1
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Fu Q, Wang P, Kartashov YV, Konotop VV, Ye F. Two-Dimensional Nonlinear Thouless Pumping of Matter Waves. PHYSICAL REVIEW LETTERS 2022; 129:183901. [PMID: 36374696 DOI: 10.1103/physrevlett.129.183901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
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Affiliation(s)
- Qidong Fu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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2
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Kartashov YV. Light bullets in moiré lattices. OPTICS LETTERS 2022; 47:4528-4531. [PMID: 36048696 DOI: 10.1364/ol.471022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 07/27/2022] [Indexed: 06/15/2023]
Abstract
We predict that photonic moiré lattices produced by two mutually twisted periodic sublattices in a medium with Kerr nonlinearity can support stable three-dimensional (3D) light bullets localized in both space and time. The stability of light bullets and their properties are closely connected with the properties of linear spatial eigenmodes of moiré lattices that undergo localization-delocalization transition (LDT) upon the increase of the depth of one of the sublattices forming the moiré lattice, but only for twist angles corresponding to incommensurate, aperiodic moiré structures. Above the LDT threshold, such incommensurate moiré lattices support stable light bullets without an energy threshold. In contrast, commensurate-or periodic-moiré lattices arising at Pythagorean twist angles, whose eigenmodes are delocalized Bloch waves, can support stable light bullets only above a certain energy threshold. Moiré lattices below the LDT threshold cannot support stable light bullets for our parameters. Our results illustrate that the periodicity/aperiodicity of the underlying lattice is a crucial factor in determining the stability properties of the nonlinear 3D states.
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3
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Milián C, Kartashov YV, Torner L. Robust Ultrashort Light Bullets in Strongly Twisted Waveguide Arrays. PHYSICAL REVIEW LETTERS 2019; 123:133902. [PMID: 31697553 DOI: 10.1103/physrevlett.123.133902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Indexed: 06/10/2023]
Abstract
We introduce a new class of stable light bullets that form in twisted waveguide arrays pumped with ultrashort pulses, where twisting offers a powerful knob to tune the properties of localized states. We find that, above a critical twist, three-dimensional wave packets are unambiguously stabilized, with no minimum energy threshold. As a consequence, when the higher-order perturbations that accompany ultrashort pulse propagation are at play, the bullets dynamically adjust and sweep along stable branches. Therefore, they are predicted to feature an unprecedented experimental robustness.
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Affiliation(s)
- Carles Milián
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, 46022 (València), Spain
| | - 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
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
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4
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Zhang X, Xu X, Zheng Y, Chen Z, Liu B, Huang C, Malomed BA, Li Y. Semidiscrete Quantum Droplets and Vortices. PHYSICAL REVIEW LETTERS 2019; 123:133901. [PMID: 31697515 DOI: 10.1103/physrevlett.123.133901] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Revised: 08/01/2019] [Indexed: 06/10/2023]
Abstract
We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable on-site- and intersite-centered semidiscrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to five, in both tightly bound and quasicontinuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semidiscrete vortex QDs, including ones with multiple vorticity.
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Affiliation(s)
- Xiliang Zhang
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Xiaoxi Xu
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Yiyin Zheng
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Zhaopin Chen
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
| | - Bin Liu
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Chunqing Huang
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
| | - Boris A Malomed
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yongyao Li
- School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and the Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel
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5
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Gustave F, Radwell N, McIntyre C, Toomey JP, Kane DM, Barland S, Firth WJ, Oppo GL, Ackemann T. Observation of Mode-Locked Spatial Laser Solitons. PHYSICAL REVIEW LETTERS 2017; 118:044102. [PMID: 28186807 DOI: 10.1103/physrevlett.118.044102] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Indexed: 06/06/2023]
Abstract
A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets.
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Affiliation(s)
- F Gustave
- Université Côte d'Azur, CNRS, 06560 Valbonne, France
| | - N Radwell
- SUPA and Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - C McIntyre
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 ONG, Scotland, United Kingdom
| | - J P Toomey
- MQ Photonics Research Centre, Department of Physics & Astronomy, Macquarie University, Sydney 2109, Australia
| | - D M Kane
- MQ Photonics Research Centre, Department of Physics & Astronomy, Macquarie University, Sydney 2109, Australia
| | - S Barland
- Université Côte d'Azur, CNRS, 06560 Valbonne, France
| | - W J Firth
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 ONG, Scotland, United Kingdom
| | - G-L Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 ONG, Scotland, United Kingdom
| | - T Ackemann
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 ONG, Scotland, United Kingdom
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6
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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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7
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Driben R, Konotop VV, Malomed BA, Meier T. Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators. Phys Rev E 2016; 94:012207. [PMID: 27575123 DOI: 10.1103/physreve.94.012207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Indexed: 06/06/2023]
Abstract
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.
