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Zeng L, Shi J, Belić MR, Mihalache D, Chen J, Li J, Zhu X. Surface gap solitons in the Schrödinger equation with quintic nonlinearity and a lattice potential. OPTICS EXPRESS 2023; 31:35471-35483. [PMID: 38017716 DOI: 10.1364/oe.497973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 09/02/2023] [Indexed: 11/30/2023]
Abstract
We demonstrate the existence of surface gap solitons, a special type of asymmetric solitons, in the one-dimensional nonlinear Schrödinger equation with quintic nonlinearity and a periodic linear potential. The nonlinearity is suddenly switched in a step-like fashion in the middle of the transverse spatial region, while the periodic linear potential is chosen in the form of a simple sin 2 lattice. The asymmetric nonlinearities in this work can be realized by the Feshbach resonance in Bose-Einstein condensates or by the photorefractive effect in optics. The major peaks in the gap soliton families are asymmetric and they are located at the position of the jump in nonlinearity (at x = 0). In addition, the major peaks of the two-peak and multi-peak solitons at the position x = 0 are higher than those after that position, at x > 0. And such phenomena are more obvious when the value of chemical potential is large, or when the difference of nonlinearity values across the jump is big. Along the way, linear stability analysis of the surface gap solitons is performed and the stability domains are identified. It is found that in this model, the solitons in the first band gap are mostly stable (excepting narrow domains of instability at the edges of the gap), while those in the second band gap are mostly unstable (excepting extremely narrow domains of stability for fundamental solitons). These findings are also corroborated by direct numerical simulations.
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2
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Qin J, Zhou L. Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system. Phys Rev E 2022; 105:054214. [PMID: 35706219 DOI: 10.1103/physreve.105.054214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023]
Abstract
The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.
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Affiliation(s)
- Jieli Qin
- School of Physics and Materials Science, Guangzhou University, 230 Wai Huan Xi Road, Guangzhou Higher Education Mega Center, Guangzhou 510006, China
| | - Lu Zhou
- Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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3
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Zhang AX, Hu XW, Jiang YF, Liang JC, Zhang Y, Zhang W, Xue JK. Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices. Phys Rev E 2021; 104:064215. [PMID: 35030834 DOI: 10.1103/physreve.104.064215] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 12/09/2021] [Indexed: 11/07/2022]
Abstract
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.
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Affiliation(s)
- Ai-Xia Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Xiao-Wen Hu
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Yan-Fang Jiang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Jun-Cheng Liang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ying Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Wei Zhang
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
| | - Ju-Kui Xue
- College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China
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4
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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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5
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Goblot V, Rauer B, Vicentini F, Le Boité A, Galopin E, Lemaître A, Le Gratiet L, Harouri A, Sagnes I, Ravets S, Ciuti C, Amo A, Bloch J. Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons. PHYSICAL REVIEW LETTERS 2019; 123:113901. [PMID: 31573264 DOI: 10.1103/physrevlett.123.113901] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Revised: 07/26/2019] [Indexed: 06/10/2023]
Abstract
Phase frustration in periodic lattices is responsible for the formation of dispersionless flatbands. The absence of any kinetic energy scale makes flatband physics critically sensitive to perturbations and interactions. We report on the experimental investigation of the nonlinear response of cavity polaritons in the gapped flatband of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and abrupt edges, a signature of the frozen propagation of switching fronts. This type of gap soliton belongs to the class of truncated Bloch waves, and has only been observed in closed systems up to now. Here, the driven-dissipative character of the system gives rise to a complex multistability of the flatband nonlinear domains. These results open up an interesting perspective regarding more complex 2D lattices and the generation of correlated photon phases.
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Affiliation(s)
- V Goblot
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - B Rauer
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - F Vicentini
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013 Paris, France
| | - A Le Boité
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013 Paris, France
| | - E Galopin
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - L Le Gratiet
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - A Harouri
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - I Sagnes
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - S Ravets
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
| | - C Ciuti
- Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS, F-75013 Paris, France
| | - A Amo
- Université de Lille, CNRS, UMR 8523 -PhLAM- Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - J Bloch
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
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6
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Colas D, Laussy FP, Davis MJ. Negative-Mass Effects in Spin-Orbit Coupled Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2018; 121:055302. [PMID: 30118304 DOI: 10.1103/physrevlett.121.055302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2017] [Revised: 06/09/2018] [Indexed: 06/08/2023]
Abstract
Negative effective masses can be realized by engineering the dispersion relation of a variety of quantum systems. A recent experiment with spin-orbit coupled Bose-Einstein condensates has shown that a negative effective mass can halt the free expansion of the condensate and lead to fringes in the density [M. A. Khamehchi et al., Phys. Rev. Lett. 118, 155301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.155301]. Here, we show that the underlying cause of these observations is the self-interference of the wave packet that arises when only one of the two effective mass parameters that characterize the dispersion of the system is negative. We show that spin-orbit coupled Bose-Einstein condensates may access regimes where both mass parameters controlling the propagation and diffusion of the condensate are negative, which leads to the novel phenomenon of counterpropagating self-interfering packets.
