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Meng H, Wang J, Fan X, Wang Q, Shao K, Zhao Y, Wang W, Shi Y. Vector gap solitons of spin-orbit-coupled Bose-Einstein condensate in honeycomb optical lattices. Phys Rev E 2023; 108:034215. [PMID: 37849209 DOI: 10.1103/physreve.108.034215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Accepted: 09/06/2023] [Indexed: 10/19/2023]
Abstract
The combination of the two hot topics of spin-orbit coupling and honeycomb lattices leads to the appearance of fascinating issues. In this paper, we investigate the existence and stability of vector gap solitons of spin-orbit-coupled Bose-Einstein condensates loaded in honeycomb optical lattices. The existence and stability of vector gap solitons are highly sensitive to the properties of interspin and intraspin atomic interaction. We numerically obtain the parametric dependence of the existence of vector gap solitons both in the semi-infinite gap and in the first gap. Since only dynamically stable localized modes in nonlinear systems are likely to be generated and observed in experiments, we examine the stability of the vector gap solitons by using the direct evolution dynamics, and obtain the phase diagram of stable and unstable vector gap solitons on the parameter plane of interspin and intraspin atomic interactions.
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Affiliation(s)
- Hongjuan Meng
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Jing Wang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Xiaobei Fan
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Qingqing Wang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Kaihua Shao
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Yuexin Zhao
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Wenyuan Wang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
| | - Yuren Shi
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China and Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Northwest Normal University, Lanzhou 730070, China
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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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Wang Y, Ding JW, Wang DL, Liu WM. Intrinsical localization of both topological (anti-kink) envelope and gray (black) gap solitons of the condensed bosons in deep optical lattices. CHAOS (WOODBURY, N.Y.) 2020; 30:123133. [PMID: 33380039 DOI: 10.1063/5.0025441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Accepted: 11/27/2020] [Indexed: 06/12/2023]
Abstract
By developing quasi-discrete multiple-scale method combined with tight-binding approximation, a novel quadratic Riccati differential equation is first derived for the soliton dynamics of the condensed bosons trapped in the optical lattices. For a lack of exact solutions, the trial solutions of the Riccati equation have been analytically explored for the condensed bosons with various scattering length as. When the lattice depth is rather shallow, the results of sub-fundamental gap solitons are in qualitative agreement with the experimental observation. For the deeper lattice potentials, we predict that in the case of as>0, some novel intrinsically localized modes of symmetrical envelope, topological (kink) envelope, and anti-kink envelope solitons can be observed within the bandgap in the system, of which the amplitude increases with the increasing lattice spacing and (or) depth. In the case of as<0, the bandgap brings out intrinsically localized gray or black soliton. This well provides experimental protocols to realize transformation between the gray and black solitons by reducing light intensity of the laser beams forming optical lattice.
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Affiliation(s)
- Y Wang
- Department of Physics and Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan 411105, Hunan, China
| | - J W Ding
- Department of Physics and Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan 411105, Hunan, China
| | - D L Wang
- Department of Physics and Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan 411105, Hunan, China
| | - W M Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
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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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Zeng J, Malomed BA. Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity. Phys Rev E 2017; 95:052214. [PMID: 28618638 DOI: 10.1103/physreve.95.052214] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2016] [Indexed: 11/07/2022]
Abstract
Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than r^{D}, in space of dimension D with radial coordinate r, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ∼r^{α} with α≤D, we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S=1. In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S=1, higher-order LDSs with multiple notches are found too, as well as double LDVs, with S=2. Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.
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Affiliation(s)
- Jianhua Zeng
- State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics of CAS, Xi'an 710119, China
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.,Laboratory of Nonlinear-Optical Informatics, ITMO University, St. Petersburg 197101, Russia
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Wen Z, Yan Z. Solitons and their stability in the nonlocal nonlinear Schrödinger equation with PT-symmetric potentials. CHAOS (WOODBURY, N.Y.) 2017; 27:053105. [PMID: 28576099 DOI: 10.1063/1.4982972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.
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Affiliation(s)
- Zichao Wen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China
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Kumar S, Perego AM, Staliunas K. Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations. PHYSICAL REVIEW LETTERS 2017; 118:044103. [PMID: 28186803 DOI: 10.1103/physrevlett.118.044103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2016] [Indexed: 06/06/2023]
Abstract
We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.
