Two- and three-dimensional oscillons in nonlinear faraday resonance

We study 2D and 3D localized oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.     

Formation of parametric solitons in coupled atom–molecule quantum gases via controlled nonlinear interactions

We consider an atomic Bose–Einstein condensate parametrically coupled to a molecular condensate with tunable interactions. The space distribution and nonlinear dynamics of this coupled system, especially the parametric solitons, are investigated within the full parameter space accounts for all the nonlinear two-body collisions, together with the atom–molecule conversion coupling and the bare formation energy of the molecular species. The results show that the exact parametric solitons can be formed via controlled nonlinear interactions, and the atom–molecule transfer term can provide an effective potential which can be used to stable the coupled system even in the absence of the external potential. We also give an experimental setup and detection of the atomic–molecular Bose–Einstein condensates in future experiments.     

Parametric solitons

We develop a general framework for understanding the characteristics of multi-frequency (multi-colour) parametric solitons. We identify two special classes of such solitons: cascaded parametric solitons, where the optical energy is shared between several harmonically-related frequency bands; and isolated-bandwidth solitons, where all of the optical energy is localized within a single frequency band. As an example, we consider the case of a five-colour isolated-bandwidth parametric soliton in a Kerr medium.     

Squeezing Exchange and Entanglement between Resonantly Coupled Modes

We study the problem of squeezing exchange between two modes of the electromagnetic field modeled by quantum oscillators for the most general weak bilinear resonance coupling. Also we introduce a new measure of entanglement based on the cross covariances of the quadrature components of interacting modes. We compare the covariance measure with the measures based on the von Neumann and linear entropies of the subsystems, studying their dependences on time, coupling constants, and the initial state in the cases of parametric amplification and parametric conversion. In particular, we show that coherent states remain disentagled for all times and for any choice of coupling constants in the case of parametric converter (with accuracy up to second-order terms with respect to the strength of coupling). Also, we demonstrate that no bilinear coupling can squeeze the initial coherent state or improve the squeezing of the initial squeezed state in the case of a parametric amplifier. A strong sensitivity of the character of evolution to the choice of the set of coupling constants is discovered in the case of a parametric converter.     

Parametric solitons on Raman resonance and self-induced transparency in silica optical fibre

An analytical and numerical analysis of the dynamics of parametric solitons on Raman resonance is performed. The results of calculations describe an effect of self-induced transparency for parameteric solitons and the influence of the initial phase on Raman Stokes gain and anti-Stokes absorption. This can be used to maintain the process of energy transfer between pulses.     

Soliton multistability as a result of double-resonance wave mixing in chi((2)) media

We investigate analytically and numerically the existence and stability properties of three-wave solitons resulting from double-resonance (type I plus type II) parametric interaction in a purely quadratic nonlinear medium. The existence of a family of stable solitons for the double-resonance model is demonstrated in a broad parameter range. Moreover, these solitons are shown to exhibit multistability, a feature that is potentially useful for optical switching applications. Finally, we find and present a novel family of quasi solitons.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.     

Bright soliton dynamics in Fourier synthesized optical lattice

We consider the dynamics of bright solitons in one dimensional Bose Einstein condensate with spin orbit coupling and trapped by an optical lattice potential. We mainly focus on the effects of the spin orbit coupling, Rabi coupling and detuning parameter on the soliton dynamics. The solution of the coupled Gross Pitaevskii equation is performed with the help of the variational and numerical methods for various parameters. The population imbalance and the center of mass motion show different dynamic behaviors depending on the parameters. We also obtain traveling bright solitons related with a given finite initial momentum.     

Solitons and collapse suppression due to parametric interaction in bulk Kerr media

We demonstrate that weak parametric interaction of a fundamental beam with its harmonic field in a Kerr medium can drastically modify the beam dynamics, giving rise to very complex bifurcation phenomena and quasi solitons. Most importantly, we reveal a novel physical mechanism of the collapse suppression in a bulk optical Kerr medium: parametric coupling to a weakly radiating harmonic field.     

Splitting of coupled bright solitons in two-component Bose-Einstein condensates under parametric perturbation

We analyze the dynamics of bright-bright solitons in two-component Bose-Einstein condensates (BECs) subject to parametric perturbations using the variational approach and direct numerical simulations. The system is described by a vector nonlinear Schrödinger equation (NLSE) appropriate to coupled multi-component BECs. A periodic variation of the inter-component coupling coefficient is used to explore nonlinear resonances and splitting of the coupled bright solitons. The analytical predictions are confirmed by direct numerical simulations of the vector NLSE.     

