Breather States Research Articles

Akhmediev breather evolution in optical fiber for realistic initial conditions

We study numerically Akhmediev breather dynamics in optical fibers under initial conditions that do not correspond to an ideal infinitesimal modulation on a plane wave. We examine two modifications that are commonly encountered in realistic experiments: (i) a finite-amplitude (not necessarily weak) initial modulation; (ii) the use of pulsed excitation. In the first case, we derive an expression for the propagation distance required to generate a train of compressed breather pulses. In the second case, we show that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope.

Discrete breathers at the interface between a diatomic and a monoatomic granular chain

In the present work, we develop a systematic examination of the existence, stability, and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an "interface breather" is more robust than its bulk diatomic counterpart throughout the gap of the linear spectrum. The latter linear spectral gap needs to exist for the breather state to arise and the relevant spectral conditions are discussed. We illustrate the minimal excitation conditions under which such an interface breather can be "nucleated" and analyze its apparently weak interaction with regular highly nonlinear solitary waveforms.

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

We study nonsymmetric collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. In this paper we have considered the following types of nonsymmetric collisions: head-on collisions of two breathers traveling with different velocities; collisions of moving breathers with a stationary trapped breather; and collisions of moving breathers traveling with the same direction. The various main observed phenomena are: one moving breather gets trapped at the collision region, and the other one is reflected; breather fusion without trapping, with the appearance of a new moving breather; and breather generation without trapping, with the appearance of new moving breathers traveling either with the same or different directions. For comparison we have included some results of a previous paper concerning to symmetric collisions, where two identical moving breathers traveling with opposite velocities collide. For symmetric collisions, the main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities and a stationary breather trapped at the collision region; and breather generation without trapping, with the appearance of new moving breathers with opposite velocities. A common feature for all types of collisions is that the collision outcome depends on the internal structure of the moving breathers and the exact number of pair-bases that initially separates the stationary breathers when they are perturbed. As some nonsymmetric collisions result in the generation of a new stationary trapped breather of larger energy, the trapping phenomenon could play an important part of the complex mechanisms involved in the initiation of the DNA transcription processes.

Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice

We study the stability of a stationary discrete breather (DB) on a nonlinear trimer in the framework of the discrete nonlinear Schr\"odinger equation (DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein condensates in leaking optical lattices, collisions between a DB and a lattice excitation, e.g. a moving breather (MB) or phonon, were studied. These collisions lead to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we show that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.

Breather states and compound solitons in a ferromagnet-insulator-metal structure

Nonlinear dynamic states with a fine internal structure, such as breathers, “breather lattices,” kinks, kink-antikink bound states, and their spatially periodic generalizations have been constructed in terms of a modified Korteweg-de Vries equation for a system of magnetostatic waves in a ferromagnet-insulator-metal structure. Specific features of the nucleation, interaction, and transformation of these states have been studied in layered magnetic structures.

Coherent matter waves of a dipolar condensate in two-dimensional optical lattices

The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.

Compact breathers in a quasi-linear Klein–Gordon equation

We study the quasi-linear complex Klein–Gordon equation − Z t t + ∇ ( | ∇ Z | 2 ∇ Z ) = P ′ ( | Z | ) Z | Z | and present two classes of strictly localized compact stationary breathers. In the first class breathers vibrate at an anharmonic rate but the site potential has to be quartic. In the second class a more general, Q-ball type, site potentials are admitted but vibrations are harmonic. Notably, unlike the Q-balls supporting models, if the chosen potential has a top then multi-nodal modes cannot accumulate there: only a finite number of multi-nodal modes is possible, each constrained by its own spectrum of harmonic vibrations.

Coherent spin-mixing and wave packets dynamics of spin-1 condensates in optical lattices

The dynamics of wave packets and spin-mixing of spin-1 condensates with repulsive spin-independent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional (1D) periodic optical lattices are discussed both analytically and numerically. In the tight-binding limit, the localized states, i.e., self-trapping, moving soliton and breather, in spin-1 condensates are obtained. The moving soliton and breather states show complex characters: if initially the condensates are prepared in spin stationary configuration, normal stable moving soliton and breather exist; however, if initially the condensates are prepared in spin non-stationary state, because of the spin-exchange process, the wave packets experience both local soliton/breather motion and larger scale periodic oscillation (with the spin-exchange period). Interestingly, we find the spin-mixing dynamics are coupled with wave packets dynamics: when the wave packets are self-trapped, the spin-mixing oscillations are also arrested to the stationary configuration; during diffusion of the wave packets, however, the spin-mixing dynamics are inhibited; a robust quasi-periodic spin-mixing oscillation maintains in moving soliton and breather states. These interesting results open up the possibility for controlled manipulation of the spin dynamics by the optical lattices.

