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Hong J, Wang C, Zhang Y. Instabilities of a Bose-Einstein condensate with mixed nonlinear and linear lattices. Phys Rev E 2023; 107:044219. [PMID: 37198863 DOI: 10.1103/physreve.107.044219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 04/13/2023] [Indexed: 05/19/2023]
Abstract
Bose-Einstein condensates (BECs) in periodic potentials generate interesting physics on the instabilities of Bloch states. The lowest-energy Bloch states of BECs in pure nonlinear lattices are dynamically and Landau unstable, which breaks down BEC superfluidity. In this paper we propose to use an out-of-phase linear lattice to stabilize them. The stabilization mechanism is revealed by the averaged interaction. We further incorporate a constant interaction into BECs with mixed nonlinear and linear lattices and reveal its effect on the instabilities of Bloch states in the lowest band.
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Affiliation(s)
- Jun Hong
- Department of Physics, Shanghai University, Shanghai 200444, China
| | - Chenhui Wang
- Department of Physics, Shanghai University, Shanghai 200444, China
| | - Yongping Zhang
- Department of Physics, Shanghai University, Shanghai 200444, China
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2
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Otlaadisa P, Tabi CB, Kofané TC. Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates. Phys Rev E 2021; 103:052206. [PMID: 34134292 DOI: 10.1103/physreve.103.052206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.
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Affiliation(s)
- Phelo Otlaadisa
- Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
| | - Conrad Bertrand Tabi
- 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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3
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Tamilthiruvalluvar R, Wamba E, Subramaniyan S, Porsezian K. Impact of higher-order nonlinearity on modulational instability in two-component Bose-Einstein condensates. Phys Rev E 2019; 99:032202. [PMID: 30999470 DOI: 10.1103/physreve.99.032202] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Indexed: 11/07/2022]
Abstract
We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.
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Affiliation(s)
| | - Etienne Wamba
- State Research Center OPTIMAS, and Fachbereich Physik, Technische Universität Kaiserslautern, D-67663 Kaiserslautern, Germany.,African Institute for Mathematical Sciences, P.O. Box 608, Limbe, Cameroon
| | - Sabari Subramaniyan
- Department of Physics, Bharathidasan University, Tiruchirappalli 620024, India
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Abdullaev FK, Salerno M. Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity. Phys Rev E 2018; 97:052208. [PMID: 29906973 DOI: 10.1103/physreve.97.052208] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Indexed: 11/07/2022]
Abstract
The modulational instability of nonlinear plane waves and the existence of periodic and localized dissipative solitons and waves of the discrete Ginzburg-Landau equation with saturable nonlinearity are investigated. Explicit analytic expressions for periodic solutions with a zero and a finite background are derived and their stability properties investigated by means of direct numerical simulations. We find that while discrete periodic waves and solitons on a zero background are stable under time evolution, they may become modulationally unstable on finite backgrounds. The effects of a linear ramp potential on stable localized dissipative solitons are also briefly discussed.
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Affiliation(s)
| | - Mario Salerno
- Dipartimento di Fisica E.R. Caianiello and INFN, Gruppo Collegato di Salerno, Universita di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
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Lingua F, Penna V. Continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer. Phys Rev E 2017; 95:062142. [PMID: 28709291 DOI: 10.1103/physreve.95.062142] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Indexed: 11/07/2022]
Abstract
A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.
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Affiliation(s)
- F Lingua
- Dipartimento di Scienza Applicata e Tecnologia and u.d.r. CNISM, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
| | - V Penna
- Dipartimento di Scienza Applicata e Tecnologia and u.d.r. CNISM, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
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6
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Chaves Filho VL, Lima RPA, Lyra ML. Interplay between modulational instability and self-trapping of wavepackets in nonlinear discrete lattices. CHAOS (WOODBURY, N.Y.) 2015; 25:063101. [PMID: 26117095 DOI: 10.1063/1.4921937] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.
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Affiliation(s)
- V L Chaves Filho
- Instituto Federal de Educação, Ciência e Tecnologia de Alagoas, Satuba, Alagoas 57120-000, Brazil
| | - R P A Lima
- GFTC, Instituto de Física, Universidade Federal de Alagoas, Maceió 57072-970, Alagoas, Brazil
| | - M L Lyra
- GFTC, Instituto de Física, Universidade Federal de Alagoas, Maceió 57072-970, Alagoas, Brazil
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Feijoo D, Ordóñez I, Paredes A, Michinel H. Drag force in bimodal cubic-quintic nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033204. [PMID: 25314556 DOI: 10.1103/physreve.90.033204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Indexed: 06/04/2023]
Abstract
We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.
