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Masi L, Petrucciani T, Ferioli G, Semeghini G, Modugno G, Inguscio M, Fattori M. Spatial Bloch Oscillations of a Quantum Gas in a "Beat-Note" Superlattice. PHYSICAL REVIEW LETTERS 2021; 127:020601. [PMID: 34296908 DOI: 10.1103/physrevlett.127.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 03/17/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We report the experimental realization of a new kind of optical lattice for ultracold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped-atom interferometers and quantum simulators.
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Affiliation(s)
- L Masi
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - T Petrucciani
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
| | - G Ferioli
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Semeghini
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
| | - G Modugno
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
| | - M Inguscio
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - M Fattori
- CNR Istituto Nazionale Ottica, 50019 Sesto Fiorentino, Italy
- European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
- Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
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2
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Gomel A, Chabchoub A, Brunetti M, Trillo S, Kasparian J, Armaroli A. Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation. PHYSICAL REVIEW LETTERS 2021; 126:174501. [PMID: 33988389 DOI: 10.1103/physrevlett.126.174501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 02/23/2021] [Accepted: 04/01/2021] [Indexed: 06/12/2023]
Abstract
We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schrödinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them.
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Affiliation(s)
- Alexis Gomel
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Amin Chabchoub
- Hakubi Center for Advanced Research, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan
- Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, Japan
- Centre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
| | - Maura Brunetti
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Stefano Trillo
- Department of Engineering, University of Ferrara, via Saragat 1, 44122 Ferrara, Italy
| | - Jérôme Kasparian
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Andrea Armaroli
- GAP, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland
- Institute for Environmental Sciences, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
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3
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Van Gorder RA. Turing and Benjamin–Feir instability mechanisms in non-autonomous systems. Proc Math Phys Eng Sci 2020. [DOI: 10.1098/rspa.2020.0003] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.
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Affiliation(s)
- Robert A. Van Gorder
- Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
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4
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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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5
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Cheng SC, Chen TW. Dark gap solitons in exciton-polariton condensates in a periodic potential. Phys Rev E 2018; 97:032212. [PMID: 29776165 DOI: 10.1103/physreve.97.032212] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2017] [Indexed: 11/07/2022]
Abstract
We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.
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Affiliation(s)
- Szu-Cheng Cheng
- Department of Optoelectric Physics, Chinese Culture University, Taipei 11114, Taiwan, Republic of China
| | - Ting-Wei Chen
- Department of Electrophysics, National Chiayi University, Chiayi city 60004, Taiwan, Republic of China
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6
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Kohler J, Gerber JA, Dowd E, Stamper-Kurn DM. Negative-Mass Instability of the Spin and Motion of an Atomic Gas Driven by Optical Cavity Backaction. PHYSICAL REVIEW LETTERS 2018; 120:013601. [PMID: 29350956 DOI: 10.1103/physrevlett.120.013601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Indexed: 06/07/2023]
Abstract
We realize a spin-orbit interaction between the collective spin precession and center-of-mass motion of a trapped ultracold atomic gas, mediated by spin- and position-dependent dispersive coupling to a driven optical cavity. The collective spin, precessing near its highest-energy state in an applied magnetic field, can be approximated as a negative-mass harmonic oscillator. When the Larmor precession and mechanical motion are nearly resonant, cavity mediated coupling leads to a negative-mass instability, driving exponential growth of a correlated mode of the hybrid system. We observe this growth imprinted on modulations of the cavity field and estimate the full covariance of the resulting two-mode state by observing its transient decay during subsequent free evolution.
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Affiliation(s)
- Jonathan Kohler
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Justin A Gerber
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Emma Dowd
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Dan M 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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7
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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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8
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Hennig H, Neff T, Fleischmann R. Dynamical phase diagram of Gaussian wave packets in optical lattices. Phys Rev E 2016; 93:032219. [PMID: 27078356 DOI: 10.1103/physreve.93.032219] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 11/07/2022]
Abstract
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
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Affiliation(s)
- H Hennig
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany.,Department of Physics, Harvard University, Cambridge, Massachesetts 02138, USA
| | - T Neff
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
| | - R Fleischmann
- Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
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9
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Taming of Modulation Instability by Spatio-Temporal Modulation of the Potential. Sci Rep 2015; 5:13268. [PMID: 26286250 PMCID: PMC4541154 DOI: 10.1038/srep13268] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Accepted: 07/13/2015] [Indexed: 11/11/2022] Open
Abstract
Spontaneous pattern formation in a variety of spatially extended nonlinear systems always occurs through a modulation instability, sometimes called Turing instability: the homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of spatial patterns initiated by that instability. We show that a spatio-temporal periodic modulation of the potential of spatially extended systems results in a modification of its pattern forming instability. Depending on the modulation character the instability can be partially suppressed, can change its spectrum (for instance the long wave instability can transform into short wave instability), can split into two, or can be completely eliminated. The latter result is of special practical interest, as it can be used to stabilize the intrinsically unstable system. The result bears general character, as it is shown here on a universal model of the Complex Ginzburg-Landau equation in one and two spatial dimensions (and time). The physical mechanism of the instability suppression can be applied to a variety of intrinsically unstable dissipative systems, like self-focusing lasers, reaction-diffusion systems, as well as in unstable conservative systems, like attractive Bose Einstein condensates.