TALKING BREATHER QUBITS

Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

Discrete breathers in a two-dimensional spring-mass lattice

We consider a two-dimensional spring-mass lattice with square symmetry in which each particle experiences a nonlinear onsite potential and nonlinear nearest-neighbour interactions. At equilibrium, the particles are equally spaced in both the horizontal and vertical directions and all springs are unextended. Motivated by the work of Marin et al (1998 Phys. Lett. A 248 225–9, 2001 Phys. Lett. A 281 21–5), we seek a solution in which most of the breather's energy is focused along three chains. We construct an asymptotic approximation to the breather using the method of multiple scales to describe the coherent oscillations in the three main chains that constitute the discrete breather. We reduce the equation of motion to a nonlinear Schrödinger equation for the leading-order term and find a family of solutions, which encompasses both stationary and moving bright soliton solutions. We use numerical simulations of the lattice to verify the shape and velocity of breathers and find that while stationary breathers are found to persist for long times, moving breathers decay by radiating energy in the direction perpendicular to their motion.

Moving breather collisions in Klein-Gordon chains of oscillators

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of oscillators. The on-site potentials are: the asymmetric and soft Morse potential, the symmetric and soft sine-Gordon potential and the symmetric and hard φ4 potential. The simulation of a collision begins generating two identical moving breathers traveling with opposite velocities, they are obtained after perturbing two identical stationary breathers which centers are separated by a fixed number of particles. If this number is odd we obtain an on-site collision, but if this number is even we obtain an inter-site collision. Apart from this distinction, we have considered symmetric collisions, if the colliding moving breathers are vibrating in phase, and anti-symmetric collisions, if the colliding moving breathers are vibrating in anti-phase. The simulations show that the collision properties of the three chains are different. The main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities, and a stationary breather trapped at the collision region; breather generation without trapping, with the appearance of new moving breathers with opposite velocities; breather trapping at the collision region, without the appearance of new moving breathers; and breather reflection. For each Klein-Gordon chain, the collision outcomes depend on the lattice parameters, the frequency of the perturbed stationary breathers, the internal structure of the moving breathers and the number of particles that initially separates the stationary breathers when they are perturbed.

Breather states in magnetic domain wall racetrack memory samples

Magnetic domain wall racetrack memory samples allow for the controlled motion of isolated magnetic domain walls in a quasi one-dimensional geometry. Here we consider the possibility of the dynamical formation of bound states of domain walls that can be prepared via a suitably chosen external field. Upon switching off the external field, these domain walls oscillate around their common center of mass, with a frequency depending on the relative initial handedness of the domain wall. Such breather states may be observed by detecting the resulting magnetization oscillations.

Analytical solution in the Ince-Gaussian form of the beam propagating in the strong nonlocal media

Based on the Snyder-Mitchell model that describes the paraxial beam propagating in strongly nonlocal nonlinear media and by constituting the trial solution with modulating the Gaussian beam by Ince polynomials in elliptic coordinate，the close forms of Ince-Gaussian beams have been accessed. Depending on the power of the beam，the Ince-Gaussian beams can be either a soliton state when the input power is equal to the critical power or a breather state. The Ince-Gaussian beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The profiles of the breather at different propagating distance are numerically obtained and the transitions of a few Ince solitons are given.

