nonlocal Nonlinearity. PHYSICAL REVIEW LETTERS 2020; 125:243902. [PMID: 33412069 DOI: 10.1103/physrevlett.125.243902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Revised: 09/05/2020] [Accepted: 10/27/2020] [Indexed: 06/12/2023]
Abstract
Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point. The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.
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Affiliation(s)
- Giulia Marcucci
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
| | - Xubo Hu
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- College of Electronics Engineering, South China Agricultural University, Guangzhou 510642, China
| | - Phillip Cala
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Weining Man
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Davide Pierangeli
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
| | - Claudio Conti
- Department of Physics, Sapienza University, P.le Aldo Moro 2, 00185 Rome, Italy
- Institute for Complex Systems, Via dei Taurini 19, 00185 Rome, Italy
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Zhigang Chen
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
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6
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Dutta S, Mueller EJ. Collective Modes of a Soliton Train in a Fermi Superfluid. PHYSICAL REVIEW LETTERS 2017; 118:260402. [PMID: 28707921 DOI: 10.1103/physrevlett.118.260402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Indexed: 06/07/2023]
Abstract
We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.
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Affiliation(s)
- Shovan Dutta
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - Erich J Mueller
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
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7
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Baronio F, Wabnitz S, Kodama Y. Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin. PHYSICAL REVIEW LETTERS 2016; 116:173901. [PMID: 27176522 DOI: 10.1103/physrevlett.116.173901] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2016] [Indexed: 06/05/2023]
Abstract
There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.
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Affiliation(s)
- Fabio Baronio
- INO CNR and Dipartimento di Ingegneria dell'Informazione, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
| | - Stefan Wabnitz
- INO CNR and Dipartimento di Ingegneria dell'Informazione, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
| | - Yuji Kodama
- Department of Mathematics, Ohio State University, Columbus, Ohio 43210, USA
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8
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Horikis TP, Frantzeskakis DJ. Ring dark and antidark solitons in nonlocal media. OPTICS LETTERS 2016; 41:583-586. [PMID: 26907429 DOI: 10.1364/ol.41.000583] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.
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9
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Scherpelz P, Padavić K, Rançon A, Glatz A, Aranson IS, Levin K. Phase imprinting in equilibrating Fermi gases: the transience of vortex rings and other defects. PHYSICAL REVIEW LETTERS 2014; 113:125301. [PMID: 25279634 DOI: 10.1103/physrevlett.113.125301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2014] [Indexed: 06/03/2023]
Abstract
We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases, which were obtained independently and are in good agreement with recent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations, we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase-imprinting tilt angle, and we illustrate their dramatic effects. As appears consistent with experiment, the former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.
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Affiliation(s)
- Peter Scherpelz
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Karmela Padavić
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Adam Rançon
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Andreas Glatz
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA and Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA
| | - Igor S Aranson
- Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
| | - K Levin
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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10
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Tosi G, Christmann G, Berloff N, Tsotsis P, Gao T, Hatzopoulos Z, Savvidis P, Baumberg J. Geometrically locked vortex lattices in semiconductor quantum fluids. Nat Commun 2012; 3:1243. [DOI: 10.1038/ncomms2255] [Citation(s) in RCA: 91] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2012] [Accepted: 11/05/2012] [Indexed: 11/09/2022] Open
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11
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Chen Z, Segev M, Christodoulides DN. Optical spatial solitons: historical overview and recent advances. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:086401. [PMID: 22836010 DOI: 10.1088/0034-4885/75/8/086401] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.
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Affiliation(s)
- Zhigang Chen
- Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132, USA
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12
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Jeng CC, Lin Y, Hong RC, Lee RK. Optical pattern transitions from modulation to transverse instabilities in photorefractive crystals. PHYSICAL REVIEW LETTERS 2009; 102:153905. [PMID: 19518635 DOI: 10.1103/physrevlett.102.153905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Indexed: 05/27/2023]
Abstract
We show by experimental measurements and theoretical analyses that there exists a pattern transition from optical modulation instability to transverse instability in nonlinear media. An input coherent beam propagating in the photorefractive crystals is observed to break up into stripe filaments at a first threshold voltage. By modeling the periodic strip filaments as cnoidal waves, we demonstrate that a second threshold voltage for forming dot filaments comes from the transverse instability, resulting in a good agreement with the experimental data.
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Affiliation(s)
- Chien-Chung Jeng
- Department of Physics, National Chung-Hsing University, Taichung 402, Taiwan
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13
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Yan H, Lü B. Dynamic evolution of an edge dislocation through aligned and misaligned paraxial optical ABCD systems. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2009; 26:985-992. [PMID: 19340274 DOI: 10.1364/josaa.26.000985] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The closed-form propagation expressions of an edge dislocation nested in a general elliptical Gaussian beam through aligned and misaligned paraxial optical ABCD systems are derived and used to study the dynamic evolution behavior of the edge dislocation propagating in free space and through a misaligned lens. It is shown that the noncanonical vortex and dynamic inversion of the topological charge, as well as a new edge dislocation may appear under certain conditions. The results are illustrated analytically and numerically.