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Affiliation(s)
- David Feijoo
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Ismael Ordóñez
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Angel Paredes
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
| | - Humberto Michinel
- Área de Óptica, Departamento de Física Aplicada, Universidade de Vigo, As Lagoas s/n, Ourense ES-32004, Spain
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Qi XY, Xue JK. Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity. Phys Rev E 2012; 86:017601. [PMID: 23005569 DOI: 10.1103/physreve.86.017601] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2012] [Indexed: 11/07/2022]
Abstract
We consider the modulational instability (MI) of Bose-Einstein condensate (BEC) described by a modified Gross-Pitaevskii (GP) equation with higher-order nonlinearity both analytically and numerically. A new explicit time-dependent criterion for exciting the MI is obtained. It is shown that the higher-order term can either suppress or enhance the MI, which is interesting for control of the system instability. Importantly, we predict that with the help of the higher-order nonlinearity, the MI can also take place in a BEC with repulsively contact interactions. The analytical results are confirmed by direct numerical simulations.
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Affiliation(s)
- Xiu-Ying Qi
- Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
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Mohamadou A, Wamba E, Lissouck D, Kofane TC. Dynamics of kink-dark solitons in Bose-Einstein condensates with both two- and three-body interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046605. [PMID: 22680596 DOI: 10.1103/physreve.85.046605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2011] [Indexed: 06/01/2023]
Abstract
The matter-wave solutions of Bose-Einstein condensates with three-body interaction are examined through the one-dimensional Gross-Pitaevskii equation. By using a modified lens-type transformation and a further extension of the tanh-function method we obtain the exact analytical solutions which describe the propagation of kink-shaped solitons, anti-kink-shaped solitons, and other families of solitary waves. We realize that the shape of a kink solitary wave depends on both the scattering length and the parameter of atomic exchange with the substrate. The stability of the solitary waves is examined using analytical and numerical methods. Our results can also be applied to nonlinear optics in the presence of cubic-quintic media.
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Affiliation(s)
- Alidou Mohamadou
- Department of Physics, Faculty of Science, University of Douala, Douala, Cameroon.
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Falcão-Filho EL, Barbosa-Silva R, Sobral-Filho RG, Brito-Silva AM, Galembeck A, de Araújo CB. High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm. OPTICS EXPRESS 2010; 18:21636-21644. [PMID: 20941062 DOI: 10.1364/oe.18.021636] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The nonlinear response of silica--gold nanoshells (SGNs) in chloroform was studied using laser pulses of 65 fs at 1560 nm. The experiments were performed using the thermally managed Z--scan technique that allows measurements of the electronic contribution for the nonlinear response, free from thermal influence. The results were analyzed using an analytical approach based on the quasi--static approximation that allowed extraction of the nonlinear susceptibility of a SGN from the data. High third--order susceptibility, χsh((3)) = - 1.5 x 10(-11) m(2)/V(2), approximately four orders of magnitude larger than for gold nanospheres in the visible, and large fifth--order susceptibility, χsh((5)) = - 1.4 x 10(-24) m(4)/V(4), were obtained. The present results offers new perspectives for nonlinear plasmonics in the near--infrared.
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Affiliation(s)
- E L Falcão-Filho
- Departamento de Física, Universidade Federal de Pernambuco, 50670 - 901, Recife, Pernambuco, Brazil
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Shrestha U, Javanainen J, Ruostekoski J. Pulsating and persistent vector solitons in a Bose-Einstein condensate in a lattice upon phase separation instability. PHYSICAL REVIEW LETTERS 2009; 103:190401. [PMID: 20365912 DOI: 10.1103/physrevlett.103.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2009] [Indexed: 05/29/2023]
Abstract
We study numerically the outcome of the phase separation instability of a dual-species Bose-Einstein condensate in an optical lattice. When only one excitation mode is unstable a bound pair of bright and dark solitonlike structures periodically appears and disappears, whereas for more than one unstable mode a persistent soliton-antisoliton pair develops. The oscillating soliton represents a regime where the two-species condensate neither remains phase-separated nor is dynamically stable.
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Affiliation(s)
- Uttam Shrestha
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA
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