Breather States Research Articles

Slow energy relaxation in anharmonic chains with and without on-site potentials: Roles of distinct types of discrete breathers

Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of Tc≃4.2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling.

Bound-in-continuum-like corner states in the type-II Dirac photonic lattice

Dirac points are special points in the energy band structure of various materials, around which the dispersion is linear. If the corresponding Fermi surface is projected as a pair of crossing lines—or touching cones in two dimensions, the Dirac point is known as the type-II; such points violate the Lorentz invariance. Until now, thanks to its unique characteristics, the Klein tunneling is successfully mimicked and the topological edge solitons are obtained in the type-II Dirac photonic lattices that naturally possess type-II Dirac points. However, the interplay between these points and corner states is still not investigated. Here, we report both linear and nonlinear corner states in the type-II Dirac photonic lattice with elaborate boundaries. The states, classified as in-phase and out-of-phase, hide in the extended bands that are similar to the bound states in the continuum (BIC). We find that the nonlinear BIC-like corner states are remarkably stable. In addition, by removing certain sites, we establish the fractal Sierpiński gasket structure in the type-II Dirac photonic lattice, in which the BIC-like corner states are also demonstrated. The differences between results in the fractal and nonfractal lattices are rather small. Last but not least, the corner breather states are proposed. Our results provide a novel view on the corner states and may inspire fresh ideas on how to manipulate/control the localized states in different photonic lattices.

Two-colour dissipative solitons and breathers in microresonator second-harmonic generation

Frequency conversion of dissipative solitons associated with the generation of broadband optical frequency combs having a tooth spacing of hundreds of giga-hertz is a topical challenge holding the key to practical applications in precision spectroscopy and data processing. The work in this direction is underpinned by fundamental problems in nonlinear and quantum optics. Here, we present the dissipative two-colour bright-bright and dark-dark solitons in a quasi-phase-matched microresonator pumped for the second-harmonic generation in the near-infrared spectral range. We also found the breather states associated with the pulse front motion and collisions. The soliton regime is found to be typical in slightly phase-mismatched resonators, while the phase-matched ones reveal broader but incoherent spectra and higher-order harmonic generation. Soliton and breather effects reported here exist for the negative tilt of the resonance line, which is possible only via the dominant contribution of second-order nonlinearity.

Spiraling elliptic hollow beams with cross phase

We introduced a class of spiraling elliptic hollow beams with the cross phase. Due to the cross phase, the spiraling elliptic hollow beams exhibit three key characteristics, having the elliptic peak ring, carrying the orbital angular momentum (OAM), and performing rotations. We investigated both linear and nonlinear evolutions of the spiraling elliptic hollow beams, and found they can propagate stably, thanks to the cross phase. Especially, we obtained the breather states of spiraling elliptic hollow beams in nonlocally nonlinear medium, and could handily control the rotation by changing optical powers. We discussed both the OAM property and optical force property. By using the spiraling elliptic hollow beams, we can achieve a jointly multiple manipulation on particles at the same time. In one step, we can trap and simultaneously rotate the particles.

Breather dynamics in a stochastic sine-Gordon equation: Evidence of noise-enhanced stability

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to illustrate the effectiveness of the noise-enhanced stability phenomenon, which manifests itself as a nonmonotonic behavior of the mean first-passage time for the breather as a function of the noise intensity. The influence of the mode’s initial frequency on the results and their robustness against an additional thermal background are also addressed. Overall, the analysis highlights a counter-intuitive, positive role of noise in the breather’s persistence.

Frequency combs with multiple offsets in THz-rate microresonators.

Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the breather combs into a sequence of sub-combs with different carrier-envelope offset frequencies. The large detuning breathers have a high frequency of oscillations associated with the perturbation extending across the whole microresonator. The small detuning breathers create oscillations localised on the soliton core and can undergo the period-doubling bifurcation, which triggers a sequence of intense sub-combs.