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Affiliation(s)
- R Driben
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
| | - V V Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016 Lisboa, Portugal
| | - B A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - T Meier
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
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8
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Driben R, Konotop VV, Meier T. Precession and nutation dynamics of nonlinearly coupled non-coaxial three-dimensional matter wave vortices. Sci Rep 2016; 6:22758. [PMID: 26964759 PMCID: PMC4786817 DOI: 10.1038/srep22758] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2015] [Accepted: 02/19/2016] [Indexed: 12/02/2022] Open
Abstract
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.
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Affiliation(s)
- R. Driben
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
- ITMO University, 49 Kronverskii Ave., St. Petersburg 197101, Russian Federation
| | - V. V. Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - T. Meier
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
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9
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Zhang YC, Zhou ZW, Malomed BA, Pu H. Stable Solitons in Three Dimensional Free Space without the Ground State: Self-Trapped Bose-Einstein Condensates with Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2015; 115:253902. [PMID: 26722921 DOI: 10.1103/physrevlett.115.253902] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Indexed: 06/05/2023]
Abstract
By means of variational methods and systematic numerical analysis, we demonstrate the existence of metastable solitons in three dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and spin-orbit coupling, which can be engineered by available experimental techniques. Depending on the relative strength of the intra- and intercomponent attraction, the stable solitons feature a semivortex or mixed-mode structure. In spite of the fact that the local cubic self-attraction gives rise to the supercritical collapse in 3D, and hence the setting produces no true ground state, the solitons are stable against small perturbations, motion, and collisions.
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Affiliation(s)
- Yong-Chang Zhang
- Key Laboratory of Quantum Information, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zheng-Wei Zhou
- Key Laboratory of Quantum Information, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Han Pu
- Department of Physics and Astronomy, and Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
- Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
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10
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Creation of vortices by torque in multidimensional media with inhomogeneous defocusing nonlinearity. Sci Rep 2015; 5:9420. [PMID: 25800140 PMCID: PMC4371187 DOI: 10.1038/srep09420] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Accepted: 03/02/2015] [Indexed: 11/08/2022] Open
Abstract
Recently, a new class of nonlinear systems was introduced, in which the self-trapping of fundamental and vortical localized modes in space of dimension D is supported by cubic self-repulsion with a strength growing as a function of the distance from the center, r, at any rate faster that rD. These systems support robust 2D and 3D modes which either do not exist or are unstable in other nonlinear systems. Here we demonstrate a possibility to create solitary vortices in this setting by applying a phase-imprinting torque to the ground state. Initially, a strong torque completely destroys the ground state. However, contrary to usual systems, where the destruction is irreversible, the present ones demonstrate a rapid restabilization and the creation of one or several shifted vortices orbiting the center. For the sake of comparison, we show analytically that, in the linear system with a 3D trapping potential, the action of a torque on the ground state is inefficient and creates only even-vorticity states with a small probability.
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11
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Kartashov YV, Malomed BA, Shnir Y, Torner L. Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity. PHYSICAL REVIEW LETTERS 2014; 113:264101. [PMID: 25615341 DOI: 10.1103/physrevlett.113.264101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2014] [Indexed: 06/04/2023]
Abstract
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis (m), appear in many fields, including field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multicomponent systems, or as trapped quasilinear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0, 1, 2 are produced. They are stable for m≤1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in a Bose-Einstein condensate (BEC) by means of the Feshbach resonance controlled by inhomogeneous magnetic fields.
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Affiliation(s)
- Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain and Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, 142190 Moscow, Russia
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Yasha Shnir
- Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia and Institute of Physics, Carl von Ossietzky University Oldenburg, Oldenburg D-26111, Germany
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
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12
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Driben R, Kartashov YV, Malomed BA, Meier T, Torner L. Soliton gyroscopes in media with spatially growing repulsive nonlinearity. PHYSICAL REVIEW LETTERS 2014; 112:020404. [PMID: 24483996 DOI: 10.1103/physrevlett.112.020404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2013] [Indexed: 06/03/2023]
Abstract
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S≥1. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation. Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.