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Affiliation(s)
- S Kumar
- Departament de Fisica, Universitat Politècnica de Catalunya, E-08222, Barcelona, Spain
| | - A M Perego
- Departament de Fisica, Universitat Politècnica de Catalunya, E-08222, Barcelona, Spain
- Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, United Kingdom
| | - K Staliunas
- Departament de Fisica, Universitat Politècnica de Catalunya, E-08222, Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, E-08010, Barcelona, Spain
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Zou P, Brand J, Liu XJ, Hu H. Traveling Majorana Solitons in a Low-Dimensional Spin-Orbit-Coupled Fermi Superfluid. PHYSICAL REVIEW LETTERS 2016; 117:225302. [PMID: 27925728 DOI: 10.1103/physrevlett.117.225302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Indexed: 06/06/2023]
Abstract
We investigate traveling solitons of a one- or two-dimensional spin-orbit-coupled Fermi superfluid in both topologically trivial and nontrivial regimes by solving the static and time-dependent Bogoliubov-de Gennes equations. We find a critical velocity v_{h} for traveling solitons that is much smaller than the value predicted using the Landau criterion due to spin-orbit coupling. Above v_{h}, our time-dependent simulations in harmonic traps indicate that traveling solitons decay by radiating sound waves. In the topological phase, we predict the existence of peculiar Majorana solitons, which host two Majorana fermions and feature a phase jump of π across the soliton, irrespective of the velocity of travel. These unusual properties of Majorana solitons may open an alternative way to manipulate Majorana fermions for fault-tolerant topological quantum computations.
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Affiliation(s)
- Peng Zou
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
| | - Joachim Brand
- New Zealand Institute for Advanced Study, Centre of Theoretical Chemistry and Physics, and Dodd-Walls Centre for Photonic and Quantum Technologies, Massey University, Auckland 0745, New Zealand
| | - Xia-Ji Liu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
| | - Hui Hu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
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Taming of Modulation Instability by Spatio-Temporal Modulation of the Potential. Sci Rep 2015; 5:13268. [PMID: 26286250 PMCID: PMC4541154 DOI: 10.1038/srep13268] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Accepted: 07/13/2015] [Indexed: 11/11/2022] Open
Abstract
Spontaneous pattern formation in a variety of spatially extended nonlinear systems always occurs through a modulation instability, sometimes called Turing instability: the homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of spatial patterns initiated by that instability. We show that a spatio-temporal periodic modulation of the potential of spatially extended systems results in a modification of its pattern forming instability. Depending on the modulation character the instability can be partially suppressed, can change its spectrum (for instance the long wave instability can transform into short wave instability), can split into two, or can be completely eliminated. The latter result is of special practical interest, as it can be used to stabilize the intrinsically unstable system. The result bears general character, as it is shown here on a universal model of the Complex Ginzburg-Landau equation in one and two spatial dimensions (and time). The physical mechanism of the instability suppression can be applied to a variety of intrinsically unstable dissipative systems, like self-focusing lasers, reaction-diffusion systems, as well as in unstable conservative systems, like attractive Bose Einstein condensates.
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Cerda-Méndez EA, Sarkar D, Krizhanovskii DN, Gavrilov SS, Biermann K, Skolnick MS, Santos PV. Exciton-polariton gap solitons in two-dimensional lattices. PHYSICAL REVIEW LETTERS 2013; 111:146401. [PMID: 24138259 DOI: 10.1103/physrevlett.111.146401] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Revised: 08/16/2013] [Indexed: 06/02/2023]
Abstract
We report on the two-dimensional gap-soliton nature of exciton-polariton macroscopic coherent phases (PMCP) in a square lattice with a tunable amplitude. The resonantly excited PMCP forms close to the negative mass M point of the lattice band structure with energy within the lattice band gap and its wave function localized within a few lattice periods. The PMCPs are well described as gap solitons resulting from the interplay between repulsive polariton-polariton interactions and effective attractive forces due to the negative mass. The solitonic nature accounts for the reduction of the PMCP coherence length and optical excitation threshold with increasing lattice amplitude.
