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  • 1.
    Belicev, P. P.
    et al.
    University of Belgrade, Serbia.
    Gligoric, G.
    University of Belgrade, Serbia.
    Maluckov, A.
    University of Belgrade, Serbia.
    Stepic, M.
    University of Belgrade, Serbia.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Localized gap modes in nonlinear dimerized Lieb lattices2017Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 96, nr 6, artikel-id 063838Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.

  • 2.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Nonlinear localized modes in flatband lattices2017Konferensbidrag (Övrigt vetenskapligt)
  • 3.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Discrete breathers for a discrete nonlinear Schrodinger ring coupled to a central site2016Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 93, nr 1, s. 012219-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrodinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

  • 4.
    Beličev, P.P.
    et al.
    University of Belgrade, Serbia.
    Gligorić, G.
    University of Belgrade, Serbia.
    Radosavljević, A.
    University of Belgrade, Serbia.
    Maluckov, A.
    University of Belgrade, Serbia.
    Stepić, M.
    University of Belgrade, Serbia.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Light Localization in Nonlinear Binary Two-Dimensional Lieb Lattices2016Ingår i: Abstract Book of RIAO-OPTILAS 2016 / [ed] Moraga, P. and Saavedra, C, Concepción - Chile: CEFOP-UdeC , 2016, s. 80-80Konferensbidrag (Refereegranskat)
    Abstract [en]

    Light localization in photonic lattices (PLs) is a well-known phenomenon which has been investigated during decades. It has been shown that light localization in the linear regime can be achieved by designing PLs with specific geometries, instead of embedding defects or disorder in otherwise periodic lattices [1]. These geometries provide conditions necessary for destructive wave interference, leading to formation of a perfectly flat (dispersionless) energy band. Eigenvectors associated to the flat-band (FB) eigenfrequencies are entirely degenerate and compact states (FB modes) and any superposition of them is nondiffracting. One of the simplest FB lattice patterns is the two-dimensional (2D) Lieb lattice [2,3] in which the primitive cell contains three sites. By appropriate spatial repetition of this fundamental block, it is possible to achieve a FB in the energy spectrum. Light confinement in PLs can also be a consequence of the interplay between nonlinearity and diffraction when these effects cancel each other, leading to formation of solitons. Recently, it has been reported that nonlinearity and “binarism” in quasi-one-dimensional FB systems can increase the range of existence and stability of FB ring modes [4].

    We model a 2D binary Lieb lattice with nonlinearity of Kerr type and analyse numerically and analytically the existence, stability and dynamical properties of various localized modes found to emerge in spectrum. From the derived dispersion relation we found that binarism does not affect the FB. However, due to the presence of additional periodicity, new gaps occur in the energy spectrum above and below the FB and their widths depend on the ratio between coupling constants. Like in the uniform Lieb lattice, we found eigenmodes in the form of a staggered four-peak “ring” structure, but only under certain conditions which require a particular relation between the field amplitudes in neighbouring sites. In the nonlinear regime, ring modes survive in the uniform Lieb lattice but lose their stability moving away from the FB. On the other hand, nonlinearity destroys the existence of ring solutions in the binary Lieb lattice, leading to a new class of stable localized solutions which can be found in minigaps. As in previous kagome and ladder binary nonlinear strips [4], it is shown that the binarism increases the existence range of stable nonlinear localized solutions.

    References

    [1] R. A. Vicencio, M. Johansson, Physical Review A 87, 061803(R) (2013).

    [2] R. A. Vicencio et al., Physical Review Letters 114, 245503 (2015).

    [3] D. Leykam, O. Bahat-Treidel, A. S. Desyatnikov, Physical Review A 86, 031805(R) (2012).

    [4] P. P. Beličev et al., Physical Review E 92, 052916 (2015).

  • 5.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Quantum signatures of charge flipping vortices in the Bose-Hubbard trimer2016Ingår i: PHYSICAL REVIEW E, ISSN 2470-0045, Vol. 94, nr 5, artikel-id 052215Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this work we study quantum signatures of charge flipping vortices, found in the classical discrete nonlinear Schrodinger trimer, by use of the Bose-Hubbard model. We are able to identify such signatures in the quantum energy eigenstates, for instance when comparing the site amplitudes of the classical charge flipping vortices with the probability distribution over different particle configurations. It is also discussed how to construct quantum states that correspond to the classical charge flipping vortices and which effects can lead to deviations between the classical and quantum dynamics. We also examine properties of certain coherent states: classical-like quantum states that can be used to derive the classical model. Several quantum signatures are identified when studying the dynamics of these coherent states, for example, when comparing the average number of particles on a site with the classical site amplitude, when comparing the quantum and classical currents and topological charge, and when studying the evolution of the quantum probability amplitudes. The flipping of the quantum currents are found to be an especially robust feature of these states.