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Affiliation(s)
- David Colas
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
| | - Fabrice P Laussy
- Faculty of Science and Engineering, University of Wolverhampton, Wulfruna Street, Wolverhampton WV1 1LY, United Kingdom
- Russian Quantum Center, Novaya 100, 143025 Skolkovo, Moscow Region, Russia
| | - Matthew J Davis
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
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7
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Stable symmetry-protected 3D embedded solitons in Bose-Einstein condensates. Sci Rep 2018; 8:10940. [PMID: 30026577 PMCID: PMC6053375 DOI: 10.1038/s41598-018-29219-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 07/05/2018] [Indexed: 11/08/2022] Open
Abstract
Embedded solitons are rare self-localized nonlinear structures that, counterintuitively, survive inside a continuous background of resonant states. While this topic has been widely studied in nonlinear optics, it has received almost no attention in the field of Bose–Einstein condensation. In this work, we consider experimentally realizable Bose–Einstein condensates loaded in one-dimensional optical lattices and demonstrate that they support continuous families of stable three-dimensional (3D) embedded solitons. These solitons can exist inside the resonant continuous Bloch bands because they are protected by symmetry. The analysis of the Bogoliubov excitation spectrum as well as the long-term evolution after random perturbations proves the robustness of these nonlinear structures against any weak perturbation. This may open up a way for the experimental realization of stable 3D matter-wave embedded solitons as well as for monitoring the gap-soliton to embedded-soliton transition.
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8
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Dong L, Huang C. Composition Relation between Nonlinear Bloch Waves and Gap Solitons in Periodic Fractional Systems. MATERIALS 2018; 11:ma11071134. [PMID: 29973535 PMCID: PMC6073517 DOI: 10.3390/ma11071134] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Revised: 06/15/2018] [Accepted: 06/21/2018] [Indexed: 11/16/2022]
Abstract
Evolution of beams in nonlinear optical media with a fractional-order diffraction is currently attracting a growing interest. We address the existence of linear and nonlinear Bloch waves in fractional systems with a periodic potential. Under a defocusing nonlinearity, nonlinear Bloch waves at the centers or edges of the first Brillouin zone bifurcate from the corresponding linear Bloch modes at different band edges. They can be constructed by directly copying a fundamental gap soliton (in one lattice site) or alternatively copying it and its mirror image to infinite lattice channels. The localized truncated-Bloch-wave solitons bridging nonlinear Bloch waves and gap solitons are also revealed. We thus prove that fundamental gap solitons can be used as unit cells to build nonlinear Bloch waves or truncated-Bloch-wave solitons, even in fractional configurations. Our results provide helpful hints for understanding the dynamics of localized and delocalized nonlinear modes and the relation between them in periodic fractional systems with an optical nonlinearity.
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Affiliation(s)
- Liangwei Dong
- Department of Physics, Shaanxi University of Science & Technology, Xi'an 710021, China.
| | - Changming Huang
- Department of Electronic Information and Physics, Changzhi University, Changzhi 046011, China.
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9
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Xiao J, Tian Z, Huang C, Dong L. Surface gap solitons in a nonlinear fractional Schrödinger equation. OPTICS EXPRESS 2018; 26:2650-2658. [PMID: 29401802 DOI: 10.1364/oe.26.002650] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2017] [Accepted: 01/19/2018] [Indexed: 06/07/2023]
Abstract
We address the propagation dynamics of gap solitons at the interface between uniform media and an optical lattice in the framework of a nonlinear fractional Schrödinger equation. Different families of solitons residing in the first and second bandgaps of the Floquet-Bloch spectrum are revealed. They feature a combination of the unique properties of fractional diffraction effects, surface waves and gap solitons. The instability of solitons can be remarkably suppressed by the decrease of Lévy index, especially obvious for solitons in the second gaps. Additionally, we study the properties of multi-peaked solitons in fractional dimensions and find that they can be made completely stable in a wide region, provided that their power exceeds a critical value. Counterintuitively, at a small Lévy index, the instability region shrinks with the increase of the number of soliton peaks.