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Affiliation(s)
- E A Cerda-Méndez
- Paul-Drude-Institut für Festkörperelektronik, 10117 Berlin, Germany
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11
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Mateo AM, Delgado V. Effective equations for matter-wave gap solitons in higher-order transversal states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042916. [PMID: 24229258 DOI: 10.1103/physreve.88.042916] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective one-dimensional (1D) model. Using a variational approach we derive effective equations of lower dimensionality for BECs in (m,n(r)) transversal states (states featuring a central vortex of charge m as well as n(r) concentric zero-density rings at every z plane) which provides us with a good approximate solution of the original 3D problem. Since the specifics of the transversal dynamics can be absorbed in the renormalization of a couple of parameters, the functional form of the equations obtained is universal. The model proposed finds its principal application in the study of the existence and classification of 3D gap solitons supported by 1D optical lattices, where in addition to providing a good estimate for the 3D wave functions it is able to make very good predictions for the μ(N) curves characterizing the different fundamental families. We have corroborated the validity of our model by comparing its predictions with those from the exact numerical solution of the full 3D GPE.
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Affiliation(s)
- A Muñoz Mateo
- Departamento de Física Fundamental II, Facultad de Física, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain
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12
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Bin-Bin LÜ, Qiang T. Different Kinds of Discrete Breathers in Three Types of One-Dimensional Models. COMMUNICATIONS IN THEORETICAL PHYSICS 2010; 54:728-734. [DOI: 10.1088/0253-6102/54/4/27] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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13
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Eilenberger F, Martijn de Sterke C, Eggleton BJ. Soliton mediated optical quantization in the transmission of one-dimensional photonic crystals. OPTICS EXPRESS 2010; 18:12708-12718. [PMID: 20588399 DOI: 10.1364/oe.18.012708] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We report the experimental and numerical observation of step-like behavior of the high-intensity transmission deep inside the bandgap of a 1D photonic crystal. We show this to be a novel manifestation of the quantization of the soliton area, and derive an upper limit for the energy of the transmission steps, which is consistent with measurements and simulations.
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Affiliation(s)
- Falk Eilenberger
- Centre for Ultra-high bandwidth Devices for Optics Systems, Institute of Photonics and Optical Science, School of Physics, University of Sydney, Sydney, NSW 2006, Australia.
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Itah A, Veksler H, Lahav O, Blumkin A, Moreno C, Gordon C, Steinhauer J. Direct observation of a sub-Poissonian number distribution of atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2010; 104:113001. [PMID: 20366471 DOI: 10.1103/physrevlett.104.113001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2009] [Indexed: 05/29/2023]
Abstract
We report single-site resolution in a lattice with tunneling between sites, allowing for an in situ study of stochastic losses. The ratio of the loss rate to the tunneling rate is seen to determine the number fluctuations, and the overall profile of the lattice. Sub-Poissonian number fluctuations are observed. Deriving the lattice beams from a microlens array results in perfect relative stability between beams.
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Affiliation(s)
- Amir Itah
- Department of Physics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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15
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Nath R, Pedri P, Santos L. Phonon instability with respect to soliton formation in two-dimensional dipolar Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2009; 102:050401. [PMID: 19257488 DOI: 10.1103/physrevlett.102.050401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Revised: 11/25/2008] [Indexed: 05/27/2023]
Abstract
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.
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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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16
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Wang DL, Yan XH, Liu WM. Localized gap-soliton trains of Bose-Einstein condensates in an optical lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026606. [PMID: 18850961 DOI: 10.1103/physreve.78.026606] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2007] [Revised: 06/10/2008] [Indexed: 05/26/2023]
Abstract
We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu's functions ce_{n-1} and se_{n} ; and the Bloch wave in the nth band gap is a linear superposition of ce_{n} and se_{n} . For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons-fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann, Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.
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Affiliation(s)
- D L Wang
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
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17
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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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18
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Lou C, Wang X, Xu J, Chen Z, Yang J. Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures. PHYSICAL REVIEW LETTERS 2007; 98:213903. [PMID: 17677773 DOI: 10.1103/physrevlett.98.213903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2007] [Indexed: 05/16/2023]
Abstract
We report the first theoretical prediction and experimental demonstration of gap soliton trains in a self-defocusing photonic lattice. Without a priori spectral or phase engineering, a stripe beam whose spatial power spectrum lies only in one transverse direction evolves into a gap soliton train with power spectrum growing also in the orthogonal direction due to nonlinear transport and spectrum reshaping. Our results suggest that, in nonlinear k-space evolution, energy can transfer not only between regions of normal and anomalous diffraction, but also from initially excited regions to initially unexcited regions.