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Affiliation(s)
- Hongwei Yan
- Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064, China
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14
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Nath R, Pedri P, Santos L. Stability of dark solitons in three dimensional dipolar Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2008; 101:210402. [PMID: 19113395 DOI: 10.1103/physrevlett.101.210402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2007] [Indexed: 05/27/2023]
Abstract
The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates, dark solitons are unstable against transverse excitations in two and three dimensions. On the contrary, due to its nonlocal character, the dipolar interaction allows for stable 3D stationary dark solitons, opening a qualitatively novel scenario in nonlinear atom optics. We discuss in detail the conditions to achieve this stability, which demand the use of an additional optical lattice, and the stability regimes.
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Affiliation(s)
- R Nath
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, D-30167, Hannover, Germany
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15
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Gorza SP, Haelterman M. Ultrafast transverse undulation of self-trapped laser beams. OPTICS EXPRESS 2008; 16:16935-16940. [PMID: 18852801 DOI: 10.1364/oe.16.016935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
The propagation of a self-trapped laser beam in a planar waveguide that exhibits a Kerr nonlinearity and a normal chromatic dispersion is considered. We demonstrate experimentally for the first time to our knowledge that such a beam undergoes an undulation responsible for ultrafast transverse oscillations of its axis. This phenomenon, called ???snake instability???, was predicted theoretically in 1973 by Zakharov and Rubenchik on the basis of a study of the soliton solutions of the hyperbolic nonlinear Schr odinger equation. The signature of this instability is observed in the spatially resolved temporal spectrum.
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Affiliation(s)
- S-P Gorza
- Service OPERA-Photonique, Université libre de Bruxelles, Bruxelles, Belgique.
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16
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Efremidis NK, Hizanidis K, Malomed BA, Di Trapani P. Three-dimensional vortex solitons in self-defocusing media. PHYSICAL REVIEW LETTERS 2007; 98:113901. [PMID: 17501055 DOI: 10.1103/physrevlett.98.113901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2006] [Indexed: 05/15/2023]
Abstract
We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schrödinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.
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Affiliation(s)
- Nikolaos K Efremidis
- Department of Applied Mathematics, University of Crete, 71409 Heraklion, Crete, Greece
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17
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Gorza SP, Emplit P, Haelterman M. Observation of the snake instability of a spatially extended temporal bright soliton. OPTICS LETTERS 2006; 31:1280-2. [PMID: 16642085 DOI: 10.1364/ol.31.001280] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
The transverse snake instability of the bright soliton solution of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation is experimentally studied. We observed this instability in the spatial distribution of the temporal spectrum of spatially extended femtosecond pulses propagating in normally dispersive self-defocusing planar semiconductor waveguide.
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Affiliation(s)
- S-P Gorza
- Service d'Optique et Acoustique, Université Libre de Bruxelles, Belgium.
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18
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Aleshkevich VA, Egorov AA, Kartashov YV, Vysloukh VA, Zelenina AS. Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 67:066605. [PMID: 16241366 DOI: 10.1103/physreve.67.066605] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2003] [Indexed: 11/07/2022]
Abstract
We analyze numerically the modulational instability of spatiotemporal cnoidal waves of cn, dn, and sn types that are periodic along a single space coordinate and are uniform in time. The band of possible increments is calculated for all three types of cnoidal waves as a function of parameter describing the degree of localization of the wave field energy. It is shown that this band transforms into a set of discrete values for waves of cn and dn types in the limit of strong spatial localization. Simulation of perturbed cnoidal-wave propagation revealed suppression of collapse and multiple-wave filamentation on the developed stage of instability. Different instability scenarios are considered in detail.
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Affiliation(s)
- Victor A Aleshkevich
- Physics Department, M. V. Lomonosov Moscow State University, 119899 Vorobiovy Gory, Moscow, Russia
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19
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Gorza SP, Roig N, Emplit P, Haelterman M. Snake instability of a spatiotemporal bright soliton stripe. PHYSICAL REVIEW LETTERS 2004; 92:084101. [PMID: 14995776 DOI: 10.1103/physrevlett.92.084101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2002] [Indexed: 05/24/2023]
Abstract
We study experimentally the snake instability of the bright soliton stripe of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. The instability is observed, through spectral measurements, on spatially extended femtosecond pulses propagating in a normally dispersive self-defocusing semiconductor planar waveguide.
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Affiliation(s)
- S-P Gorza
- Service d'Optique et Acoustique, Université Libre de Bruxelles, 50 Avenue Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
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20
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Dreischuh A, Neshev D, Paulus GG, Grasbon F, Walther H. Ring dark solitary waves: experiment versus theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:066611. [PMID: 12513433 DOI: 10.1103/physreve.66.066611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2002] [Indexed: 05/24/2023]
Abstract
Experimental results on optical ring dark solitary wave dynamics are presented, emphasizing the interplay between initial dark beam contrast, total phase shift, background-beam intensity, and saturation of the nonlinearity. The results are found to confirm qualitatively the existing analytical theory and are in agreement with the numerical simulations carried out.
