Soliton Physics Research Articles

Topologically-mediated energy release by relativistic antiferromagnetic solitons

Magnetic solitons offer functionalities as information carriers in multiple spintronic and magnonic applications. However, their potential for nanoscale energy transport has not been revealed. Here we demonstrate that antiferromagnetic solitons, e.g. domain walls, can uptake, transport and release energy. The key for this functionality resides in their relativistic kinematics; their self-energy increases with velocity due to Lorentz contraction of the soliton and their dynamics can be accelerated up to the effective speed of light of the magnetic medium. Furthermore, their classification in robust topological classes allows to selectively release this energy back into the medium by colliding solitons with opposite topology. Our work uncovers important energy-related aspects of the physics of antiferromagnetic solitons and opens up the attractive possibility for spin-based nanoscale and ultra-fast energy transport devices.

Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities

• The existence, property and stability of one-dimensional gap solitons and soliton clusters in periodic nonlinear media with competing cubic-quintic nonlinearities are theoretical studied. • The linear-stability analysis and direct perturbed calculations are adopted to identify the stability and instability of the corresponding dark gap modes. • The model can find its realization in periodic optical media with cubic-quintic nonlinear nonlinearities and in Bose-Einstein condensates trapped by an optical lattice. Solitons are nonlinear self-sustained wave excitations and probably among the most interesting and exciting emergent nonlinear phenomenon in the corresponding theoretical settings. Bright solitons with sharp peak and dark solitons with central notch have been well known and observed in various nonlinear systems . The interplay of periodic potentials, like photonic crystals and lattices in optics and optical lattices in ultracold atoms, with the dispersion has brought about gap solitons within the finite band gaps of the underlying linear Bloch-wave spectrum and, particularly, the bright gap solitons have been experimentally observed in these nonlinear periodic systems, while little is known about the underlying physics of dark gap solitons. Here, we theoretically and numerically investigate the existence, property and stability of one-dimensional matter-wave gap solitons and soliton clusters of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearity, the higher-order of which is self-defocusing and the lower-order (cubic) one is chosen as self-defocusing or focusing nonlinearities. By means of the conventional linear-stability analysis and direct numerical calculations with initial perturbations, we identify the stability and instability areas of the corresponding dark gap solitons and clusters ones.

Chiral Helimagnetism and One-Dimensional Magnetic Solitons in a Cr-Intercalated Transition Metal Dichalcogenide.

Chiral magnets endowed with topological spin textures are expected to have promising applications in next-generation magnetic memories. In contrast to the well-studied 2D or 3D magnetic skyrmions, the authors report the discovery of 1D nontrivial magnetic solitons in a transition metal dichalcogenide 2H-TaS2 via precise intercalation of Cr elements. In the synthetic Cr1/3 TaS2 (CTS) single crystal, the coupling of the strong spin-orbit interaction from TaS2 and the chiral arrangement of the magnetic Cr ions evoke a robust Dzyaloshinskii-Moriya interaction. A magnetic helix having a short spatial period of ≈25nm is observed in CTS via Lorentz transmission electron microscopy. In a magnetic field perpendicular to the helical axis, the helical spin structure transforms into a chiral soliton lattice (CSL) with the spin structure evolution being consistent with the chiral sine-Gordon theory, which opens promising perspectives for the application of CSL to fast-speed nonvolatile magnetic memories. This work introduces a new paradigm to soliton physics and provides an effective strategy for seeking novel 2D magnets.

Cage Solitons

The theoretical framework of the Haus master equation of passive mode-locking is revisited. Reformulating the equation in the frequency domain as coupled ordinary differential equations, the complete set of fundamental soliton solutions is surveyed. For large values of anomalous dispersion, this leads to the well known bell-shaped solutions originally found by inverse scattering. Closer to zero dispersion, mode-locked spectra are affected by the available gain bandwidth, and solitons with Bessel-like temporal profiles are found. These spectrally caged solitons match previously unexplained pulse characterization measurements of few-cycle oscillators and mode-locked fiber lasers in the normal dispersion regime. Moreover, the frequency domain formalism suggests that a phase lock between the modes can even be established in the absence of saturable absorption. This finding may explain numerous mysterious experimental reports of mode-locking or comb formation in passive microring resonators and semiconductor lasers. Therefore our frequency-domain approach sheds new light into soliton physics from a completely different perspective.

Elliptically-Polarized Soliton Self-Frequency Shift in Isotropic Optical Fiber

Solitons are prevalent in various nonlinear physical systems. Optical solitons in optical fibers are exceptionally intriguing due to the multitude of both linear and nonlinear optical effects that are involved during their propagation. Here we demonstrate elliptically-polarized soliton self-frequency shift (SSFS) in a novel isotropic fiber, photonic-crystal (PC) rod. We combine three methodologies, i.e., experimental, numerical, and analytical, to elucidate the fundamental aspects of this novel physical process. Our results show that wavelength-shifted, elliptically-polarized solitons can be generated through the elliptically-polarized SSFS in PC rod. Our research sheds new light on the soliton physics.

