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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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Fu Q, Wang P, Kartashov YV, Konotop VV, Ye F. Nonlinear Thouless Pumping: Solitons and Transport Breakdown. PHYSICAL REVIEW LETTERS 2022; 128:154101. [PMID: 35499898 DOI: 10.1103/physrevlett.128.154101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.
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Affiliation(s)
- Qidong Fu
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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3
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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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4
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Leung TH, Schwarz MN, Chang SW, Brown CD, Unnikrishnan G, Stamper-Kurn D. Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice. PHYSICAL REVIEW LETTERS 2020; 125:133001. [PMID: 33034463 DOI: 10.1103/physrevlett.125.133001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 08/28/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
Geometric frustration of particle motion in a kagome lattice causes the single-particle band structure to have a flat s-orbital band. We probe this band structure by placing a Bose-Einstein condensate into excited Bloch states of an optical kagome lattice, and then measuring the group velocity through the atomic momentum distribution. We find that interactions renormalize the band structure, greatly increasing the dispersion of the third band, which is nearly non-dispersing the single-particle treatment. Calculations based on the lattice Gross-Pitaevskii equation indicate that band structure renormalization is caused by the distortion of the overall lattice potential away from the kagome geometry by interactions.
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Affiliation(s)
- Tsz-Him Leung
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Malte N Schwarz
- Department of Physics, University of California, Berkeley, California 94720, USA
- Fakultät für Physik und Astronomie, Universität Würzburg, 97074 Würzburg, Germany
| | - Shao-Wen Chang
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Charles D Brown
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Govind Unnikrishnan
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - Dan Stamper-Kurn
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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5
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Campbell R, Oppo GL, Borkowski M. Interactions and collisions of discrete breathers in two-species Bose-Einstein condensates in optical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012909. [PMID: 25679684 DOI: 10.1103/physreve.91.012909] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Indexed: 06/04/2023]
Abstract
The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.
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Affiliation(s)
- Russell Campbell
- Institute of Complex Systems, SUPA and Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, Scotland, United Kingdom
| | - Gian-Luca Oppo
- Institute of Complex Systems, SUPA and Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, Scotland, United Kingdom
| | - Mateusz Borkowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
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6
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Veselago lensing with ultracold atoms in an optical lattice. Nat Commun 2014; 5:3327. [PMID: 24525693 DOI: 10.1038/ncomms4327] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Accepted: 01/27/2014] [Indexed: 11/08/2022] Open
Abstract
Veselago pointed out that electromagnetic wave theory allows for materials with a negative index of refraction, in which most known optical phenomena would be reversed. A slab of such a material can focus light by negative refraction, an imaging technique strikingly different from conventional positive refractive index optics, where curved surfaces bend the rays to form an image of an object. Here we demonstrate Veselago lensing for matter waves, using ultracold atoms in an optical lattice. A relativistic, that is, photon-like, dispersion relation for rubidium atoms is realized with a bichromatic optical lattice potential. We rely on a Raman π-pulse technique to transfer atoms between two different branches of the dispersion relation, resulting in a focusing that is completely analogous to the effect described by Veselago for light waves. Future prospects of the demonstrated effects include novel sub-de Broglie wavelength imaging applications.
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Fabre CM, Cheiney P, Gattobigio GL, Vermersch F, Faure S, Mathevet R, Lahaye T, Guéry-Odelin D. Realization of a distributed Bragg reflector for propagating guided matter waves. PHYSICAL REVIEW LETTERS 2011; 107:230401. [PMID: 22182068 DOI: 10.1103/physrevlett.107.230401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2011] [Indexed: 05/31/2023]
Abstract
We report on the experimental study of a Bragg reflector for guided, propagating Bose-Einstein condensates. A one-dimensional attractive optical lattice of finite length created by red-detuned laser beams selectively reflects some velocity components of the incident matter wave packet. We find quantitative agreement between the experimental data and one-dimensional numerical simulations and show that the Gaussian envelope of the optical lattice has a major influence on the properties of the reflector. In particular, it gives rise to multiple reflections of the wave packet between two symmetric locations where Bragg reflection occurs. Our results are a further step towards integrated atom-optics setups for quasi-cw matter waves.
