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Li J, Zhang Y, Zeng J. Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices. iScience 2022; 25:104026. [PMID: 35345461 PMCID: PMC8957030 DOI: 10.1016/j.isci.2022.104026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Revised: 01/17/2022] [Accepted: 03/01/2022] [Indexed: 11/26/2022] Open
Abstract
Past decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems 3D parity-time (PT)-symmetric optical lattices are used to overcome the collapse of 3D ultracold atoms. 3D matter-wave gap solitons and vortices are found in PT-symmetric optical lattices. Rich properties and dynamics of 3D matter-wave localized modes are disclosed. In-depth soliton physics is provided in 3D non-Hermitian periodic physical systems.
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Cookson T, Kalinin K, Sigurdsson H, Töpfer JD, Alyatkin S, Silva M, Langbein W, Berloff NG, Lagoudakis PG. Geometric frustration in polygons of polariton condensates creating vortices of varying topological charge. Nat Commun 2021; 12:2120. [PMID: 33837211 PMCID: PMC8035188 DOI: 10.1038/s41467-021-22121-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 02/25/2021] [Indexed: 11/09/2022] Open
Abstract
Vorticity is a key ingredient to a broad variety of fluid phenomena, and its quantised version is considered to be the hallmark of superfluidity. Circulating flows that correspond to vortices of a large topological charge, termed giant vortices, are notoriously difficult to realise and even when externally imprinted, they are unstable, breaking into many vortices of a single charge. In spite of many theoretical proposals on the formation and stabilisation of giant vortices in ultra-cold atomic Bose-Einstein condensates and other superfluid systems, their experimental realisation remains elusive. Polariton condensates stand out from other superfluid systems due to their particularly strong interparticle interactions combined with their non-equilibrium nature, and as such provide an alternative testbed for the study of vortices. Here, we non-resonantly excite an odd number of polariton condensates at the vertices of a regular polygon and we observe the formation of a stable discrete vortex state with a large topological charge as a consequence of antibonding frustration between nearest neighbouring condensates.
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Affiliation(s)
- Tamsin Cookson
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation.,Department of Physics and Astronomy, University of Southampton, Southampton, UK
| | - Kirill Kalinin
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation.,Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
| | - Helgi Sigurdsson
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation.,Department of Physics and Astronomy, University of Southampton, Southampton, UK
| | - Julian D Töpfer
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation.,Department of Physics and Astronomy, University of Southampton, Southampton, UK
| | - Sergey Alyatkin
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation
| | - Matteo Silva
- Department of Physics and Astronomy, University of Southampton, Southampton, UK
| | | | - Natalia G Berloff
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation. .,Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
| | - Pavlos G Lagoudakis
- Skolkovo Institute of Science and Technology, Skolkovo, Russian Federation. .,Department of Physics and Astronomy, University of Southampton, Southampton, UK.
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Kartashov YV, Zezyulin DA. Stable Multiring and Rotating Solitons in Two-Dimensional Spin-Orbit-Coupled Bose-Einstein Condensates with a Radially Periodic Potential. PHYSICAL REVIEW LETTERS 2019; 122:123201. [PMID: 30978069 DOI: 10.1103/physrevlett.122.123201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Revised: 12/10/2018] [Indexed: 06/09/2023]
Abstract
We consider two-dimensional spin-orbit-coupled atomic Bose-Einstein condensate in a radially periodic potential. The system supports different types of stable self-sustained states including radially symmetric vorticity-carrying modes with different topological charges in two spinor components that may have multiring profiles and at the same time remain remarkably stable for repulsive interactions. Solitons of the second type show persistent rotation with constant angular frequency. They can be stable for both repulsive and attractive interatomic interactions. Because of the inequivalence between clockwise and counterclockwise rotation directions introduced by spin-orbit coupling, the properties of such solitons strongly differ for positive and negative rotation frequencies. The collision of solitons located in the same or different rings is accompanied by a change of the rotation frequency that depends on the phase difference between colliding solitons.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia
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Ma X, Driben R, Malomed BA, Meier T, Schumacher S. Two-dimensional symbiotic solitons and vortices in binary condensates with attractive cross-species interaction. Sci Rep 2016; 6:34847. [PMID: 27703235 PMCID: PMC5050495 DOI: 10.1038/srep34847] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 09/12/2016] [Indexed: 11/09/2022] Open
Abstract
We consider a two-dimensional (2D) two-component spinor system with cubic attraction between the components and intra-species self-repulsion, which may be realized in atomic Bose-Einstein condensates, as well as in a quasi-equilibrium condensate of microcavity polaritons. Including a 2D spatially periodic potential, which is necessary for the stabilization of the system against the critical collapse, we use detailed numerical calculations and an analytical variational approximation (VA) to predict the existence and stability of several types of 2D symbiotic solitons in the spinor system. Stability ranges are found for symmetric and asymmetric symbiotic fundamental solitons and vortices, including hidden-vorticity (HV) modes, with opposite vorticities in the two components. The VA produces exceptionally accurate predictions for the fundamental solitons and vortices. The fundamental solitons, both symmetric and asymmetric ones, are completely stable, in either case when they exist as gap solitons or regular ones. The symmetric and asymmetric vortices are stable if the inter-component attraction is stronger than the intra-species repulsion, while the HV modes have their stability region in the opposite case.