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10
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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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11
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Wamba E, Sabari S, Porsezian K, Mohamadou A, Kofané TC. Dynamical instability of a Bose-Einstein condensate with higher-order interactions in an optical potential through a variational approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052917. [PMID: 25353871 DOI: 10.1103/physreve.89.052917] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Indexed: 06/04/2023]
Abstract
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.
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Affiliation(s)
- E Wamba
- Department of Physics, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon and African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, 7945, South Africa
| | - S Sabari
- Department of Physics, Pondicherry University, Puducherry 605014, India
| | - K Porsezian
- Department of Physics, Pondicherry University, Puducherry 605014, India
| | - A Mohamadou
- Department of Physics, Faculty of Science, University of Douala, P. O. Box 24157, Douala, Cameroon and The Abdus Salam International Centre for Theoretical Physics, P. O. Box 586, Strada Costiera 11, I-34014, Trieste, Italy
| | - T C Kofané
- Department of Physics, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon
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12
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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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13
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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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14
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He JR, Li HM. Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials. Phys Rev E 2011; 83:066607. [PMID: 21797507 DOI: 10.1103/physreve.83.066607] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2010] [Revised: 01/04/2011] [Indexed: 11/07/2022]
Abstract
A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutions corresponding to these potentials are then studied. Also, properties of a few solutions and physical applications of interest to the field are discussed. Finally, the stability of the solitary wave solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed numerically; the results reveal that the solitary waves can propagate in a stable way under slight disturbance of the constraint conditions and the initial perturbation of white noise.
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Affiliation(s)
- Jun-Rong He
- Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Republic of China
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15
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Egorov OA, Skryabin DV, Yulin AV, Lederer F. Bright cavity polariton solitons. PHYSICAL REVIEW LETTERS 2009; 102:153904. [PMID: 19518634 DOI: 10.1103/physrevlett.102.153904] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2008] [Indexed: 05/27/2023]
Abstract
The lower branch of the dispersion relation of exciton polaritons in semiconductor microcavities, operating in the strong-coupling regime, contains sections of both positive and negative curvature along one spatial direction. We show that this leads to the existence of stable one-dimensional bright microcavity solitons supported by the repulsive polariton nonlinearity. To achieve localization along the second transverse direction we propose to create a special soliton waveguide by changing the cavity detuning and hence the boundary of the soliton existence in such a way that the solitons are allowed only within the stripe of the desired width.
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Affiliation(s)
- O A Egorov
- Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
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16
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Gaididei YB, Christiansen PL. Ising and Bloch domain walls in a two-dimensional parametrically driven Ginzburg-Landau equation model with nonlinearity management. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026610. [PMID: 18850965 DOI: 10.1103/physreve.78.026610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/26/2023]
Abstract
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under the action of direct ac forces is shown.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, Metrologichna Street 14 B, 03680, Kiev, Ukraine
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17
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Widera A, Trotzky S, Cheinet P, Fölling S, Gerbier F, Bloch I, Gritsev V, Lukin MD, Demler E. Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases. PHYSICAL REVIEW LETTERS 2008; 100:140401. [PMID: 18518006 DOI: 10.1103/physrevlett.100.140401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2007] [Indexed: 05/26/2023]
Abstract
We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.
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Affiliation(s)
- Artur Widera
- Johannes Gutenberg-Universität, Institut für Physik, Staudingerweg 7, 55099 Mainz, Germany.
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Moore KL, Gupta S, Murch KW, Stamper-Kurn DM. Probing the quantum state of a guided atom laser pulse. PHYSICAL REVIEW LETTERS 2006; 97:180410. [PMID: 17155527 DOI: 10.1103/physrevlett.97.180410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2006] [Indexed: 05/12/2023]
Abstract
We describe bichromatic superradiant pump-probe spectroscopy as a tomographic probe of the Wigner function of a dispersing particle beam. We employed this technique to characterize the quantum state of an ultracold atomic beam, derived from a 87Rb Bose-Einstein condensate, as it propagated in a 2.5 mm diameter circular waveguide. Our measurements place an upper bound on the longitudinal phase space area occupied by the 3 x 10(5) atom beam of 9(1)Planck's constant and a lower bound on the coherence length of L>or=13(1) microm. These results are consistent with full quantum degeneracy after multiple orbits around the waveguide.