Trapping of slowly moving or stationary two-color gap solitons

We address the important problem of excitation of gap solitons of a parametric nature, which are sustained in periodically corrugated frequency-doubling media near Bragg resonance with both the fundamental frequency and its second harmonic. We demonstrate that a zero-velocity soliton can be trapped in a finite Bragg structure by the quiescence of two counterpropagating moving solitons, which in turn might be formed by injection of appropriate light pulses at a single carrier frequency.     

The Effect of Electromagnetically Induced Transparency in Classical Systems

We develop a classical model of the recently popular parametric effect of electromagnetically induced transparency (EIT), i.e., the formation of a “transparency window” inside a resonance absorption line of a three-level quantum system, which is accompanied by a record strong slowing of the probe wave. Based on this model, we consider the EIT effect for electromagnetic waves at frequencies of the electron-cyclotron resonance in a cold plasma. The parametric (three-wave) interaction of two electromagnetic modes (the frequency of one of these modes is equal to the electron gyrofrequency) with the electrostatic mode is considered. It is shown that the resonance growth in the electron oscillations at the gyrofrequency can be damped due to the parametric coupling with the collective electrostatic oscillations. Similar to analogous quantum systems, the group slowing of the probe electron-cyclotron wave in the transparency window takes place in the case considered.     

Fully three dimensional breather solitons can be created using feshbach resonances

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover a new island of stability in the 3D case, not present in the quasi-2D treatment. Stable solutions from this region have non-trivial dynamics in the lattice direction; hence, they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose-Einstein condensate in a one-dimensional lattice. We point out other possible applications.     

Stability analysis of embedded solitons in the generalized third-order nonlinear Schrodinger equation

We study the generalized third-order nonlinear Schrodinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons.     

Gap solitons of spin-orbit-coupled Bose-Einstein condensates in $\mathcal{PT}$ periodic potential

We numerically investigate the gap solitons in Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in the parity-time ($\mathcal{PT}$)-symmetric periodic potential. We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap. The dynamics of these gap solitons are checked by the split-time-step Crank-Nicolson method. It is proved that the depths of the imaginary part of the $\mathcal{PT}$-symmetric periodic potential gradually increase, and the gap solitons become unstable. But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.     

简并光学参量振荡器的超混沌控制与周期态同步

针对简并光学参量振荡器的非线性动力学特点,应用互耦合参量调制法研究了两台简并光学参量振荡器之间的超混沌控制与周期态同步.理论研究结果表明,对于全同或不完全相同的简并光学参量振荡器均可实现从超混沌输出到周期输出的转化,当满足最大条件Lyapunov指数小于零时,两台全同简并光学参量振荡器之间可以实现两种方式的周期态精确同步,即同向同步和反向同步,同步方式与初始条件和调制系数有关.     

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons—intrinsically multi-component localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in diffractive and/or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classification and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary significance.     

半导体三量子点中的多透明窗口及弱光孤子的调控

考虑半导体量子点间隧穿耦合效应,研究非对称半导体三量子点分子中的弱探测光的传播特性。线性情况下,由于点间隧穿耦合和外部控制光的协同调控,探测光的吸收特性将出现共振吸收、隧穿诱导透明单窗口、隧穿诱导透明双窗口及隧穿诱导透明三窗口的转变。此外,从反常色散到正常色散的开关效应可通过改变隧穿强度及光学控制场强度来实现。对于非线性情况,发现孤子的振幅随着点间隧穿耦合系数增大呈先增大再减小随即再次增大并减小的波动变化趋势且出现最大振幅及其对应的点间隧穿耦合强度随着外部控制光场的增大而减小。此外,发现孤子的群速度随着耦合强度的增加呈逐渐减小的趋势。     

扩散效应对光伏孤子相互作用的影响

用数值方法研究扩散效应对两个平行传播相干光伏孤子光束相互作用的影响. 结果表明，在扩散效应的影响下，两相干孤子光束同相相互作用不是使它们相互融合, 而是使它们趋向相互分离，且光束之间存在能量耦合；异相孤子相互作用不再是简单地互相排斥，在一定的条件下，两光束既互相排斥，又同时向同侧偏转. 关键词： 光伏空间孤子 相干相互作用 扩散效应     

Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose-Einstein condensates(BECs) by a perturbation method.Starting with the one-dimensional Gross-Pitaevskii equations,we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spinorbit coupling.The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs.We find different types of moving solitons:dark-bright,bright-bright and dark-dark solitons.Interestingly,moving dark-dark soliton for attractive intra- and inter-species interactions is found,which depends on the Raman coupling.The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin-orbit coupling.