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Affiliation(s)
- A Dreischuh
- Department of Quantum Electronics, Sofia University, 5 J. Bourchier Boulevard, Bulgaria
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21
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Neshev D, Krolikowski W, Pelinovsky DE, McCarthy G, Kivshar YS. Transverse instability of vector solitons and generation of dipole arrays. PHYSICAL REVIEW LETTERS 2001; 87:103903. [PMID: 11531480 DOI: 10.1103/physrevlett.87.103903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2001] [Indexed: 05/23/2023]
Abstract
We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.
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Affiliation(s)
- D Neshev
- Nonlinear Physics Group, Research School of Physical Sciences and Engineering, The Institute of Advanced Studies, The Australian National University, Canberra ACT 0200, Australia
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22
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Anderson BP, Haljan PC, Regal CA, Feder DL, Collins LA, Clark CW, Cornell EA. Watching dark solitons decay into vortex rings in a Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2001; 86:2926-2929. [PMID: 11290074 DOI: 10.1103/physrevlett.86.2926] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2000] [Indexed: 05/23/2023]
Abstract
We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.
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Affiliation(s)
- B P Anderson
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder 80309-0440, USA
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Liu X, Beckwitt K, Wise F. Transverse instability of optical spatiotemporal solitons in quadratic media. PHYSICAL REVIEW LETTERS 2000; 85:1871-1874. [PMID: 10970635 DOI: 10.1103/physrevlett.85.1871] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2000] [Indexed: 05/23/2023]
Abstract
We present experimental and numerical observations of transverse instability in quadratic media under conditions that emphasize the inherently spatiotemporal and multidimensional nature of the wave propagation. Intensity-dependent beam filamentation is shown to be closely connected to the periodic evolution of quadratic solitons, and implications for the generation of three-dimensional spatiotemporal solitons are discussed.
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Affiliation(s)
- X Liu
- Department of Applied Physics, Cornell University, Ithaca, New York 14853, USA
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Kivshar YS, Nepomnyashchy A, Tikhonenko V, Christou J, Luther-Davies B. Vortex-stripe soliton interactions. OPTICS LETTERS 2000; 25:123-125. [PMID: 18059803 DOI: 10.1364/ol.25.000123] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study the interaction of an optical vortex soliton with a dark-soliton stripe in a bulk nonlinear defocusing medium. We develop a multiscale asymptotic theory to predict the main effect of the interaction and then study it experimentally, observing vortex-induced stripe bending, development of the transverse instability, and stripe breakup.
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25
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Dreischuh A, Paulus GG, Zacher F, Grasbon F, Neshev D, Walther H. Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:7518-24. [PMID: 11970702 DOI: 10.1103/physreve.60.7518] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/1998] [Revised: 07/28/1999] [Indexed: 04/18/2023]
Abstract
We present a linear analysis and numerical simulations of the instability of optical vortex solitons (OVSs) of arbitrary topological charge. They show a rich variety of instability scenarios depending on the type of perturbation. The saturation of the nonlinearity is shown to be able to slow down the decay of multiple charged dark beams at an intermediate evolution stage and to prevent their ultimate decay into charge-1 OVSs. This concept is experimentally verified by the observation of a partial decay of a triple-charged OV beam and by comparing this dynamic with the behavior of OV beams of topological charges m=1, 2, 3, and 4.
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Affiliation(s)
- A Dreischuh
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
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Dreischuh A, Paulus GG, Zacher F, Grasbon F, Walther H. Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:6111-7. [PMID: 11970516 DOI: 10.1103/physreve.60.6111] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/1998] [Indexed: 04/18/2023]
Abstract
Multiply charged optical vortex solitons (OVS) (m=1,...,4) are generated in a thermal nonlinear medium with saturation. The respective soliton constants are found to be linearly proportional to the topological charges. Special attention is paid to the modulational instability, which is effectively suppressed by a moderate saturation but still remains an increasing function of the topological charge. For the particular experimental conditions, the recorded OVS profiles are found to be in good qualitative agreement with the numerical stationary solutions of the generalized nonlinear Schrödinger equation.
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Affiliation(s)
- A Dreischuh
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
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Malos JT, Dykstra R, Vaupel M, Weiss CO. Vortex streets in a cavity with higher-order standing waves. OPTICS LETTERS 1997; 22:1056-1058. [PMID: 18185749 DOI: 10.1364/ol.22.001056] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Recently a laser analog of vortex generation behind an obstacle in a flow was demonstrated. Vortex generation occurs when tilted waves of different transverse structures are simultaneously excited in a laser. We have generalized this phenomenon to higher-order standing waves. Here typical phenomena expected for optical vortices, such as the excitation and disappearance of single vortices out of and into dark lines and dark areas, as well as vortex-pair creation and annihilation become apparent.
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Mamaev AV, Saffman M, Zozulya AA. Vortex Evolution and Bound Pair Formation in Anisotropic Nonlinear Optical Media. PHYSICAL REVIEW LETTERS 1996; 77:4544-4547. [PMID: 10062565 DOI: 10.1103/physrevlett.77.4544] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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