The observation of strong dynamic electron‐phonon couplings due to a breather state in trans ‐polyacetylene

AbstractThe dynamics preceding the separation process of a charged soliton pair after photoexcitation in trans ‐polyacetylene was successfully time‐resolved using ultrafast spectroscopy with a few‐optical‐cycle laser. It was directly verified that after photoexcitation, the electron‐hole pair relaxes with a breather mode as theory predicts with an electron‐hole pair lifetime of 33–50 fs, which is in agreement with the electronic dephasing time. By applying the spectrogram analysis to the time trace of the absorbance change, the ultrafast amplitude and frequency modulations of C–C and C=C stretching modes lasting only shorter than 100 fs induced by breather modes can be observed simultaneously for the first time. The frequency shift of C–C and C=C stretching modes caused by the breather mode are observed in good agreement with the SSH Hamiltonian. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ince–Gaussian beams in strongly nonlocal nonlinear media

Based on the Snyder–Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince–Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite–Gaussian beams and Laguerre–Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schrdinger equation.

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

We consider the classical and quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. In the classical case the equations of motion admit discrete breather solutions, which are time periodic and localized predominantly on one of the junctions. In the quantum case breather states are found in the central part of the energy spectrum of the confined nonescaping states of the system. We perform a systematic analysis of their tunneling frequency, site correlations, fluctuations of the number of quanta, and entanglement. Quantum breather states show strong site correlation of quanta and are characterized by a strong excitation of quanta on one junction which perform slow coherent tunneling motion from one junction to the other. They suppress fluctuations of the total number of excited quanta. Quantum breather states are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We describe how quantum breather excitations could be experimentally observed by employing the already developed techniques for quantum information processing using Josephson junctions.

Finite volume spectrum of [formula omitted] superminimal models perturbed by [formula omitted

We describe an extension of the nonlinear integral equation (NLIE) technique to N = 1 superminimal models perturbed by Φ 13 . Along the way, we also complete our previous studies of the finite volume spectrum of the N = 1 supersymmetric sine-Gordon model by considering the attractive regime and more specifically, breather states.

Energy transfer in coupled nonlinear phononic waveguides: transition from wandering breather to nonlinear self-trapping

We consider, both analytically and numerically, the dynamics of stationary and slowly-moving breathers (localized short-wavelength excitations) in two weakly coupled nonlinear oscillator chains (nonlinear phononic waveguides). We show that there are two qualitatively different dynamical regimes of the coupled breathers: the oscillatory exchange of the low-amplitude breather between the phononic waveguides (wandering breather), and one-waveguide-localization (nonlinear self-trapping) of the high-amplitude breather. We also show that phase-coherent dynamics of the coupled breathers in two weakly linked nonlinear phononic waveguides has a profound analogy, and is described by a similar pair of equations, to the tunnelling quantum dynamics of two weakly linked Bose-Einstein condensates in a symmetric double-well potential (single bosonic Josephson junction). The exchange of phonon energy and excitations between the coupled phononic waveguides takes on the role which the exchange of atoms via quantum tunnelling plays in the case of the coupled condensates. On the basis of this analogy, we predict a new tunnelling mode of the coupled Bose-Einstein condensates in a single bosonic Josephson junction in which their relative phase oscillates around π/2. The dynamics of relative phase of two weakly linked Bose-Einstein condensates can be studied by means of interference, while the dynamics of the exchange of lattice excitations in coupled nonlinear phononic waveguides can be observed by means of light scattering.

Discrete breathers in a two-dimensional hexagonal Fermi–Pasta–Ulam lattice

We consider a two-dimensional Fermi–Pasta–Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrödinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher order analysis yielding a generalized NLS, which includes known stabilizing terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximized for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt and Wattis 2006 J. Phys. A: Math. Gen. 39 4955), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalized NLS equation.

Analysis of breather state in thin bar by using collective coordinate

Considering Peierls-Nabarro (P-N) force and viscous effect of material, the dynamic behavior of one-dimensional infinite metallic thin bar subjected to axially periodic load is investigated. Governing equation, which is sine-Gordon type equation, is derived. By means of collective-coordinates, the partial equation can be reduced to ordinary differential dynamical system to describe motion of breather. Nonlinear dynamic analysis shows that the amplitude and frequency of P-N force would influence positions of hyperbolic saddle points and change subharmonic bifurcation point, while the path to chaos through odd subharmonic bifurcations remains. Several examples are taken to indicate the effects of amplitude and period of P-N force on the dynamical response of the bar. The simulation states that the area of chaos is half-infinite. This area increases along with enhancement of the amplitude of P-N force. And the frequency of P-N force has similar influence on the system.