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10
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Khamehchi MA, Hossain K, Mossman ME, Zhang Y, Busch T, Forbes MM, Engels P. Negative-Mass Hydrodynamics in a Spin-Orbit-Coupled Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2017; 118:155301. [PMID: 28452531 DOI: 10.1103/physrevlett.118.155301] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 06/07/2023]
Abstract
A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.
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Affiliation(s)
- M A Khamehchi
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
| | - Khalid Hossain
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
| | - M E Mossman
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
| | - Yongping Zhang
- Quantum Systems Unit, OIST Graduate University, Onna, Okinawa 904-0495, Japan
- Department of Physics, Shanghai University, Shanghai 200444, China
| | - Th Busch
- Quantum Systems Unit, OIST Graduate University, Onna, Okinawa 904-0495, Japan
| | - Michael McNeil Forbes
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
- Department of Physics, University of Washington, Seattle, Washington 98105, USA
| | - P Engels
- Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA
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11
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Lebedev ME, Alfimov GL, Malomed BA. Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity. CHAOS (WOODBURY, N.Y.) 2016; 26:073110. [PMID: 27475070 DOI: 10.1063/1.4958710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.
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Affiliation(s)
- M E Lebedev
- National Research University of Electronic Technology MIET, Zelenograd, Moscow 124498, Russia
| | - G L Alfimov
- National Research University of Electronic Technology MIET, Zelenograd, Moscow 124498, Russia
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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12
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Alexander TJ, Yan D, Kevrekidis PG. Complex mode dynamics of coupled wave oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062908. [PMID: 24483532 DOI: 10.1103/physreve.88.062908] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2013] [Revised: 10/30/2013] [Indexed: 06/03/2023]
Abstract
We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these "coupled wave oscillators" and find that they can be extended into the large amplitude regime, where some "ring" for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.
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Affiliation(s)
- T J Alexander
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, Australia 2600
| | - D Yan
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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13
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Ostrovskaya EA, Abdullaev J, Fraser MD, Desyatnikov AS, Kivshar YS. Self-localization of polariton condensates in periodic potentials. PHYSICAL REVIEW LETTERS 2013; 110:170407. [PMID: 23679692 DOI: 10.1103/physrevlett.110.170407] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2012] [Indexed: 06/02/2023]
Abstract
We predict the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic in-plane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We reveal that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultracold alkali atoms.
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Affiliation(s)
- E A Ostrovskaya
- Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia
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14
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Reinhard A, Riou JF, Zundel LA, Weiss DS, Li S, Rey AM, Hipolito R. Self-trapping in an array of coupled 1D Bose gases. PHYSICAL REVIEW LETTERS 2013; 110:033001. [PMID: 23373918 DOI: 10.1103/physrevlett.110.033001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2012] [Indexed: 06/01/2023]
Abstract
We study the transverse expansion of arrays of ultracold (87)Rb atoms weakly confined in tubes created by a 2D optical lattice and observe that transverse expansion is delayed because of mutual atom interactions. A mean-field model of a coupled array shows that atoms become localized within a roughly square fortlike self-trapping barrier with time-evolving edges. But the observed dynamics are poorly described by the mean-field model. The theoretical introduction of random phase fluctuations among tubes improves the agreement with experiment but does not correctly predict the density at which the atoms start to expand with larger lattice depths. Our results suggest a new type of self-trapping, where quantum correlations suppress tunneling even when there are no density gradients.
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Affiliation(s)
- Aaron Reinhard
- Physics Department, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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15
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Tanese D, Flayac H, Solnyshkov D, Amo A, Lemaître A, Galopin E, Braive R, Senellart P, Sagnes I, Malpuech G, Bloch J. Polariton condensation in solitonic gap states in a one-dimensional periodic potential. Nat Commun 2013; 4:1749. [PMID: 23612290 PMCID: PMC3644099 DOI: 10.1038/ncomms2760] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2013] [Accepted: 03/18/2013] [Indexed: 11/09/2022] Open
Abstract
Manipulation of nonlinear waves in artificial periodic structures leads to spectacular spatial features, such as generation of gap solitons or onset of the Mott insulator phase transition. Cavity exciton-polaritons are strongly interacting quasiparticles offering large possibilities for potential optical technologies. Here we report their condensation in a one-dimensional microcavity with a periodic modulation. The resulting mini-band structure dramatically influences the condensation process. Contrary to non-modulated cavities, where condensates expand, here, we observe spontaneous condensation in localized gap soliton states. Depending on excitation conditions, we access different dynamical regimes: we demonstrate the formation of gap solitons either moving along the ridge or bound to the potential created by the reservoir of uncondensed excitons. We also find Josephson oscillations of gap solitons triggered between the two sides of the reservoir. This system is foreseen as a building block for polaritonic circuits, where propagation and localization are optically controlled and reconfigurable.