Data-driven intrinsic localized mode detection and classification in one-dimensional crystal lattice model

In this work we propose Support Vector Machine classification algorithms to classify one-dimensional crystal lattice waves from locally sampled data. Different learning datasets of particle displacements, momenta and energy density values are considered. Efficiency of the classification algorithms is further improved by two dimensionality reduction techniques: Principal Component Analysis and Locally Linear Embedding. Robustness of classifiers is investigated and demonstrated. Developed algorithms are successfully applied to detect localized intrinsic modes in three numerical simulations considering a case of two localized stationary breather solutions, a single stationary breather solution in noisy background and two mobile breather collision.

Breather solitons in AlN microresonators

In this work, we demonstrate the generation of breather solitons in an aluminum nitride (AlN) microresonator. Our study shows different techniques for excitation of breather solitons together with stimulated Raman scattering (SRS) by pumping the fundamental transverse electric (TE00) mode. With suitable pump power and laser scan speed, we can eliminate the Raman effect and achieve a single soliton comb (FSR ∼ 374 GHz) beyond 4/5 of an octave-spanning bandwidth (1200–2100 nm). We have also demonstrated the breather and single soliton (FSR ∼ 364 GHz) states by pumping the first-order TE (TE10) mode using another device with a similar geometry. Our study adds significant development in the dynamics of solitons in the AlN platform.

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices.

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

Breather solitons in AlN microresonators

In this work, we demonstrate the generation of breather solitons in an aluminum nitride (AlN) microresonator. Our study shows different techniques for excitation of breather solitons together with stimulated Raman scattering (SRS) by pumping the fundamental transverse electric (TE00) mode. With suitable pump power and laser scan speed, we can eliminate the Raman effect and achieve a single soliton comb (FSR ∼ 374 GHz) beyond 4/5 of an octave-spanning bandwidth (1200–2100 nm). We have also demonstrated the breather and single soliton (FSR ∼ 364 GHz) states by pumping the first-order TE (TE10) mode using another device with a similar geometry. Our study adds significant development in the dynamics of solitons in the AlN platform.

Quantum Breathers in a Two-Dimensional Hexangular Heisenberg Ferromagnet

We present a theoretical study on quantum breathers in a XXZ Heisenberg ferromagnet with the single-ion uniaxial anisotropy on a two-dimensional hexangular lattice. In our work, the full quantum and the semiclassical cases are considered, respectively. For the full quantum case, we find that some isolated two-magnon bands can exist below the free magnon band. Physically, each isolated two-magnon band correspond to a two-magnon bound state, which is the simplest quantum breather state. For the semiclassical case, the analytical form of the discrete breather solution with a line localized structure is obtained by adopting the Glauber’s coherent-state representation. Furthermore, the influence of the anisotropy on the properties of quantum breathers is discussed in detail.

Two-dimensional mobile breather scattering in a hexagonal crystal lattice.

We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box" harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60^{∘} scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11764039, 11847304, 11865014, 11475027, 11305132, and 11274255), the Natural Science Foundation of Gansu Province, China (Grant No. 17JR5RA076), and Scientific Research Project of Gansu Higher Education, China (Grant No. 2016A-005).

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.

Mobile Dissipative Breathers in a Chain of Nonlinear Oscillators

In a numerical experiment, it is found that at least three localized stationary breather type modes can exist in a chain of Rayleigh oscillators with a nonlinear coupling between them: immobile, “slow,” and “fast” dissipative breathers. The dynamics of synchronous motions of chain elements depends on the relation of characteristic time scales of the system related to the frequency of the oscillators and rigidity of the coupling between them; it is multistable.

The essential spectrum of periodically stationary solutions of the complex Ginzburg–Landau equation

We establish the existence and regularity properties of a monodromy operator for the linearization of the cubic–quintic complex Ginzburg–Landau equation about a periodically stationary (breather) solution. We derive a formula for the essential spectrum of the monodromy operator in terms of that of the associated asymptotic linear differential operator. This result is obtained using the theory of analytic semigroups under the assumption that the Ginzburg–Landau equation includes a spectral filtering (diffusion) term. We discuss applications to the stability of periodically stationary pulses in ultrafast fiber lasers.

Мобильные диссипативные бризеры в цепочке нелинейных осцилляторов

In a numerical experiment, it was found that in a chain of Raleigh oscillators with a nonlinear connection between them, at least three localized stationary breathers modes may exist: non-mobile, "slow" and "fast" dissipative breathers. The dynamics of the chain elements depends on the ratio of characteristic time scales of the system which determined by the frequency of oscillators and the rigidity of the connection between them. Considered system is multistable.