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Affiliation(s)
- Cibo Lou
- The Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education and TEDA Applied Physical School, Nankai University, Tianjin 300457, China
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Richter T, Motzek K, Kaiser F. Long distance stability of gap solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:016601. [PMID: 17358269 DOI: 10.1103/physreve.75.016601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2006] [Indexed: 05/14/2023]
Abstract
We numerically investigate the stability of one- and two-dimensional gap solitons for very long propagation distances both in self-focusing and in self-defocusing nonlinear photonic media. We demonstrate that the existence of stable solitons in the first gap requires much stronger lattices in a self-focusing than in a self-defocusing medium. Moreover, we present a one-dimensional linear stability analysis of the fundamental solitary mode in the first gap considering a self-focusing photorefractive nonlinearity.
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Affiliation(s)
- T Richter
- Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 4a, D-64289 Darmstadt, Germany
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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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21
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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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22
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Staliunas K, Serrat C, Herrero R, Cojocaru C, Trull J. Subdiffractive light pulses in photonic crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016605. [PMID: 16907202 DOI: 10.1103/physreve.74.016605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2006] [Indexed: 05/11/2023]
Abstract
We investigate propagation of light pulses in photonic crystals in the vicinity of the zero diffraction point. We show that Gaussian pulses due to nonzero width of their temporal spectrum spread weakly in space and time during the propagation. We also find the family of nonspreading pulses, propagating invariantly in the vicinity of the zero diffraction point of photonic crystals.
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Affiliation(s)
- K Staliunas
- Institució Catalana de Reserca i Estudis Avançats (ICREA), Departament de Fisica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, E-08222 Terrassa, Barcelona, Spain
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23
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Staliunas K, Herrero R, de Valcárcel GJ. Subdiffractive band-edge solitons in Bose-Einstein condensates in periodic potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:065603. [PMID: 16906906 DOI: 10.1103/physreve.73.065603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2005] [Indexed: 05/11/2023]
Abstract
A type of matter wave diffraction management is presented that leads to subdiffractive solitonlike structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g., optical lattices). For suitable lattice parameters, a different type of atomic bandgap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way, normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes subdiffractive.
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Affiliation(s)
- Kestutis Staliunas
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, 08222 Terrassa, Spain
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24
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Staliunas K, Herrero R. Nondiffractive propagation of light in photonic crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:016601. [PMID: 16486289 DOI: 10.1103/physreve.73.016601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2004] [Revised: 09/22/2005] [Indexed: 05/06/2023]
Abstract
We investigate nondiffractive propagation of electromagnetic radiation, including visible light, through materials with a periodic space modulation of the refraction index, i.e., through photonic crystals. We calculate analytically and numerically the regimes where the dominating order of diffraction vanishes, i.e., the light beams of arbitrary width propagate without diffractive broadening and, equivalently, arbitrary light patterns can propagate without diffractive "smearing." We investigate the subdiffractive light propagation, where the propagation is governed by the higher (fourth) diffraction order, when the dominating order of diffraction vanishes.
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Affiliation(s)
- Kestutis Staliunas
- ICREA, Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Colom 11, E-08222 Terrassa, Barcelona, Spain
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25
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Ahufinger V, Sanpera A. Lattice solitons in quasicondensates. PHYSICAL REVIEW LETTERS 2005; 94:130403. [PMID: 15903975 DOI: 10.1103/physrevlett.94.130403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2004] [Indexed: 05/02/2023]
Abstract
We analyze finite temperature effects in the generation of bright solitons in condensates in optical lattices. We show that even in the presence of strong phase fluctuations solitonic structures with a well defined phase profile can be created. We propose a novel family of variational functions which describe well the properties of these solitons and account for the nonlinear effects in the band structure. We discuss also the mobility and collisions of these localized wave packets.
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Affiliation(s)
- V Ahufinger
- Institut für Theoretische Physik, Universität Hannover, D-30167 Hannover, Germany
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26
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Mihalache D, Mazilu D, Lederer F, Kartashov YV, Crasovan LC, Torner L. Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:055603. [PMID: 15600685 DOI: 10.1103/physreve.70.055603] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2004] [Indexed: 05/24/2023]
Abstract
We investigate the existence and stability of three-dimensional spatiotemporal solitons in self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic transverse modulation of the refractive index. We demonstrate that two-dimensional photonic Kerr-type nonlinear lattices can support stable one-parameter families of three-dimensional spatiotemporal solitons provided that their energy is within a certain interval and the strength of the lattice potential, which is proportional to the refractive index modulation depth, is above a certain threshold value.