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Affiliation(s)
- C M Fabre
- Université de Toulouse, UPS, Laboratoire Collisions Agrégats Réactivité, IRSAMC, F-31062 Toulouse, France
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8
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Zhu Q, Hai W, Rong S. Transition probability from matter-wave soliton to chaos. Phys Rev E 2009; 80:016203. [PMID: 19658788 DOI: 10.1103/physreve.80.016203] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2008] [Revised: 05/08/2009] [Indexed: 11/07/2022]
Abstract
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.
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Affiliation(s)
- Qianquan Zhu
- Department of Physics, Hunan Normal University, Changsha 410081, China
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9
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Franke-Arnold S, Leach J, Padgett MJ, Lembessis VE, Ellinas D, Wright AJ, Girkin JM, Ohberg P, Arnold AS. Optical ferris wheel for ultracold atoms. OPTICS EXPRESS 2007; 15:8619-8625. [PMID: 19547196 DOI: 10.1364/oe.15.008619] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We propose a versatile optical ring lattice suitable for trapping cold and quantum degenerate atomic samples. We demonstrate the realisation of intensity patterns from pairs of Laguerre-Gauss (exp(i??) modes with different ? indices. These patterns can be rotated by introducing a frequency shift between the modes. We can generate bright ring lattices for trapping atoms in red-detuned light, and dark ring lattices suitable for trapping atoms with minimal heating in the optical vortices of blue-detuned light. The lattice sites can be joined to form a uniform ring trap, making it ideal for studying persistent currents and the Mott insulator transition in a ring geometry.
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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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11
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Alexander TJ, Ostrovskaya EA, Kivshar YS. Self-trapped nonlinear matter waves in periodic potentials. PHYSICAL REVIEW LETTERS 2006; 96:040401. [PMID: 16486792 DOI: 10.1103/physrevlett.96.040401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2005] [Indexed: 05/06/2023]
Abstract
We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.
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Affiliation(s)
- Tristram J Alexander
- 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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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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13
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Fallani L, De Sarlo L, Lye JE, Modugno M, Saers R, Fort C, Inguscio M. Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice. PHYSICAL REVIEW LETTERS 2004; 93:140406. [PMID: 15524775 DOI: 10.1103/physrevlett.93.140406] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2004] [Indexed: 05/24/2023]
Abstract
We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.
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Affiliation(s)
- L Fallani
- LENS, Dipartimento di Fisica, and INFM, Università di Firenze, via Nello Carrara 1, I-50019 Sesto Fiorentino (FI), Italy.
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Chong G, Hai W, Xie Q. Transient and stationary chaos of a Bose-Einstein condensate loaded into a moving optical lattice potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036213. [PMID: 15524618 DOI: 10.1103/physreve.70.036213] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2004] [Indexed: 05/24/2023]
Abstract
Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.
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Affiliation(s)
- Guishu Chong
- Department of Physics, Hunan Normal University, Changsha 410081, People's Republic of China
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Ostrovskaya EA, Kivshar YS. Localization of two-component Bose-Einstein condensates in optical lattices. PHYSICAL REVIEW LETTERS 2004; 92:180405. [PMID: 15169475 DOI: 10.1103/physrevlett.92.180405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2003] [Indexed: 05/24/2023]
Abstract
We study nonlinear localization of a two-component Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our theory shows that spin-dependent optical lattices can be used to effectively manipulate the nonlinear interactions between the BEC components, and to observe composite localized states of a BEC in both bands and gaps of the matter-wave spectrum.
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Affiliation(s)
- Elena A Ostrovskaya
- Nonlinear Physics Group 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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