  • 6.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Quantum signatures of charge-flipping vortices in the Bose-Hubbard trimer2016Konferensbidrag (Övrigt vetenskapligt)
  • 7.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Quantum Signatures Of Charge-Flipping Vortices In The Bose-HubbardTrimer2016Ingår i: Abstract Book of RIAO-OPTILAS 2016 / [ed] Moraga, P. and Saavedra, C, Concepción - Chile: CEFOP-UdeC , 2016, s. 99-99Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this work we study quantum signatures of charge flipping vortices[1], found in the classical discrete nonlinear Schrödinger trimer[2], by use of the Bose-Hubbard model. We are able to identify such signatures in the quantum energy eigenstates, for instance when comparing the site amplitudes of the classical charge flipping vortices with the probability distribution over different particle configurations. It is also discussed how to construct quantum states that correspond to the classical charge flipping vortices, and which effects that can lead to deviations between the classical and quantum dynamics.

    We also examine properties of certain coherent states: classical-like quantum states that can be used to derive the classical model. Several quantum signatures are identified when studying the dynamics of these coherent states, for example when comparing the average number of particles on a site with the classical site amplitude, when comparing the quantum and classical currents and topological charge, and when studying the evolution of the quantum probability amplitudes. The flipping of the quantum currents are found to be an especially robust feature of these states.

    References

    [1] A.S. Desyatnikov, M.R. Dennis, A. Ferrando, Physical Review A 83, 063822 (2011)

    [2] P. Jason, M. Johansson, Physical Review E 91, 022910 (2015).

  • 8.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Jason, Peter
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Breather mobility and the Peierls-Nabarro potential: brief review and recent progress2015Ingår i: Quodons in Mica: nonlinear localized travelling excitations in crystals / [ed] Juan F. R. Archilla, Noé Jiménez, Victor J. Sánchez-Morcillo, Luis M. García-Raffi, Cham: Springer, 2015, s. 147-178Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framework of an extended Bose-Hubbard model, we show that while quantum fluctuations destroy the mobility of slowly moving, strongly localized classical modes, coherent mobility of rapidly moving states survives even in a strongly quantum regime

  • 9.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Charge Flipping Vortices in DNLS trimer and hexamer2015Ingår i: PHOTONICA 2015. V International School and Conference on Photonics& COST actions: MP1204 and BM1205 & the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices“, Belgrad 2015: Book of Abstracts / [ed] Suzana Petrović , Goran Gligorić and Milutin Stepić, Belgrade, Serbia: Vinča Institute of Nuclear Sciences , 2015, s. 65-65Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    We examine the existence and properties of Charge Flipping Vortices (CFVs), rtices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrödinger (DNLS) lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes.

    We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied to. The concept of a charge flipping energy barrier is introduced and discussed.

    REFERENCES

    [1]P. Jason, M. Johansson, Phys. Rev. E. 91, 022910 (2015).

  • 10.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Charge flipping vortices in the discrete nonlinear Schrodinger trimer and hexamer2015Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, nr 2, s. 022910-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We examine the existence and properties of charge flipping vortices (CFVs), vortices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrodinger lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes. We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied. The concept of a charge flipping energy barrier is introduced and discussed.

  • 11.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Naether, Uta
    University of Zaragoza, Spain; University of Zaragoza, Spain.
    Vicencio, Rodrigo A.
    University of Chile, Chile; University of Chile, Chile.
    Compactification tuning for nonlinear localized modes in sawtooth lattices2015Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, nr 3-1, s. 032912-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrodinger modelwith general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise noncompact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yields further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.

  • 12.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Editorial Material: Comment on "Localization-delocalization transition in self-dual quasi-periodic lattices" by Sun M. L. et al. in EPL, vol 112, issue 1, pp2015Ingår i: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 112, nr 1, s. 17002-Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    n/a

  • 13.
    Belicev, P. P.
    et al.
    University of Belgrade, Serbia.
    Gligoric, G.
    University of Belgrade, Serbia.
    Radosavljevic, A.
    University of Belgrade, Serbia.
    Maluckov, A.
    University of Belgrade, Serbia.
    Stepic, M.
    University of Belgrade, Serbia.
    Vicencio, R. A.
    University of Chile, Chile; University of Chile, Chile.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Localized modes in nonlinear binary kagome ribbons2015Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, nr 5, s. 052916-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system "binarism" various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.