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Affiliation(s)
- Kevin L Moore
- Department of Physics, University of California, Berkeley, California 94720, USA.
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19
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Centurion M, Porter MA, Kevrekidis PG, Psaltis D. Nonlinearity management in optics: experiment, theory, and simulation. PHYSICAL REVIEW LETTERS 2006; 97:033903. [PMID: 16907502 DOI: 10.1103/physrevlett.97.033903] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2006] [Indexed: 05/11/2023]
Abstract
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the (2+1)-dimensional focusing cubic nonlinear Schrödinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method.
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Affiliation(s)
- Martin Centurion
- Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125, USA and Center for the Physics of Information, California Institute of Technology, Pasadena, California 91125, USA
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20
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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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21
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Henderson K, Kelkar H, Gutiérrez-Medina B, Li TC, Raizen MG. Experimental study of the role of atomic interactions on quantum transport. PHYSICAL REVIEW LETTERS 2006; 96:150401. [PMID: 16712132 DOI: 10.1103/physrevlett.96.150401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2005] [Indexed: 05/09/2023]
Abstract
We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and Bose-Einstein condensation (BEC) initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.
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Affiliation(s)
- K Henderson
- Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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22
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Polkovnikov A, Altman E, Demler E. Interference between independent fluctuating condensates. Proc Natl Acad Sci U S A 2006; 103:6125-9. [PMID: 16601103 PMCID: PMC1458842 DOI: 10.1073/pnas.0510276103] [Citation(s) in RCA: 139] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We consider a problem of interference between two independent condensates that lack true long-range order. We show that their interference pattern contains information about correlation functions within each condensate. As an example, we analyze the interference between a pair of one-dimensional interacting Bose liquids. We find universal scaling of the average fringe contrast with system size and temperature that depends only on the Luttinger parameter. Moreover, the full distribution of the fringe contrast, which is also equivalent to the full counting statistics of the interfering atoms, changes with interaction strength and lends information on high-order correlation functions. We also demonstrate that the interference between two-dimensional condensates at finite temperature can be used as a direct probe of the Kosterlitz-Thouless transition. Finally, we discuss the generalization of our results to describe the interference of a periodic array of independent fluctuating condensates.
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23
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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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24
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Campbell GK, Mun J, Boyd M, Streed EW, Ketterle W, Pritchard DE. Parametric amplification of scattered atom pairs. PHYSICAL REVIEW LETTERS 2006; 96:020406. [PMID: 16486549 DOI: 10.1103/physrevlett.96.020406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2005] [Indexed: 05/06/2023]
Abstract
We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.
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Affiliation(s)
- Gretchen K Campbell
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Cambridge, Massachusetts 02139, USA
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25
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Murch KW, Moore KL, Gupta S, Stamper-Kurn DM. Dispersion management using betatron resonances in an ultracold-atom storage ring. PHYSICAL REVIEW LETTERS 2006; 96:013202. [PMID: 16486451 DOI: 10.1103/physrevlett.96.013202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2005] [Indexed: 05/06/2023]
Abstract
Particles circulating at specific velocities in a storage ring can undergo betatron resonances at which static perturbations of the particles' orbit yield large transverse (betatron) oscillations. We have observed betatron resonances in an ultracold-atom storage ring and found these resonances to cause the near-elimination of the longitudinal dispersion of atomic beams propagating at resonant velocities. This effect can improve atom-interferometric devices. Both the resonant velocities and the resonance strengths were varied by deliberate modifications to the storage ring.
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Affiliation(s)
- K W Murch
- Department of Physics, University of California, Berkeley, California 94720, USA
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26
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Mosk AP. Atomic gases at negative kinetic temperature. PHYSICAL REVIEW LETTERS 2005; 95:040403. [PMID: 16090784 DOI: 10.1103/physrevlett.95.040403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2005] [Indexed: 05/03/2023]
Abstract
We show that thermalization of the motion of atoms at negative temperature is possible in an optical lattice, for conditions that are feasible in current experiments. We present a method for reversibly inverting the temperature of a trapped gas. Moreover, a negative-temperature ensemble can be cooled (reducing |T|) by evaporation of the lowest-energy particles. This enables the attainment of the Bose-Einstein condensation phase transition at negative temperature.