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Affiliation(s)
- D. Tanese
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - H. Flayac
- Institut Pascal, PHOTON-N2, Clermont Université, Université Blaise Pascal, CNRS, 24 Avenue des Landais, 63177 Aubière Cedex, France
| | - D. Solnyshkov
- Institut Pascal, PHOTON-N2, Clermont Université, Université Blaise Pascal, CNRS, 24 Avenue des Landais, 63177 Aubière Cedex, France
| | - A. Amo
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - A. Lemaître
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - E. Galopin
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - R. Braive
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - P. Senellart
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - I. Sagnes
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
| | - G. Malpuech
- Institut Pascal, PHOTON-N2, Clermont Université, Université Blaise Pascal, CNRS, 24 Avenue des Landais, 63177 Aubière Cedex, France
| | - J. Bloch
- Laboratoire de Photonique et Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis, France
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16
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Li C, Huang C, Liu H, Dong L. Multipeaked gap solitons in PT-symmetric optical lattices. OPTICS LETTERS 2012; 37:4543-4545. [PMID: 23114357 DOI: 10.1364/ol.37.004543] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We report the existence and stability properties of multipeaked solitons in a defocusing Kerr medium with an imprinted complex optical lattice featuring a parity-time (PT) symmetry. Various families of soliton solutions with a different number of peaks are found in the first finite gap of the lattice. Linear stability analysis corroborated by direct propagation simulations reveals that multipeaked gap solitons can propagate stably in a wide range, provided that their propagation constant exceeds a critical value. Our findings demonstrate, for the first time, the existence of stable multipeaked gap solitons in a PT-symmetric lattice.
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Affiliation(s)
- Chunyan Li
- Institute of Information Optics, Zhejiang Normal University, Jinhua, China
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Bersch C, Onishchukov G, Peschel U. Optical gap solitons and truncated nonlinear Bloch waves in temporal lattices. PHYSICAL REVIEW LETTERS 2012; 109:093903. [PMID: 23002837 DOI: 10.1103/physrevlett.109.093903] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2012] [Indexed: 05/22/2023]
Abstract
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form gap solitons and nonlinear truncated Bloch waves. Multi-pulse solitons with defects, as well as novel structures composed of a strong soliton riding on a weaker truncated nonlinear Bloch wave are shown to propagate over up to eleven coupling lengths. The nonlinear dynamics of all pulse structures is monitored over the full propagation distance which provides detailed insight into the soliton dynamics.
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Affiliation(s)
- Christoph Bersch
- Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Erlangen, Germany
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Akylas TR, Hwang G, Yang J. From non-local gap solitary waves to bound states in periodic media. Proc Math Phys Eng Sci 2011. [DOI: 10.1098/rspa.2011.0341] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two non-local solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.
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Affiliation(s)
- T. R. Akylas
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Guenbo Hwang
- Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA
| | - Jianke Yang
- Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401, USA
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Bennet FH, Alexander TJ, Haslinger F, Mitchell A, Neshev DN, Kivshar YS. Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays. PHYSICAL REVIEW LETTERS 2011; 106:093901. [PMID: 21405621 DOI: 10.1103/physrevlett.106.093901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2010] [Revised: 01/06/2011] [Indexed: 05/30/2023]
Abstract
We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.
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Affiliation(s)
- Francis H Bennet
- Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, Australia
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Yang J, Zhang P, Yoshihara M, Hu Y, Chen Z. Image transmission using stable solitons of arbitrary shapes in photonic lattices. OPTICS LETTERS 2011; 36:772-774. [PMID: 21368978 DOI: 10.1364/ol.36.000772] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We demonstrate both theoretically and experimentally that photonic lattices under self-defocusing nonlinearity support gap solitons in various shapes such as cross and H shapes. These solitons, with their intensity humps all in-phase, are stable against perturbations, thus they propagate robustly throughout the lattices. Based on this finding, we propose soliton-based text/image transmission through bulk photonic structures.
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Affiliation(s)
- Jianke Yang
- Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.