  • 14.
    Beličev, P.P.
    et al.
    University of Belgrade, Serbia..
    Gligorić, G.
    University of Belgrade, Serbia..
    Radosavljević, A.
    University of Belgrade, Serbia..
    Maluckov, A.
    University of Belgrade, Serbia..
    Stepić, M.
    University of Belgrade, Serbia..
    Vicencio, R.A.
    University of Chile, Chile..
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    On localized modes in nonlinear binary kagome ribbons2015Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    One of the attractive two-dimensional [2D] lattice configurations is characterized by kagome geometry. The specific arrangement of its elements, i.e. waveguides, in the form of periodic hexagons renders completely flat the first energy band in linear case. As a consequence, the localized ring-like eigenmodes belonging to the lowest energy state propagate without diffraction through the system [1, 2]. Here we study kagome ribbon [3], which can be interpreted as one-dimensional counterpart of the standard 2D kagome lattice, and can be fabricated by dint of the direct femtosecond laser inscription [4, 5].

    The existence, stability and dynamical properties of various localized modes in binary kagome ribbon with defocusing Kerr type of nonlinearity have been explored, both numerically and analytically. We derived the corresponding dispersion relation and the bandgap spectrum, confirmed the opening of mini-gaps in it and found several types of stable ring-like modes to exist: staggered, unstaggered and vortex. Beside these nonlinear mode configurations occurring in a semi-infinite gap, we investigated features of "hourglass" solutions, identified in [3] as interesting structures when kagome lattice dimensionality is reduced to 1D. In nonlinear binary kagome ribbon dynamically stable propagation of unstaggered rings, vortex modes with certain topological charge and hourglass solutions are observed, while the staggered ring solutions are destabilized. In addition, we examined possibility to generate stable propagating solitary modes inside the first mini-gap and found that these mode patterns localize within sites mutually coupled by smaller coupling constant. The last feature is opposite to the nonlinear localized solutions found in the semi-infinite gap.

    REFERENCES

    [1] R. A. Vicencio, C. Mejía-Cortés, J. Opt. 16, 015706 (2014).

    [2] R. A. Vicencio, M. Johansson, Phys. Rev. A 87, R061803 (2013).

    [3] M. Molina, Phys. Lett. A 376, 3458 (2012).

    [4] K. Davies et al., Opt. Lett. 21, 1729 (1996).

    [5] K. Itoh et al., MRS Bulletin 31, 620 (2006).

  • 15.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska fakulteten.
    Rotational energy barriers: Charge-flipping of discrete vortices and rotation of dipole discrete gap solitons2015Konferensbidrag (Övrigt vetenskapligt)
  • 16.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Breather mobility and the PN potential - Brief review and recent progress2014Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors.

  • 17.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Dynamical properties of the DNLS2014Konferensbidrag (Övrigt vetenskapligt)
  • 18.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Existence, dynamics and mobility of Quantum Compactons in an extended Bose-Hubbard model2014Konferensbidrag (Refereegranskat)
    Abstract [en]

    Lattice Compactons, discrete breathers with compact support, were found for a discrete nonlinear Schrödinger (DNLS) equation extended with nearest neighbour intersite nonlinearities [1], a model originally studied with waveguide arrays in mind. These compactons were shown to exhibit very good mobility if the parameters are tuned close to the compactons stability boundary. The DNLS can also be used to model the behaviour of Bose-Einstein condensates in optical lattices, and the remarkable control over the experiments in this field of research has made it possible to study the quantum mechanics of strongly correlated atoms.

    We will define the concept of a Quantum Lattice Compacton [2] and discuss the existence and dynamics, with special emphasis on mobility [3], of these in an extended Bose-Hubbard model corresponding to above-mentioned extended DNLS equation in the quantum mechanical limit. The compactons is given 'a kick' by means of a phase-gradient and it is shown that the size of this phase is crucial for the mobility of the compactons. For small phase-gradients, corresponding to a slow coherent motion in the classical model, the time-scales of the quantum tunnelings become of the same order as the time-scale of the translational motion and the classical mobility is destroyed by quantum  fluctuations. For large phase-gradients, corresponding to rapid classical motion, the classical and quantum time-scales separate so that a mobile, localized coherent quantum state can be translated many sites in the lattice already for small particle numbers of the order of 10 [3].

    Acknowledgements: This project has been financed by the Swedish Research Council.

    References

    [1] M. Öster, M. Johansson, and A. Eriksson 2003 Phys. Rev. E 67 056606

    [2] P. Jason and M. Johansson 2012 Phys. Rev. A 85 011603(R)

    [3] P. Jason and M. Johansson 2013 Phys. Rev. A 88 033605

  • 19.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Prilepsky, Jaroslaw E.
    Aston University, Birmingham, UK.
    Derevyanko, Stanislav A.
    Weizmann Institute Science, Rehovot, Israel .
    Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain2014Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 89, nr 4, s. 042912-1-042912-9Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically walking modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime formoving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder.