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Affiliation(s)
- A P Mosk
- Department of Science & Technology, University of Twente, AE Enschede, The Netherlands
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27
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Staliūnas K, Tlidi M. Hyperbolic transverse patterns in nonlinear optical resonators. PHYSICAL REVIEW LETTERS 2005; 94:133902. [PMID: 15903991 DOI: 10.1103/physrevlett.94.133902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2004] [Indexed: 05/02/2023]
Abstract
We consider a nonlinear optical system in general, and a broad aperture laser, in particular, in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic Maxwell-Bloch equations, where the spatial coupling is provided by the D'Alambert operator rather than by the Laplace operator. We show that this system supports hyperbolic transverse patterns residing on hyperbolas in far-field domain, and consisting of stretched vortices in near-field domain.
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Affiliation(s)
- Kestutis Staliūnas
- ICREA, Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Colom 11, E-08222 Terrassa, Barcelona, Spain
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28
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Anker T, Albiez M, Gati R, Hunsmann S, Eiermann B, Trombettoni A, Oberthaler MK. Nonlinear self-trapping of matter waves in periodic potentials. PHYSICAL REVIEW LETTERS 2005; 94:020403. [PMID: 15698152 DOI: 10.1103/physrevlett.94.020403] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2004] [Indexed: 05/24/2023]
Abstract
We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.
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Affiliation(s)
- Th Anker
- Kirchhoff Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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29
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Adhikari SK. Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016611. [PMID: 15697751 DOI: 10.1103/physreve.71.016611] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2004] [Indexed: 05/24/2023]
Abstract
Using the numerical solution of the nonlinear Schrödinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.
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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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30
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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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31
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32
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Eiermann B, Anker T, Albiez M, Taglieber M, Treutlein P, Marzlin KP, Oberthaler MK. Bright Bose-Einstein gap solitons of atoms with repulsive interaction. PHYSICAL REVIEW LETTERS 2004; 92:230401. [PMID: 15245143 DOI: 10.1103/physrevlett.92.230401] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2003] [Indexed: 05/24/2023]
Abstract
We report on the first experimental observation of bright matter wave solitons for 87Rb atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a weak periodic potential, where anomalous dispersion can be realized at the Brillouin zone boundary. If the coherent atomic wave packet is prepared at the corresponding band edge, a bright soliton is formed inside the gap. The strength of our system is the precise control of preparation and real time manipulation, allowing the systematic investigation of gap solitons.
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Affiliation(s)
- B Eiermann
- Kirchhoff Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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33
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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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34
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Sukhorukov AA, Neshev D, Krolikowski W, Kivshar YS. Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices. PHYSICAL REVIEW LETTERS 2004; 92:093901. [PMID: 15089464 DOI: 10.1103/physrevlett.92.093901] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2003] [Indexed: 05/24/2023]
Abstract
We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.
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Affiliation(s)
- Andrey A Sukhorukov
- Nonlinear Physics Group and Laser Physics Center, Center for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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35
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Yulin AV, Skryabin DV, Russell PSJ. Transition radiation by matter-wave solitons in optical lattices. PHYSICAL REVIEW LETTERS 2003; 91:260402. [PMID: 14754031 DOI: 10.1103/physrevlett.91.260402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2003] [Indexed: 05/24/2023]
Abstract
We demonstrate that matter-wave solitary pulses formed from Bose condensed atoms moving inside optical lattices continuously radiate dispersive matter waves with prescribed momentum. Our analytical results for the radiation parameters and the soliton decay rate are found to be in excellent agreement with numerical modeling performed for experimentally relevant parameters.
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Affiliation(s)
- A V Yulin
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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36
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Fallani L, Cataliotti FS, Catani J, Fort C, Modugno M, Zawada M, Inguscio M. Optically induced lensing effect on a Bose-Einstein condensate expanding in a moving lattice. PHYSICAL REVIEW LETTERS 2003; 91:240405. [PMID: 14683097 DOI: 10.1103/physrevlett.91.240405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2003] [Indexed: 05/24/2023]
Abstract
We report the experimental observation of a lensing effect on a Bose-Einstein condensate expanding in a moving 1D optical lattice. The effect of the periodic potential can be described by an effective mass dependent on the condensate quasimomentum. By changing the velocity of the atoms in the frame of the optical lattice, we induce a focusing of the condensate along the lattice direction. The experimental results are compared with the numerical predictions of an effective 1D theoretical model. In addition, a precise band spectroscopy of the system is carried out by looking at the real-space propagation of the atomic wave packet in the optical lattice.
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Affiliation(s)
- L Fallani
- European Laboratory for Non-Linear Spectroscopy (LENS), INFM and Dipartimento di Fisica, Università di Firenze, via Nello Carrara 1, I-50019 Sesto Fiorentino (FI), Italy.
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37
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Abdullaev FK, Baizakov BB, Salerno M. Stable two-dimensional dispersion-managed soliton. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066605. [PMID: 14754334 DOI: 10.1103/physreve.68.066605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2003] [Indexed: 05/24/2023]
Abstract
The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrödinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.
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