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Affiliation(s)
- Rodislav Driben
- Department of Physics & CeOPP, University of Paderborn, Warburger Straße 100, Paderborn D-33098, Germany and Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yaroslav V Kartashov
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain and Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 142190, Russia
| | - 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 & CeOPP, University of Paderborn, Warburger Straße 100, Paderborn D-33098, Germany
| | - Lluis Torner
- ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
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13
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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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14
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Sakaguchi H, Malomed BA. Vortical light bullets in second-harmonic-generating media supported by a trapping potential. OPTICS EXPRESS 2013; 21:9813-9823. [PMID: 23609688 DOI: 10.1364/oe.21.009813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We introduce a three-dimensional (3D) model of optical media with the quadratic (χ((2))) nonlinearity and an effective 2D isotropic harmonic-oscillator (HO) potential. While it is well known that 3D χ((2)) solitons with embedded vorticity ("vortical light bullets") are unstable in the free space, we demonstrate that they have a broad stability region in the present model, being supported by the HO potential against the splitting instability. The shape of the vortical solitons may be accurately predicted by the variational approximation (VA). They exist above a threshold value of the total energy (norm) and below another critical value, which determines a stability boundary. The existence threshold vanishes is a part of the parameter space, depending on the mismatch parameter, which is explained by means of the comparison with the 2D counterpart of the system. Above the stability boundary, the vortex features shape oscillations, periodically breaking its axisymmetric form and restoring it. Collisions between vortices moving in the longitudinal direction are studied too. The collision is strongly inelastic at relatively small values of the velocities, breaking the two colliding vortices into three, with the same vorticity. The results suggest a possibility of the creation of stable 3D optical solitons with the intrinsic vorticity.
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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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15
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Burlak G, Malomed BA. Matter-wave solitons with the minimum number of particles in two-dimensional quasiperiodic potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:057601. [PMID: 23004912 DOI: 10.1103/physreve.85.057601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2012] [Indexed: 06/01/2023]
Abstract
We report results of systematic numerical studies of two-dimensional matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution attains a minimum, facilitating the creation of the soliton. The model is based on the Gross-Pitaevskii equation for the self-attractive condensate loaded into a quasiperiodic (QP) optical lattice (OL). The same model applies to spatial optical solitons in QP photonic crystals. Dynamical properties and stability of the solitons are analyzed with respect to variations of the depth and wave number of the OL. In particular, it is found that the single-peak solitons are stable or not in exact accordance with the Vakhitov-Kolokolov (VK) criterion, while double-peak solitons, which are found if the OL wave number is small enough, are always unstable against splitting.
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Affiliation(s)
- Gennadiy Burlak
- Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
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Panagiotopoulos P, Couairon A, Efremidis NK, Papazoglou DG, Tzortzakis S. Intense dynamic bullets in a periodic lattice. OPTICS EXPRESS 2011; 19:10057-10062. [PMID: 21643264 DOI: 10.1364/oe.19.010057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Femtosecond filamentation inside a periodic lattice in air is numerically shown to form intense dynamic bullets. The long propagation distance of the bullet structure is primarily attributed to the effect of the lattice that regulates the competition between linear and nonlinear spatiotemporal effects in the region of normal dispersion.
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Affiliation(s)
- P Panagiotopoulos
- Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas, PO Box 1527, 71110 Heraklion, Greece.
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Minardi S, Eilenberger F, Kartashov YV, Szameit A, Röpke U, Kobelke J, Schuster K, Bartelt H, Nolte S, Torner L, Lederer F, Tünnermann A, Pertsch T. Three-dimensional light bullets in arrays of waveguides. PHYSICAL REVIEW LETTERS 2010; 105:263901. [PMID: 21231663 DOI: 10.1103/physrevlett.105.263901] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2010] [Indexed: 05/30/2023]
Abstract
We report the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index. Stringent evidence of the excitation of light bullets is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the light bullets to follow varying dispersion or diffraction conditions, until they leave their existence range and decay.
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Affiliation(s)
- S Minardi
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Jena, Germany
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Ye F, Kartashov YV, Hu B, Torner L. Light bullets in Bessel optical lattices with spatially modulated nonlinearity. OPTICS EXPRESS 2009; 17:11328-11334. [PMID: 19582047 DOI: 10.1364/oe.17.011328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We address the stability of light bullets supported by Bessel optical lattices with out-of-phase modulation of the linear and nonlinear refractive indices. We show that spatial modulation of the nonlinearity significantly modifies the shapes and stability domains of the light bullets. The addressed bullets can be stable, provided that the peak intensity does not exceed a critical value. We show that the width of the stability domain in terms of the propagation constant may be controlled by varying the nonlinearity modulation depth. In particular, we show that the maximum energy of the stable bullets grows with increasing nonlinearity modulation depth.
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Affiliation(s)
- Fangwei Ye
- Department of Physics, Centre for Nonlinear Studies, and The Beijing-Hong Kong Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, China.
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Abstract
We address the concept of three-dimensional light bullet formation in structures where nonlinearity and dispersion are contributed by different materials, including metamaterials, which are used at their best to create suitable conditions where bullets can form. The particular geometry considered here consists of alternating rings made of highly dispersive but weakly nonlinear media and strongly nonlinear but weakly dispersive media. We show that light bullets form for a wide range of parameters.