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Zhang P, Egger R, Chen Z. Optical induction of three-dimensional photonic lattices and enhancement of discrete diffraction. OPTICS EXPRESS 2009; 17:13151-13156. [PMID: 19654720 DOI: 10.1364/oe.17.013151] [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 demonstrate experimentally the formation of three-dimensional (3D) reconfigurable photonic lattices in a bulk nonlinear crystal by employing the optical induction technique. Such 3D lattices are established by inducing 2D square lattices in two orthogonal directions. The induced 3D periodic index structures are monitored by plane-wave guidance and Brillouin zone spectroscopy. Enhanced discrete diffraction due to the waveguide modulation and coupling in 3D lattices is also observed.
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Affiliation(s)
- Peng Zhang
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
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Zhang Y, Wu B. Composition relation between gap solitons and Bloch waves in nonlinear periodic systems. PHYSICAL REVIEW LETTERS 2009; 102:093905. [PMID: 19392522 DOI: 10.1103/physrevlett.102.093905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2008] [Indexed: 05/27/2023]
Abstract
We show with numerical computation and analysis that Bloch waves, at either the center or edge of the Brillouin zone, of a one dimensional nonlinear periodic system can be regarded as infinite chains composed of fundamental gap solitons (FGSs). This composition relation between Bloch waves and FGSs leads us to predict that there are n families of FGSs in the nth band gap of the corresponding linear periodic system, which is confirmed numerically. Furthermore, this composition relation can be extended to construct a class of solutions similar to Bloch waves but with multiple periods.
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Affiliation(s)
- Yongping Zhang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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Xue JK, Zhang AX. Superfluid fermi gas in optical lattices: self-trapping, stable, moving solitons and breathers. PHYSICAL REVIEW LETTERS 2008; 101:180401. [PMID: 18999797 DOI: 10.1103/physrevlett.101.180401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2008] [Indexed: 05/27/2023]
Abstract
We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.
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Affiliation(s)
- Ju-Kui Xue
- Physics and Electronics Engineering College, Northwest Normal University, Lanzhou 730070, People's Republic of China.
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Terhalle B, Richter T, Desyatnikov AS, Neshev DN, Krolikowski W, Kaiser F, Denz C, Kivshar YS. Observation of multivortex solitons in photonic lattices. PHYSICAL REVIEW LETTERS 2008; 101:013903. [PMID: 18764113 DOI: 10.1103/physrevlett.101.013903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2008] [Indexed: 05/26/2023]
Abstract
We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.
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Affiliation(s)
- Bernd Terhalle
- Nonlinear Physics Center and Laser Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia
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Wang X, Chen Z, Wang J, Yang J. Observation of in-band lattice solitons. PHYSICAL REVIEW LETTERS 2007; 99:243901. [PMID: 18233449 DOI: 10.1103/physrevlett.99.243901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2007] [Indexed: 05/25/2023]
Abstract
We report the first experimental and theoretical demonstrations of in-band (or embedded) lattice solitons. Such solitons appear in trains, and their propagation constants reside inside the first Bloch band of a square lattice, different from all previously observed solitons. We show that these solitons bifurcate from Bloch modes at the interior high-symmetry X points within the first band, where normal and anomalous diffractions coexist along two orthogonal directions. At high powers, the in-band soliton can move into the first band gap and turn into a gap soliton.
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Affiliation(s)
- Xiaosheng Wang
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
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Alexander TJ, Desyatnikov AS, Kivshar YS. Multivortex solitons in triangular photonic lattices. OPTICS LETTERS 2007; 32:1293-5. [PMID: 17440565 DOI: 10.1364/ol.32.001293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
We introduce a novel class of stable lattice solitons with a complex phase structure composed of many single-charge discrete vortices in a triangular photonic lattice. We demonstrate that such nonlinear self-trapped states are linked to the resonant Bloch modes, which bear a honeycomb pattern of phase dislocations.
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Affiliation(s)
- Tristram J Alexander
- Nonlinear Physics Centre and Centre for Ultra-high Bandwidth Devices for Optical Systems, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT, Australia
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Liu B, Fu LB, Yang SP, Liu J. Josephson oscillation and transition to self-trapping for Bose-Einstein condensates in a triple-well trap. PHYSICAL REVIEW A 2007; 75:033601. [DOI: 10.1103/physreva.75.033601] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Livi R, Franzosi R, Oppo GL. Self-localization of Bose-Einstein condensates in optical lattices via boundary dissipation. PHYSICAL REVIEW LETTERS 2006; 97:060401. [PMID: 17026150 DOI: 10.1103/physrevlett.97.060401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2006] [Indexed: 05/12/2023]
Abstract
We introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries.
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Affiliation(s)
- Roberto Livi
- Dipartimento di Fisica, CNR-INFM and CSDC, Università di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Italy
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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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