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Affiliation(s)
- D Mihalache
- ICFO-Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain
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Ostrovskaya EA, Kivshar YS. Matter-wave gap vortices in optical lattices. PHYSICAL REVIEW LETTERS 2004; 93:160405. [PMID: 15524961 DOI: 10.1103/physrevlett.93.160405] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2004] [Indexed: 05/24/2023]
Abstract
We predict the existence of spatially localized nontrivial topological states of a Bose-Einstein condensate with repulsive atomic interactions confined by an optical lattice. These nonlinear localized states, matter-wave gap vortices, carry a vortexlike phase dislocation and exist in the gaps of the matter-wave band-gap spectrum due to the Bragg scattering. We discuss the structure, stability, and formation dynamics of the gap vortices in the case of two-dimensional optical lattices.
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Affiliation(s)
- Elena A Ostrovskaya
- 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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Kartashov YV, Egorov AA, Torner L, Christodoulides DN. Stable soliton complexes in two-dimensional photonic lattices. OPTICS LETTERS 2004; 29:1918-1920. [PMID: 15357359 DOI: 10.1364/ol.29.001918] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.
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Affiliation(s)
- Yaroslav V Kartashov
- Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain.
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29
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Alexander TJ, Sukhorukov AA, Kivshar YS. Asymmetric vortex solitons in nonlinear periodic lattices. PHYSICAL REVIEW LETTERS 2004; 93:063901. [PMID: 15323631 DOI: 10.1103/physrevlett.93.063901] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2004] [Indexed: 05/24/2023]
Abstract
We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice and also describe novel coherent states where the populations of clockwise and anticlockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems, including optically induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.
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Affiliation(s)
- Tristram J Alexander
- Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200
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Eiermann B, Anker T, Albiez M, Taglieber M, Treutlein P, Marzlin KP, Oberthaler MK. Bright Bose-Einstein gap solitons of atoms with repulsive interaction. PHYSICAL REVIEW LETTERS 2004; 92:230401. [PMID: 15245143 DOI: 10.1103/physrevlett.92.230401] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2003] [Indexed: 05/24/2023]
Abstract
We report on the first experimental observation of bright matter wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wave packet is prepared at the corresponding band edge, a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.
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Affiliation(s)
- B Eiermann
- Kirchhoff Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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31
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Conti C, Trillo S. Nonspreading wave packets in three dimensions formed by an ultracold bose gas in an optical lattice. PHYSICAL REVIEW LETTERS 2004; 92:120404. [PMID: 15089656 DOI: 10.1103/physrevlett.92.120404] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2003] [Indexed: 05/24/2023]
Abstract
We predict that an ultracold Bose gas in an optical lattice can give rise to a new form of condensation, namely, nonspreading 3D wave packets that reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction and are allowed to exist in the absence of any trapping potential even in the limit of noninteracting atoms. This result also has strong implications for optical propagation in periodic structures.
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Affiliation(s)
- Claudio Conti
- National Institute for the Physics of Matter, INFM, Università Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
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32
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Efremidis NK, Hudock J, Christodoulides DN, Fleischer JW, Cohen O, Segev M. Two-dimensional optical lattice solitons. PHYSICAL REVIEW LETTERS 2003; 91:213906. [PMID: 14683306 DOI: 10.1103/physrevlett.91.213906] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2003] [Indexed: 05/24/2023]
Abstract
We study various families of two-dimensional discrete or lattice solitons, and show that they are possible only when their power level exceeds a critical threshold. In addition, we show that gap-lattice solitons exist only when the lattice possesses a complete 2D band gap. Our results suggest that these conditions are universally valid, irrespective of the nature of the nonlinearity or the specific structure of the index lattice. The analysis explains fundamental aspects of behavior of two-dimensional discrete solitons that have been very recently observed in photosensitive optical crystals.
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33
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Desyatnikov AS, Ostrovskaya EA, Kivshar YS, Denz C. Composite band-gap solitons in nonlinear optically induced lattices. PHYSICAL REVIEW LETTERS 2003; 91:153902. [PMID: 14611467 DOI: 10.1103/physrevlett.91.153902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2003] [Indexed: 05/24/2023]
Abstract
We introduce novel optical solitons that consist of a periodic and a spatially localized component coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.
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Affiliation(s)
- Anton S Desyatnikov
- Nonlinear Photonics Group, Institute of Applied Physics, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
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34
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Kivshar YS, Flach S. Introduction: Nonlinear localized modes. CHAOS (WOODBURY, N.Y.) 2003; 13:586-587. [PMID: 12777123 DOI: 10.1063/1.1577332] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Affiliation(s)
- Yuri S Kivshar
- Nonlinear Physics Group, Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia
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