Stationary breather model in a two-dimensional hexagonal spring-mass lattice

In the present paper, the form of stationary breather modes in a two-dimensional (2D) FPU-KG spring mass lattice that exhibits square and hexagonal symmetry is studied. Inspired by the work of Marin et al. (1998) [6], we develop a solution with the breathers' energy primarily focused in 3 major chains. To express the approximate shape of breather in the small amplitude limit, an asymptotic approximation to the breathers is built by applying the method of multiple scales. The dispersion relation formed exhibits intriguing forms, i.e., -3 types of solution at certain wavenumbers. Numerical simulations of the lattices are conducted to verify the shape of breathers, and it is noticed that the breather persists for long times at a relatively larger natural frequency Ω0. When Ω0≫O(1), the breather may remain a relatively long-lived mode as we observe that the energy is slowly transferred from the centre of the lattice to the rest of sites with the wave propagating though the lattice.

Unidirectional energy transport in the symmetric system of non-linearly coupled oscillators and oscillatory chains

In the present paper, we study the fundamental mechanism of unidirectional energy transport in the symmetric, weakly dissipative system of two coupled nonlinear oscillators and weakly coupled oscillatory chains. We demonstrate that under particular choice of system parameters the model under consideration allows the irreversible transfer of energy from the initially excited oscillator to the initially resting one. In the second part of the paper, we implement the mechanism for control of spatially localized nonlinear waves (discrete breathers) in weakly dissipative, coupled oscillatory chains. This mechanism is implemented on the symmetric system of two weakly dissipative, non-linearly coupled oscillatory chains. Using the regular multi-scale asymptotic analysis, we derive the slow flow system. Further applying the method of collective coordinates on the slow flow system, we were able to describe analytically the mechanism of unidirectional inter-chain transport of static breathers. In general, the analytical method developed in the paper allows one to predict the special regions in the parametric space corresponding to the formation of the aforementioned regimes of irreversible energy transfer in the system of non-linearly coupled oscillators and oscillatory chains.

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame.

In this article we perform a thorough analysis of breathers in a one-dimensional model for a layered silicate for which there exists fossil and experimental evidence of moving excitations along the close-packed lines of the K^{+} layers. Some of these excitations are likely breathers with a small energy of about 0.2eV as the numerically obtained breathers described in the present model. Moving breathers as exact solutions of the dynamical equations are obtained at the price of being generically associated with a plane wave, a wing, with finite amplitude, although this amplitude can be very small. We call them pterobreathers. For some frequencies the wings disappear and the solutions become exact moving breathers with no wings, showing the phenomenon of supertransmission of energy. We perform a theoretical analysis of pterobreathers in systems with substrate potential and show that they are characterized by a single frequency in the moving frame plus the frequency of the wings. We have also studied high-energy stationary breathers which transform into single and double kinks and stable multibreathers with very strong localization.

Observation of Breathing Dark Pulses in Normal Dispersion Optical Microresonators.

Breathers are localized waves in nonlinear systems that undergo a periodic variation in time or space. The concept of breathers is useful for describing many nonlinear physical systems including granular lattices, Bose-Einstein condensates, hydrodynamics, plasmas, and optics. In optics, breathers can exist in either the anomalous or the normal dispersion regimes, but they have only been characterized in the former, to our knowledge. Here, externally pumped optical microresonators are used to characterize the breathing dynamics of localized waves in the normal dispersion regime. High-Q optical microresonators featuring normal dispersion can yield mode-locked Kerr combs whose time-domain waveform corresponds to circulating dark pulses in the cavity. We show that with relatively high pump power these Kerr combs can enter a breathing regime, in which the time-domain waveform remains a dark pulse but experiences a periodic modulation on a time scale much slower than the microresonator round trip time. The breathing is observed in the optical frequency domain as a significant difference in the phase and amplitude of the modulation experienced by different spectral lines. In the highly pumped regime, a transition to a chaotic breathing state where the waveform remains dark-pulse-like is also observed, for the first time to our knowledge; such a transition is reversible by reducing the pump power.