  • 20.
    Vicencio, Rodrigo A.
    et al.
    University of Chile, Chile.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Discrete flat-band solitons in the kagome lattice2013Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, nr 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a model for a two-dimensional kagome lattice with defocusing nonlinearity, and show that families of localized discrete solitons may bifurcate from localized linear modes of the flat band with zero power threshold. Each family of such fundamental nonlinear modes corresponds to a unique configuration in the strong-nonlinearity limit. By choosing well-tuned dynamical perturbations, small-amplitude, strongly localized solutions from different families may be switched into each other, as well as moved between different lattice positions. In a window of small power, the lowest-energy state is a symmetry-broken localized state, which may appear spontaneously.

  • 21.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Existence, dynamics and mobility of Quantum Compactons in an extended Bose-Hubbard model2013Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Lattice Compactons, discrete breathers with compact support, were found for a discrete nonlinear Schrödinger (DNLS) equation extended with nearest neighbour intersite nonlinearities, a model originally studied with waveguide arrays in mind. These compactons were shown to exhibit very good mobility if the parameters are tuned close to the compactons stability boundary. The DNLS can also be used to model the behaviour of Bose-Einstein condensates in optical lattices, and the remarkable control over the experiments in this field of research has made it possible to study the quantum mechanics of strongly correlated atoms.

    We will define the concept of a Quantum Lattice Compacton and discuss the existence and dynamics, with special emphasis on mobility, of these in an extended Bose-Hubbard model corresponding to above-mentioned extended DNLS equation in the quantum mechanical limit.

    The compactons is given 'a kick' by means of a phase-gradient and it is shown that the size of this phase is crucial for the mobility of the compactons. For small phase-gradients, corresponding to a slow coherent motion in the classical model, the time-scales of the quantum tunnelings become of the same order as the time-scale of the translational motion and the classical mobility is destroyed by quantum fluctuations. For large phase-gradients, corresponding to rapid classical motion, the classical and quantum time-scales separate so that a mobile, localized coherent quantum state can be translated many sites in the lattice already for small particle numbers of the order of 10.

  • 22.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Quantum dynamics of lattice states with compact support in an extended Bose-Hubbard model2013Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, nr 3, s. 033605-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the dynamical properties, with special emphasis on mobility, of quantum lattice compactons (QLCs) in a one-dimensional Bose-Hubbard model extended with pair-correlated hopping. These are quantum counterparts of classical lattice compactons (localized solutions with exact zero amplitude outside a given region) of an extended discrete nonlinear Schrödinger equation, which can be derived in the classical limit from the extended Bose-Hubbard model. While an exact one-site QLC eigenstate corresponds to a classical one-site compacton, the compact support of classical several-site compactons is destroyed by quantum fluctuations. We show that it is possible to reproduce the stability exchange regions of the one-site and two-site localized solutions in the classical model with properly chosen quantum states. Quantum dynamical simulations are performed for two different types of initial conditions: “localized ground states” which are localized wave packets built from superpositions of compactonlike eigenstates, and SU(4) coherent states corresponding to classical two-site compactons. Clear signatures of the mobility of classical lattice compactons are seen, but this crucially depends on the magnitude of the applied phase gradient. For small phase gradients, which classically correspond to a slow coherent motion, the quantum time scale is of the same order as the time scale of the translational motion, and the classical mobility is therefore destroyed by quantum fluctuations. For a large phase instead, corresponding to fast classical motion, the time scales separate so that a mobile, localized, coherent quantum state can be translated many sites for particle numbers already of the order of 10.

  • 23.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Strongly localized moving discrete solitons (breathers): new ways to beat the Peierls-Nabarro barrier2013Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. In particular, for any system modelled by a Discrete Nonlinear Schrödinger (DNLS) type equation, this concept can be defined as the maximum difference in energy (Hamiltonian) between solutions at fixed power (norm), centered at different lattice positions. For the most commonly studied case with on-site, cubic (Kerr) nonlinearity, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile.

    Several ways to improve the mobility by reducing the PN-barrier for strongly localized modes have been proposed during the last decade, and the first part of this talk will give a brief review of two such scenarios. In 1D, one option is to utilize a competition between on-site and inter-site nonlinearities. In 2D, the mobility is normally much worse than in 1D, due to the fact that also broad solitons are prone to excitation thresholds and quasicollapse instabilities. Utilizing a saturable nonlinearity was found to considerably improve the 2D mobility by reducing the PN barrier in certain parameter regimes for large power.