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Affiliation(s)
- Xuekai Ma
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Rodislav Driben
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Torsten Meier
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Stefan Schumacher
- Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
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Dror N, Malomed BA. Stability of two-dimensional gap solitons in periodic potentials: beyond the fundamental modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063203. [PMID: 23848798 DOI: 10.1103/physreve.87.063203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/02/2023]
Abstract
Gross-Pitaevskii or nonlinear-Schrödinger equations with a sinusoidal potential is commonly used to describe nonlinear periodic media, such as photonic lattices in optics and Bose-Einstein condensates (BECs) loaded into optical lattices (OLs). Previous studies have shown that the 2D version of this equation, with the self-focusing (SF) nonlinearity, supports stable solitons in the semi-infinite gap. It is known, too, that under both the self-defocusing (SDF) and SF nonlinearities, several families of gap solitons (GSs) exist in finite bandgaps. Here, we investigate the stability of 2D dipole-mode GS families, via the computation of their linear-stability eigenvalues and direct simulations of the perturbed evolution. We demonstrate that, under the SF nonlinearity, one species of dipole GSs is stable in a part of the first finite bandgap, provided that the OL depth exceeds a threshold value, while other dipole and multipole modes are unstable in that case. Bidipole bound states (vertical, horizontal, and diagonal), as well as square- and rhombic-shaped vortices and quadrupoles, built of stable fundamental dipoles, are stable too. Under the SDF nonlinearity, the family of dipole solitons is shown to be stable in a part of the second finite bandgap. Transformations of unstable dipole GSs are studied by means of direct simulations. Direct simulations are also performed to investigate the stability of other GS families, in the first and second bandgaps, under both types of the nonlinearity. In particular, "tripole" solitons, sustained in the second bandgap under the action of the SF nonlinearity, demonstrate stable behavior in the course of long propagation, in a certain region within the bandgap.
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Affiliation(s)
- Nir Dror
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Ye F, Mihalache D, Hu B, Panoiu NC. Subwavelength vortical plasmonic lattice solitons. OPTICS LETTERS 2011; 36:1179-1181. [PMID: 21479022 DOI: 10.1364/ol.36.001179] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.
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Affiliation(s)
- Fangwei Ye
- Department of Physics, The State Key Laboratory on Fiber Optic Local Area Communication Networks and Advanced Optical Communication Systems, Shanghai Jiao Tong University, Shanghai 200240, China
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Theocharis G, Kavousanakis M, Kevrekidis PG, Daraio C, Porter MA, Kevrekidis IG. Localized breathing modes in granular crystals with defects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:066601. [PMID: 20365288 DOI: 10.1103/physreve.80.066601] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2009] [Indexed: 05/29/2023]
Abstract
We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations.
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Affiliation(s)
- G Theocharis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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Sakaguchi H, Malomed BA. Two-dimensional dissipative gap solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:026606. [PMID: 19792271 DOI: 10.1103/physreve.80.026606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2009] [Indexed: 05/28/2023]
Abstract
We introduce a model which integrates the complex Ginzburg-Landau equation in two dimensions (2Ds) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D dissipative gap solitons (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite band gap of the system's linear spectrum. The solutions are obtained in a numerical form and also by means of an analytical approximation, which combines the variational description of the shape of the fundamental and vortical solitons and the balance equation for their total power. The analytical results agree with numerical findings. The model may be implemented as a laser medium in a bulk self-defocusing optical waveguide equipped with a transverse 2D grating, the predicted DGSs representing spatial solitons in this setting.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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Zhang Y, Wu B. Composition relation between gap solitons and Bloch waves in nonlinear periodic systems. PHYSICAL REVIEW LETTERS 2009; 102:093905. [PMID: 19392522 DOI: 10.1103/physrevlett.102.093905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2008] [Indexed: 05/27/2023]
Abstract
We show with numerical computation and analysis that Bloch waves, at either the center or edge of the Brillouin zone, of a one dimensional nonlinear periodic system can be regarded as infinite chains composed of fundamental gap solitons (FGSs). This composition relation between Bloch waves and FGSs leads us to predict that there are n families of FGSs in the nth band gap of the corresponding linear periodic system, which is confirmed numerically. Furthermore, this composition relation can be extended to construct a class of solutions similar to Bloch waves but with multiple periods.
