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Tabi CB, Wamba E, Nare E, Kofané TC. Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates. Phys Rev E 2023; 107:044206. [PMID: 37198763 DOI: 10.1103/physreve.107.044206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Accepted: 03/21/2023] [Indexed: 05/19/2023]
Abstract
The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.
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Affiliation(s)
- Conrad Bertrand Tabi
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Etienne Wamba
- Faculty of Engineering and Technology, University of Buea, P.O. Box 63, Buea, Cameroon
- STIAS, Wallenberg Research Centre, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Emmanual Nare
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Timoléon Crépin Kofané
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
- Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaoundé I, Yaoundé, Cameroon
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2
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Driben R, Konotop VV, Malomed BA, Meier T. Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators. Phys Rev E 2016; 94:012207. [PMID: 27575123 DOI: 10.1103/physreve.94.012207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Indexed: 06/06/2023]
Abstract
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.
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Affiliation(s)
- R Driben
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
| | - V V Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016 Lisboa, Portugal
| | - B A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
| | - T Meier
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
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Driben R, Konotop VV, Meier T. Precession and nutation dynamics of nonlinearly coupled non-coaxial three-dimensional matter wave vortices. Sci Rep 2016; 6:22758. [PMID: 26964759 PMCID: PMC4786817 DOI: 10.1038/srep22758] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2015] [Accepted: 02/19/2016] [Indexed: 12/02/2022] Open
Abstract
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.
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Affiliation(s)
- R. Driben
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
- ITMO University, 49 Kronverskii Ave., St. Petersburg 197101, Russian Federation
| | - V. V. Konotop
- Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - T. Meier
- Department of Physics and CeOPP, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
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Soljacić M, Steiglitz K, Sears SM, Segev M, Jakubowski MH, Squier R. Collisions of two solitons in an arbitrary number of coupled nonlinear Schrödinger equations. PHYSICAL REVIEW LETTERS 2003; 90:254102. [PMID: 12857135 DOI: 10.1103/physrevlett.90.254102] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2002] [Indexed: 05/24/2023]
Abstract
We show that pairwise soliton collisions in N>2 intensity-coupled nonlinear Schrödinger equations can be reduced to pairwise soliton collisions in two coupled equations. The reduction applies to a wide class of systems, including the N-component Manakov system. This greatly simplifies the analysis of such systems and has important implications for the application of soliton collisions to all-optical computing.
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Affiliation(s)
- Marin Soljacić
- Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
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5
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Saito H, Ueda M. Split instability of a vortex in an attractive Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2002; 89:190402. [PMID: 12443103 DOI: 10.1103/physrevlett.89.190402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2002] [Indexed: 05/24/2023]
Abstract
An attractive Bose-Einstein condensate with a vortex splits into two pieces via the quadrupole dynamical instability, which arises at a weaker strength of interaction than the monopole and the dipole instabilities. The split pieces subsequently unite to restore the original vortex or collapse.
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Affiliation(s)
- Hiroki Saito
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
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6
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Adhikari SK. Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:016703. [PMID: 11800816 DOI: 10.1103/physreve.65.016703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2001] [Indexed: 05/23/2023]
Abstract
The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.
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Affiliation(s)
- Sadhan K Adhikari
- Instituto de Física Teórica, Universidade Estadual Paulista, 01.405-900 São Paulo, São Paulo, Brazil
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7
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Coen S, Haelterman M. Domain wall solitons in binary mixtures of Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2001; 87:140401. [PMID: 11580632 DOI: 10.1103/physrevlett.87.140401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2000] [Revised: 04/23/2001] [Indexed: 05/23/2023]
Abstract
The structure and dynamics of the domain walls separating segregated condensates in trapped mixtures of repulsive Bose-Einstein condensates are studied. Our work reveals that, under fairly general conditions, these domain walls behave as independent dynamical entities, which allows us to identify them as constituting a novel class of multicomponent solitons in Bose-Einstein condensates.
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Affiliation(s)
- S Coen
- Physics Department, The University of Auckland, Private Bag 92019, Auckland, New Zealand
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García-Ripoll JJ, Molina-Terriza G, Pérez-García VM, Torner L. Structural instability of vortices in Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2001; 87:140403. [PMID: 11580634 DOI: 10.1103/physrevlett.87.140403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2001] [Revised: 06/14/2001] [Indexed: 05/23/2023]
Abstract
In this paper we study a gaseous Bose-Einstein condensate and show the following: (i) A minimum value of the interaction is needed for the existence of stable persistent currents. (ii) Vorticity is not a fundamental invariant of the system, as there exists a conservative mechanism which can destroy a vortex and change its sign. (iii) This mechanism is suppressed by strong interactions.
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Affiliation(s)
- J J García-Ripoll
- Departamento de Matemáticas, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
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Musslimani ZH, Soljacić M, Segev M, Christodoulides DN. Delayed-action interaction and spin-orbit coupling between solitons. PHYSICAL REVIEW LETTERS 2001; 86:799-802. [PMID: 11177943 DOI: 10.1103/physrevlett.86.799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2000] [Revised: 08/15/2000] [Indexed: 05/23/2023]
Abstract
We report on new fundamental phenomena in soliton interactions: delayed-action interaction and "spin"-orbit coupling upon collision between two-dimensional composite solitons carrying topological charges.
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Affiliation(s)
- Z H Musslimani
- Department of Mathematics, Technion--Israel Institute of Technology, Haifa
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Anderson BP, Haljan PC, Wieman CE, Cornell EA. Vortex precession in Bose-Einstein condensates: observations with filled and empty cores. PHYSICAL REVIEW LETTERS 2000; 85:2857-2860. [PMID: 11005953 DOI: 10.1103/physrevlett.85.2857] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2000] [Indexed: 05/23/2023]
Abstract
We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of 2.
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Affiliation(s)
- B P Anderson
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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Garcia-Ripoll JJ, Perez-Garcia VM, Ostrovskaya EA, Kivshar YS. Dipole-mode vector solitons. PHYSICAL REVIEW LETTERS 2000; 85:82-85. [PMID: 10991164 DOI: 10.1103/physrevlett.85.82] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/1999] [Indexed: 05/23/2023]
Abstract
We find a new type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides. These solitons, which appear as a consequence of the vector nature of the two-component system, are more stable than the previously found optical vortex solitons and represent a new type of extremely robust nonlinear vector structure.
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Affiliation(s)
- JJ Garcia-Ripoll
- Departamento de Matematicas, Escuela Tecnica Superior de Industriales, Universidad de Castilla-La Mancha 13071 Ciudad Real, Spain
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