The origin of spin wave pulse-induced domain wall inertia

The fundamental problem of domain wall (DW) inertia—the property that gives to inertial behaviors remains unclear in the physics of magnetic solitons. To understand its nature as well as to achieve accurate DW positioning and efficient manipulation of domain wall motion (DWM), spin wave (SW) pulse-induced DW transient effect is studied both numerically and theoretically in a magnetic nanostrip. It is shown for the first time that there occurs inevitable deceleration/automotion after SW pulse, which indicates nonzero DW inertia. The induced DWM is revealed to relate to two factors: energy storing within DW and out-of-plane tilting of DW. To explain the DWM dynamics, a one-dimensional collective model is developed to account for the excitation of spin wave pulse. The model successfully bridges DW energy, DW tilting and DW displacement and provides descriptions in accordance with numerical findings. It is made clear that the DW automotion hence DW inertia originate from the process of DW relaxation toward equilibrium. The DW inertia is expressed in terms of effective mass and turns out to be a time-dependent function with damping constant α as the governing parameter, which opposes the nature of intrinsic mass. For case containing multiple DWs, the total effective mass is shown to concern the reached velocity and stored energy of DWs instead of the number of DWs, which is against common intuition.

Dynamics of Many-Body Photon Bound States in Chiral Waveguide QED

We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through a system of $N$ two-level systems chirally coupled to a waveguide. We show that the system supports correlated multi-photon bound states, which have a well-defined photon number $n$ and propagate through the system with a group delay scaling as $1/n^2$. This has the interesting consequence that, during propagation, an incident coherent state pulse breaks up into different bound state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of $n$-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. For longer systems, however, the solitons break apart through quantum correlated dynamics. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.

3D analytical model of skyrmion-like structures in an antiferromagnet with DMI

The purpose of the research is the construction of the analytical model for description of a number of topological objects in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) including vortices, antivortices, skyrmions, antiskyrmions, skyrmioniums and their bound states, which are the exact dynamic solutions of the nonlinear Landau-Lifshitz equations. “Relativistic contraction” of skyrmion-like topological object size in the direction of motion is demonstrated for “subcritical” case when its velocity is less than spin wave velocity in antiferromagnet. Lorentz-like “supercritical” transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet. In particular, the results of the analytical model are applied for an antiferromagnet in the form of cylindrical nanoshell; in this case, there are more than one solution of the nonlinear Landau-Lifshitz equations for the same boundary and initial conditions. It means that vortices, skyrmions, skyrmioniums and their bound states represent the ground state and the excited states in an antiferromagnetic cylindrical nanoshell. The particular cases of the exact static solutions of the nonlinear Landau-Lifshitz equations include the well-known one-dimensional solutions such as Bloch domain, Neel domain wall, Shirobokov domain structure, antiferromagnetic vortices, two-dimensional Belavin-Polyakov soliton, three-dimensional Hodenkov soliton and target type soliton. The results of this paper can be used for further development of theory of the antiferromagnetic soliton and skyrmion physics. Besides, the exact dynamic solutions of the nonlinear Landau-Lifshitz equations can serve as the reference solutions for testing the results of micromagnetic simulations.

Solitons supported by intensity-dependent dispersion.

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion.

Magnetic stripe soliton and localized stripe wave in spin-1 Bose-Einstein condensates

The recent experimental realization of spin-orbit coupling for ultracold atomic gases opens a new avenue for engineering solitons with internal spatial structures through tuning atomic band dispersions. However, the types of the resulting stripe solitons in a spin-1/2 Bose-Einstein condensate (BEC) have been limited to dark-dark or bright-bright with the same density profiles for different spins. Here we propose that general types of stripe solitons, including magnetic stripe (e.g., dark-bright) and localized stripe waves (neither bright nor dark), could be realized in a spin-1 BEC with widely tunable band dispersions through modulating the coupling between three spin states and the linear momentum of atoms. \ Surprisingly, a moving magnetic stripe soliton can possess both negative and positive effective masses at different velocities, leading to a zero mass soliton at certain velocity. Our work showcases the great potential of realizing novel types of solitons through band dispersion engineering, which may provide a new approach for exploring soliton physics in many physical branches.