    We then proceed to discuss two (if time allows) recently discovered novel mobility scenarios. The first example discussed is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows small-power, strongly localized nonlinear modes to appear without excitation threshold. The nonlinearity lifts the degeneracy of linear modes and causes a small energy shift between modes centered at different lattice positions, yielding a very small PN-barrier and mobility of highly localized modes in a small-power regime.

    The second example discusses a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping. It is shown that exponentially localized, travelling discrete dissipative solitons may exist as stable attractors, supported only by intrinsic properties of the medium (i.e., in absence of any external field or symmetry-breaking perturbations). With a standard, on-site Kerr-nonlinearity the solitons are pinned by the PN-barrier, but decreasing the barrier with inter-site nonlinearities allows for the existence of breathing (i.e., with oscillating size) solitons as stable attractors at certain velocities, related to lattice commensurability effects. The stable moving breathers also survive in presence of weak disorder.

  • 24.
    Prilepsky, Jaroslaw E.
    et al.
    Aston University, England .
    Yulin, Alexey V.
    University of Lisbon, Portugal .
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Derevyanko, Stanislav A.
    Aston University, England .
    Discrete solitons in coupled active lasing cavities2012Ingår i: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 37, nr 22, s. 4600-4602Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent.

  • 25.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Exact localized eigenstates for an extended Bose-Hubbard model with pair-correlated hopping2012Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, nr 1, s. 016603(R)-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show that a Bose-Hubbard model extended with pair-correlated hopping has exact eigenstates, quantum lattice compactons, with complete single-site localization. These appear at parameter values where the one-particle tunneling is exactly canceled by nonlocal pair correlations, and correspond in a classical limit to compact solutions of an extended discrete nonlinear Schrödinger model. Classical compactons at other parameter values, as well as multisite compactons, generically get delocalized by quantum effects, but strong localization appears asymptotically for increasing particle number.

  • 26.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Jason, Peter
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kirr, Katarina
    Institute of Electrophysics and Radiation Technologies, Kharkiv, Ukraine.
    Quantum signatures of an oscillatory instability in the Bose-Hubbard trimer2012Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    We study the Bose-Hubbard model for three sites in a symmetric, triangular configuration, and search for quantumsignatures of the classical regime of oscillatory instabilities, known to appear through Hamiltonian Hopfbifurcations for the single-depleted well family of stationary states in the Discrete Nonlinear Schrödinger equation.In the regimes of classical stability, single quantum eigenstates with properties analogous to the classicalstationary states can be identified already for rather small particle numbers. On the other hand, in the instabilityregime the interaction with other eigenstates through avoided crossings leads to strong mixing, andno single eigenstate with classical-like properties can be seen. We compare the quantum dynamics resultingfrom initial conditions taken as perturbed quantum eigenstates, and SU(3) coherent states, respectively, in aquantum-semiclassical transitional regime of 10-100 particles. While the perturbed quantum eigenstates donot show a classical-like behaviour in the instability regime, a coherent state behaves analogously to a perturbedclassical stationary state, and exhibits initially resonant oscillations with oscillation frequencies welldescribed by classical internal-mode oscillations.

  • 27.
    Jason, Peter
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kirr, Katarina
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Quantum signatures of an oscillatory instability in the Bose-Hubbard trimer2012Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, nr 1, s. 016214-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the Bose-Hubbard model for three sites in a symmetric, triangular configuration and search for quantum signatures of the classical regime of oscillatory instabilities, known to appear through Hamiltonian Hopf bifurcations for the "single-depleted-well" family of stationary states in the discrete nonlinear Schrodinger equation. In the regimes of classical stability, single quantum eigenstates with properties analogous to those of the classical stationary states can be identified already for rather small particle numbers. On the other hand, in the instability regime the interaction with other eigenstates through avoided crossings leads to strong mixing, and no single eigenstate with classical-like properties can be seen. We compare the quantum dynamics resulting from initial conditions taken as perturbed quantum eigenstates and SU(3) coherent states, respectively, in a quantum-semiclassical transitional regime of 10-100 particles. While the perturbed quantum eigenstates do not show a classical-like behavior in the instability regime, a coherent state behaves analogously to a perturbed classical stationary state, and exhibits initially resonant oscillations with oscillation frequencies well described by classical internal-mode oscillations.