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Affiliation(s)
- Yongping Zhang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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10
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Sakaguchi H, Malomed BA. Gap solitons in Ginzburg-Landau media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056606. [PMID: 18643185 DOI: 10.1103/physreve.77.056606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2008] [Indexed: 05/26/2023]
Abstract
We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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Tikhonenkov I, Malomed BA, Vardi A. Anisotropic solitons in dipolar bose-einstein condensates. PHYSICAL REVIEW LETTERS 2008; 100:090406. [PMID: 18352684 DOI: 10.1103/physrevlett.100.090406] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2007] [Indexed: 05/26/2023]
Abstract
Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized perpendicular to the confinement direction. Unlike isotropic solitons predicted for the moments aligned with the confinement axis [Phys. Rev. Lett. 95, 200404 (2005)10.1103/PhysRevLett.95.200404], no sign reversal of the dipole-dipole interaction is necessary to support the solitons. Direct 3D simulations confirm their stability.
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Affiliation(s)
- I Tikhonenkov
- Department of Chemistry, Ben-Gurion University of the Negev, POB. 653, Beer-Sheva 84105, Israel
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Lee C, Alexander TJ, Kivshar YS. Melting of discrete vortices via quantum fluctuations. PHYSICAL REVIEW LETTERS 2006; 97:180408. [PMID: 17155525 DOI: 10.1103/physrevlett.97.180408] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2006] [Indexed: 05/12/2023]
Abstract
We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or q vortices), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.
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Affiliation(s)
- Chaohong Lee
- Nonlinear Physics Centre and ARC Centre of Excellence for Quantum-Atom Optics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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Sakaguchi H, Malomed BA. Gap solitons in quasiperiodic optical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:026601. [PMID: 17025551 DOI: 10.1103/physreve.74.026601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2006] [Revised: 05/25/2006] [Indexed: 05/12/2023]
Abstract
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a fivefold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three band gaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.
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Affiliation(s)
- Hidetsugu Sakaguchi
- Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
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Oster M, Johansson M. Stable stationary and quasiperiodic discrete vortex breathers with topological charge S = 2. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066608. [PMID: 16906998 DOI: 10.1103/physreve.73.066608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2006] [Indexed: 05/11/2023]
Abstract
We demonstrate the stability of a stationary vortex breather with vorticity S = 2 in the two-dimensional discrete nonlinear Schrödinger model for a square lattice and also discuss the effects of exciting internal sites in a vortex ring. We also point out the fundamental difficulties of observing these solutions with current experimental techniques. Instead, we argue that relevant initial conditions will lead to the formation of quasiperiodic vortex breathers.
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Affiliation(s)
- Michael Oster
- Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden.
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Alexander TJ, Ostrovskaya EA, Kivshar YS. Self-trapped nonlinear matter waves in periodic potentials. PHYSICAL REVIEW LETTERS 2006; 96:040401. [PMID: 16486792 DOI: 10.1103/physrevlett.96.040401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2005] [Indexed: 05/06/2023]
Abstract
We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.
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Affiliation(s)
- Tristram J Alexander
- Nonlinear Physics Centre and ARC Centre of Excellence for Quantum-Atom Optics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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Kevrekidis PG, Frantzeskakis DJ. Stabilizing the discrete vortex of topological charge S=2. Phys Rev E 2005; 72:016606. [PMID: 16090106 DOI: 10.1103/physreve.72.016606] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2005] [Indexed: 11/07/2022]
Abstract
We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we analyze the model with the central site being inert. We identify analytically and observe numerically the existence of a range of linearly stable discrete vortices with S=2 in the latter model. The range of stability is comparable to that of the recently observed experimentally S=1 discrete vortex, suggesting the potential for observation of such higher charge discrete vortices.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst Massachusetts 01003-4515, USA
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Kevrekidis PG, Malomed BA, Chen Z, Frantzeskakis DJ. Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056612. [PMID: 15600784 DOI: 10.1103/physreve.70.056612] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2003] [Revised: 04/20/2004] [Indexed: 05/24/2023]
Abstract
Vortex solitons with the topological charge S=3 , and "quasivortex" (multipole) solitons, which exist instead of the vortices with S=2 and 4, are constructed on a square lattice in the discrete nonlinear Schrödinger equation (true vortices with S=2 were known before, but they are unstable). For each type of solitary wave, its stability interval is found, in terms of the intersite coupling constant. The interval shrinks with increase of S . At couplings above a critical value, oscillatory instabilities set in, resulting in breakup of the vortex or quasivortex into lattice solitons with a lower vorticity. Such localized states may be observed in optical guiding structures, and in Bose-Einstein condensates loaded into optical lattices.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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