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Affiliation(s)
- Lluis Torner
- Institut de Ciencies Fotoniques, Mediterranean Technology Park, Barcelona, Spain
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Szameit A, Kartashov YV, Dreisow F, Heinrich M, Pertsch T, Nolte S, Tünnermann A, Vysloukh VA, Lederer F, Torner L. Soliton excitation in waveguide arrays with an effective intermediate dimensionality. PHYSICAL REVIEW LETTERS 2009; 102:063902. [PMID: 19257591 DOI: 10.1103/physrevlett.102.063902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2008] [Indexed: 05/27/2023]
Abstract
We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.
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Affiliation(s)
- A Szameit
- Institute of Applied Physics, Friedrich Schiller University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
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Sivan Y, Fibich G, Ilan B, Weinstein MI. Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:046602. [PMID: 18999546 DOI: 10.1103/physreve.78.046602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2008] [Revised: 08/14/2008] [Indexed: 05/27/2023]
Abstract
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.
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Affiliation(s)
- Y Sivan
- Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
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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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Leblond H, Malomed BA, Mihalache D. Three-dimensional vortex solitons in quasi-two-dimensional lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:026604. [PMID: 17930164 DOI: 10.1103/physreve.76.026604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2006] [Indexed: 05/25/2023]
Abstract
We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts piS2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ("spinning light bullets," in terms of optics) with S>1 , and vortex solitons (with any S not equal 0 ) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.
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Affiliation(s)
- Hervé Leblond
- Laboratoire POMA, UMR 6136, Université d'Angers, 2 Bd Lavoisier, 49000 Angers, France
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Baizakov BB, Malomed BA, Salerno M. Matter-wave solitons in radially periodic potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066615. [PMID: 17280170 DOI: 10.1103/physreve.74.066615] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2006] [Revised: 08/16/2006] [Indexed: 05/13/2023]
Abstract
We investigate two-dimensional (2D) states in Bose-Einstein condensates with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity (l=0) , while with l not equal 0 they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal dark-soliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while pi-out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton.
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Affiliation(s)
- Bakhtiyor B Baizakov
- Physical-Technical Institute of the Uzbek Academy of Sciences, 2-b, G. Mavlyanov Strasse, 700084, Tashkent, Uzbekistan
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Mayteevarunyoo T, Malomed BA. Two-dimensional solitons in saturable media with a quasi-one-dimensional lattice potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:036615. [PMID: 16605685 DOI: 10.1103/physreve.73.036615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2005] [Indexed: 05/08/2023]
Abstract
We study families of solitons in a two-dimensional model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum values of the peak and total power. Narrow solitons have a single maximum, while broader ones feature side lobes. Stability of the solitons is checked by direct simulations. The solitons can be set in motion across the lattice (actually, made tilted in the spatial domain), provided that the respective boost parameter does not exceed a critical value. Collisions between moving solitons are studied too. Collisions destroy the solitons, unless their velocities are sufficiently small. In the latter case, the colliding solitons merge into a single stable pulse.
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Affiliation(s)
- Thawatchai Mayteevarunyoo
- Department of Telecommunication Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand
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Leblond H. Spatiotemporal optical pulse control using microwaves. PHYSICAL REVIEW LETTERS 2005; 95:033902. [PMID: 16090744 DOI: 10.1103/physrevlett.95.033902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/03/2023]
Abstract
The Davey-Stewartson system allows us to describe the interaction between a spatiotemporal optical pulse and adequately matched microwaves. We show that the interaction can lead to the formation of a two-dimensional soliton which is robust in the sense that it occurs in a wide range of parameters of the incident optical pulse and microwaves, and of the material used.
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Affiliation(s)
- H Leblond
- Laboratoire POMA, UMR 6136, Université d'Angers, 2 Boulevard Lavoisier, 49000 Angers, France
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Mihalache D, Mazilu D, Lederer F, Malomed BA, Kartashov YV, Crasovan LC, Torner L. Stable spatiotemporal solitons in bessel optical lattices. PHYSICAL REVIEW LETTERS 2005; 95:023902. [PMID: 16090683 DOI: 10.1103/physrevlett.95.023902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2004] [Indexed: 05/03/2023]
Abstract
We investigate the existence and stability of three-dimensional solitons supported by cylindrical Bessel lattices in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian versus norm diagram has a swallowtail shape with three cuspidal points. The model applies to Bose-Einstein condensates and to optical media with saturable nonlinearity, suggesting new ways of making stable three-dimensional solitons and "light bullets" of an arbitrary size.
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Affiliation(s)
- D Mihalache
- Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universität Jena, Max-Wien-Platz 1, D-077743 Jena, Germany
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