  • 28.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kirr, K
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Kovalev, A S
    National Academy of Science Ukraine.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Gap and out-gap solitons in modulated systems of finite length: exact solutions in the slowly varying envelope limit2011Ingår i: PHYSICA SCRIPTA, ISSN 0031-8949, Vol. 83, nr 6Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss nonlinear excitations in finite-size one-dimensional modulated systems. Considering a binary modulated discrete nonlinear Schrodinger chain of large but finite length with periodic boundary conditions, we obtain exact elliptic-function solutions corresponding to stationary excitations in the slowly varying envelope limit. From these solutions, we analyze how the transformation between (localized) gap and (delocalized) out-gap solitons manifests itself in a system of finite length. The analogue of a localized gap soliton appears through a bifurcation at a critical point, so that gap soliton analogues exist only for chains longer than a critical value, which scales inversely proportional to the modulation depth. The total norm of these gap-out-gap states is found to be a monotonic function of the frequency, always inside a nonlinear gap with edges defined by the main nonlinear modes which approach the linear spectrum gap boundaries in the small-amplitude limit. The transformation from a gap to an out-gap state is associated with a particular frequency, close to the lower boundary of the linear gap; at this point the elliptic functions become trigonometric, corresponding to a finite-size analogue of an algebraic soliton. We compare the scenario with earlier results obtained numerically for purely discrete chains with few degrees of freedom.

  • 29.
    Naether, Uta
    et al.
    University of Chile.
    Vicencio, Rodrigo A
    University of Chile.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrodinger lattices2011Ingår i: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 83, nr 3, s. 036601-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrodinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to the existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.

  • 30.
    Makela, H
    et al.
    Umeå University.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Zelan, M
    Umeå University.
    Lundh, E
    Umeå University.
    Stability of nonstationary states of spin-1 Bose-Einstein condensates2011Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 84, nr 4, s. 043646-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The stability of nonstationary states of homogeneous spin-1 Bose-Einstein condensates is studied by performing Bogoliubov analysis in a frame of reference where the state is stationary. In particular, the effect of an external magnetic field is examined. It is found that a nonzero magnetic field introduces instability in a (23)Na condensate. The wavelengths of this instability can be controlled by tuning the strength of the magnetic field. In a (87)Rb condensate this instability is present already at zero magnetic field. Furthermore, an analytical bound for the size of a stable condensate is found, and a condition for the validity of the single-mode approximation is presented. Realization of the system in a toroidal trap is discussed, and the full time development is simulated.

  • 31.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kopidakis, G
    University of Crete.
    Aubry, S
    CEA Saclay.
    KAM tori in 1D random discrete nonlinear Schrodinger model?2010Ingår i: EPL, ISSN 0295-5075, Vol. 91, nr 5Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the random discrete nonlinear Schrodinger equation, appearing with a finite probability for a given initial condition with sufficiently small norm. Numerical support for the existence of a fat Cantor set of initial conditions generating almost periodic oscillations is obtained by analyzing i) sets of recurrent trajectories over successively larger time scales, and ii) finite-time Lyapunov exponents. The norm region where such KAM-like tori may exist shrinks to zero when the disorder strength goes to zero and the localization length diverges.

  • 32.
    Kroon, Lars
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kovalev, A S
    National Acadamy of Science Ukraine.
    Yu Malyuta, E
    National Acadamy of Science Ukraine.
    The appearance of gap solitons in a nonlinear Schrodinger lattice2010Ingår i: PHYSICA D-NONLINEAR PHENOMENA, ISSN 0167-2789, Vol. 239, nr 5, s. 269-278Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the appearance of discrete gap solitons in a nonlinear Schrodinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q = pi/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this "nonlinear gap boundary" are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gal) edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.

  • 33.
    Vicencio, Rodrigo A
    et al.
    University of Chile.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Discrete gap solitons in waveguide arrays with alternating spacings2009Ingår i: PHYSICAL REVIEW A, ISSN 1050-2947, Vol. 79, nr 6, s. 065801-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider an array of waveguides with identical widths but alternating spacings using the discrete nonlinear Schroumldinger model (tight-binding approximation). In the highly discrete (anticontinuous) limit when one of the spacings is infinite, the model reduces to an integrable chain of uncoupled dimers. From this limit, we identify the two fundamental, antisymmetric and symmetric, discrete gap solitons, which can be numerically continued to a continuum limit gap soliton at one band edge. Other composite solutions at the uncoupled limit disappear in bifurcations. Similarly to the case of waveguides with alternating widths and constant spacings, oscillatory instabilities appear for the fundamental solutions only for frequencies in the upper half of the gap. In contrast to the alternating-width case, there is no stability exchange between the two fundamental solutions: the symmetric solution is always unstable while the antisymmetric solution is always stable in the lower half of the gap. Thus, the Peierls-Nabarro barrier can vanish only in the continuum limit.