Imaging soliton dynamics in optical microcavities

Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for the study of nonlinear optical physics with practical implications for miniaturization of time standards, spectroscopy tools, and frequency metrology systems. However, despite its importance to the understanding of soliton physics, as well as development of new applications, imaging the rich dynamical behavior of solitons in microcavities has not been possible. These phenomena require a difficult combination of high-temporal-resolution and long-record-length in order to capture the evolving trajectories of closely spaced microcavity solitons. Here, an imaging method is demonstrated that visualizes soliton motion with sub-picosecond resolution over arbitrary time spans. A wide range of complex soliton transient behavior are characterized in the temporal or spectral domain, including soliton formation, collisions, spectral breathing, and soliton decay. This method can serve as a visualization tool for developing new soliton applications and understanding complex soliton physics in microcavities.

Sine-Gordon soliton as a model for Hawking radiation of moving black holes and quantum soliton evaporation

The intriguing connection between black holes’ evaporation and physics of solitons is opening novel roads to finding observable phenomena. It is known from the inverse scattering transform that velocity is a fundamental parameter in solitons theory. Taking this into account, the study of Hawking radiation by a moving soliton gets a growing relevance. However, a theoretical context for the description of this phenomenon is still lacking. Here, we adopt a soliton geometrization technique to study the quantum emission of a moving soliton in a one-dimensional model. Representing a black hole by the one soliton solution of the Sine-Gordon equation, we consider Hawking emission spectra of a quantized massless scalar field on the soliton-induced metric. We study the relation between the soliton velocity and the black hole temperature. Our results address a new scenario in the detection of new physics in the quantum gravity panorama.

Analysis and design of fibers for pure-quartic solitons

The recently discovered pure-quartic solitons, arising from the interaction of quartic dispersion and Kerr nonlinearity, open the door to unexplored soliton regimes and ultrafast laser science. Here, we report a general analysis of the dispersion and nonlinear properties necessary to observe pure-quartic solitons in optical platforms. We apply this analysis, in combination with numerical calculations, to the design of pure-quartic soliton supporting microstructured optical fibers. The designs presented here, which have realistic fabrication tolerances, support unperturbed pure-quartic soliton propagation providing access to an unmatched platform to study novel soliton physics.

Nonlinear Fourier Methods for Ocean Waves

Multiperiodic Fourier series solutions of integrable nonlinear wave equations are applied to the study of ocean waves for scientific and engineering purposes. These series can be used to compute analytical formulae for the stochastic properties of nonlinear equations, in analogy to the standard approach for linear equations. Here I emphasize analytically computable results for the correlation functions, power spectra and coherence functions of a nonlinear random process associated with an integrable nonlinear wave equation. The multiperiodic Fourier series have the advantage that the coherent structures of soliton physics are encoded in the formulation, so that solitons, breathers, vortices, etc. are contained in the temporal evolution of the nonlinear power spectrum and phases. I illustrate the method for the Korteweg-deVries and nonlinear SchrÖdinger equations. Applications of the method to the analysis of data are discussed.

Intermode Breather Solitons in Optical Microresonators

The observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Gauge fields and related forces in antiferromagnetic soliton physics

We derive equations of motion for topological solitons in antiferromagnets under the combined action of perturbations such as an external magnetic field and torque-generating electrical current. Aside from conservative forces, such perturbations generate an effective "magnetic field" exerting a gyrotropic force on the soliton and an induced "electric field" if the perturbation is time-dependent. We apply the general formalism to the cases of a domain wall and of a vortex. An antiferromagnetic vortex can be effectively moved by combined applications of a magnetic field and an electric current.

Superresonant Radiation Stimulated by Higher Harmonics.

Solitons propagating in media with higher-order dispersion will shed radiation known as resonant radiation, with applications in frequency broadening, deep UV sources for spectroscopy, and fundamental studies of soliton physics. Using a recently proposed equation that models the behavior of ultrashort optical pulses in nonlinear media using the analytic signal, we find that the resonant radiation associated with the third-harmonic generation term of the equation is parametrically stimulated with an unprecedented gain. Resonant radiation levels, typically only a small fraction of the soliton, are now as intense as the soliton itself. The mechanism is universal and works also in normal dispersion and with harmonics higher than the third. We report experimental hints of this superresonant radiation stimulated by the fifth harmonic in diamond.

Symbolic computation and abundant travelling wave solutions to KdV–mKdV equation

In this article, the novel (G ′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Soliton physics with semiconductor exciton–polaritons in confined systems

In the past decade, there has been a significant progress in the study of non-linear polariton phenomena in semiconductor microcavities. One of the key features of non-linear systems is the emergence of solitons. The complexity and the inherently strong nonlinearity of the polariton system made it a perfect sandpit for observing solitonic effects in half-light half-matter environment. This review focuses on the theory and the latest experimental elucidating physics as well as potential applications of conservative and dissipative solitons in exciton–polariton systems.

New travelling wave solutions of the (1 + 1)-dimensional cubic nonlinear Schrodinger equation using novel (G′/G)-expansion method

In this paper, the novel (G′/G)-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.