  • 34.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Sukhorukov, Andrey A
    Australian National University.
    Kivshar, Yuri S
    Australian National University.
    Discrete reduced-symmetry solitons and second-band vortices in two-dimensional nonlinear waveguide arrays2009Ingår i: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 80, nr 4, s. 046604-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Considering a two-dimensional lattice of weakly coupled waveguides, where each waveguide may carry two orthogonal modes of dipolar character, we present a nonlinear discrete vector model for the study of Kerr optical solitons with profiles having a reduced symmetry relative to the underlying lattice. We describe analytically and numerically existence and stability properties of such states in square and triangular lattices and also reveal directional mobility properties of two-dimensional gap solitons which were recently observed in experiment. The model also describes one-site peaked discrete vortices corresponding to experimentally observed "second-band" vortex lattice solitons, for which oscillatory instabilities are predicted. We also introduce a concept of "rotational Peierls-Nabarro barrier" characterizing the minimum energy needed for rotation of stable dipole modes and compare numerically translational and rotational energy barriers in regimes of good mobility.

  • 35.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Nonlinearity, discreteness and disorder: localization, delocalization and transmission threshold in time-periodically driven systems2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    After a brief introduction to the physics of nonlinear localization and Anderson localization, the talk will focus on discussing how these two effects may compete with each other. Examples will be given showing that in different circumstances, nonlinearity may either enhance Anderson localization or lead to delocalization in a disordered system. In the end, we will discuss recent results showing that a locally acting time-periodic driving force may destroy Anderson localization, and due to nonlinear effects yield transmission of energy through a disordered system if the force strength is above some threshold value. The application of these results to experiments on light waves in optical wave guide arrays, as well as to quantum mechanical matter waves of Bose-Einstein condensates trapped in optical lattice potentials, will also be briefly discussed.

  • 36.
    Öster, Michael
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson , Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling2009Ingår i: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 238, nr 1, s. 88-99Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with nontrivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.

  • 37.
    Johansson, Magnus
    et al.
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Kopidakis, G
    University of Crete.
    Lepri, S
    CNR.
    Aubry , S
    CEA Saclay.
    Transmission thresholds in time-periodically driven nonlinear disordered systems2009Ingår i: EPL, ISSN 0295-5075 , Vol. 86, nr 1, s. 10009-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) below threshold, localized quasiperiodic oscillations and no spreading; 2) three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times and finally strong diffusion; 3) immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

  • 38.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Transmission thresholds in time-periodically driven nonlinear disordered systems2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    (Joint work with G. Kopidakis, S. Lepri, and S. Aubry) We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below threshold, localized quasiperiodic oscillations and no spreading; 2) Three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times, and finally strong diffusion; 3) Immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning-points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

  • 39.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Discrete solitons, breathers and vortices in nonlinear Schroedinger-type lattices: stability, mobility and thermodynamics.2008Ingår i: WEH Seminar Discrete Optics and Beyond,2008, 2008Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

      

  • 40.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Effects of nonlinear coupling in nonlinear Schrödinger lattices2008Ingår i: BICS Workshop: Lattice Models,2008, Bath: University of Bath , 2008Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

      

  • 41.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Nonlinearity, discreteness and disorder: localization, delocalization and transmission threshold in time-periodically driven systems2008Ingår i: Aspectos en fisica no lineal, Mini-workshop internacional,2008, 2008Konferensbidrag (Övrigt vetenskapligt)
  • 42.
    Usatenko, O. V.
    et al.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Melnik, S. S.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Apostolov, A. A.
    A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, Kharkov, Ukraine.
    Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wire2008Ingår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 387, nr 19-20, s. 4733-4739Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Spectral properties of 1D systems with long-range correlated disorder and their response to an applied field are examined. An algorithm based on the additive multi-step Markov chains is used to analyze and synthesize layered systems consisting of two randomly alternated elements. Using an equation connecting the correlation and memory functions enables one to reveal the microscopic structure, which can be expressed in terms of the Markov chain conditional probability function. Specifically, a method of designing complex gratings with prescribed characteristics that simultaneously display periodic, quasi-periodic and random properties is emphasized. The tight-binding Schrödinger equation with a weak correlated disorder in the dichotomic potential exhibiting sharp transition in conductivity is studied.

  • 43.
    Johansson, Magnus
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Kopidakis, Georgios
    Lepri, Stefano
    Aubry, Serge
    Transmission thresholds in time-periodically driven nonlinear disordered systems2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

      

  • 44.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Discrete reduced-symmetry solitons in two dimensional nonlinear waveguide arrays2007Ingår i: Nonlinear Physics in Periodic Structures and Metamaterials,2007, 2007Konferensbidrag (Refereegranskat)
    Abstract [en]

       

  • 45.
    Johansson, Magnus
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Öster, Michael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Gaididei, Yu.B.
    Christiansen, P.L.
    Eriksson, A.
    Some properties of a physically motivated generalized DNLS equation with inter-site nonlinearities2007Ingår i: Hamiltonian Lattice Dynamical Systems,2007, 2007Konferensbidrag (Refereegranskat)
  • 46.
    Usatenko, O.V.
    et al.
    A. Ya. Usikov Inst. for Radiophys. & Electron., Ukrainian Acad. of Sci., Kharkov.
    Melnik, S.S.
    A. Ya. Usikov Inst. for Radiophys. & Electron., Ukrainian Acad. of Sci., Kharkov.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik. Linköpings universitet, Tekniska högskolan.
    Spectral Analysis and Syntesis of Long-Rang Correlated Systems: Antennas, Diffraction Gratings and Solids2007Ingår i: Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop on Terahertz Technologies, 2007: Volume 1, IEEE , 2007, s. 246-248Konferensbidrag (Refereegranskat)
    Abstract [en]

    A new method for constructing a long-range correlated sequence of two-valued random elements with a given correlator is discussed. A Fourier transform of a correlation function having an arbitrary complexity is designed. The real-space correlator, the memory function, and the conditional probability function of the additive Markov chain are calculated sequentially. The diffraction grating and the antenna are considered as a series of 2M+1 scatterers.

  • 47.
    Usatenko, O.V.
    et al.
    National Academy of Sciences of Ukraine.
    Melnyk, S.S.
    National Academy of Sciences of Ukraine.
    Yampolski, V.A.
    National Academy of Sciences of Ukraine.
    Johansson, Magnus
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Kroon, Lars
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Riklund, Rolf
    Linköpings universitet, Institutionen för fysik, kemi och biologi. Linköpings universitet, Tekniska högskolan.
    Three types of spectra in one-dimensional systems with random correlated binary potential2007Ingår i: Telecommunications and Radio Engineering, ISSN 0040-2508, Vol. 66, nr 4, s. 353-362Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid spectrum with three different spectral components (absolutely continues, singular continues and point) ordered in any predefined manner in the region of energy and/or wave number is presented. A new approach to generating a binary sequence with the long-range memory based on a concept of additive Markov chains is used.

  • 48.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Discrete nonlinear Schrödinger approximation of a mixed Klein-Gordon/Fermi-Pasta-Ulam chain: Modulational instability and a statistical condition for creation of thermodynamic breathers2006Ingår i: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 216, nr 1 SPEC. ISS., s. 62-70Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We analyze certain aspects of the classical dynamics of a one-dimensional discrete nonlinear Schrödinger model with inter-site as well as on-site nonlinearities. The equation is derived from a mixed Klein-Gordon/Fermi-Pasta-Ulam chain of anharmonic oscillators coupled with anharmonic inter-site potentials, and approximates the slow dynamics of the fundamental harmonic of discrete small-amplitude modulational waves. We give explicit analytical conditions for modulational instability of travelling plane waves, and find in particular that sufficiently strong inter-site nonlinearities may change the nature of the instabilities from long-wavelength to short-wavelength perturbations. Further, we describe thermodynamic properties of the model using the grand-canonical ensemble to account for two conserved quantities: norm and Hamiltonian. The available phase space is divided into two separated parts with qualitatively different properties in thermal equilibrium: one part corresponding to a normal thermalized state with exponentially small probabilities for large-amplitude excitations, and another part typically associated with the formation of high-amplitude localized excitations, interacting with an infinite-temperature phonon bath. A modulationally unstable travelling wave may exhibit a transition from one region to the other as its amplitude is varied, and thus modulational instability is not a sufficient criterion for the creation of persistent localized modes in thermal equilibrium. For pure on-site nonlinearities the created localized excitations are typically pinned to particular lattice sites, while for significant inter-site nonlinearities they become mobile, in agreement with well-known properties of localized excitations in Fermi-Pasta-Ulam-type chains. © 2006 Elsevier Ltd. All rights reserved.

  • 49.
    Vicencio, Rodrigo
    et al.
    Max-Planck-Institut für Physic Komplexer Systeme.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Discrete soliton mobility in two-dimensional waveguide arrays2006Ingår i: EPS - 21st General Conference of the Condensed Matter Division,2006, 2006Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

      

  • 50.
    Vicencio, Rodrigo A.
    et al.
    Max Planck Institute for the Physics of Complex Systems, Dresden, Tyskland.
    Johansson, Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för fysik, kemi och biologi, Teoretisk Fysik.
    Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity2006Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 73, s. 046602-1-046602-9Artikel i tidskrift (Refereegranskat)
12 1 - 50 av 71
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