Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the
tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.     

超流费米气体中两维孤子的动力学

我们利用解析和数值的方法,研究从Bardeen-Cooper-Schrieffer(BCS)超流到玻色-爱因斯坦凝聚(BEC)渡越的过程里超流费米气体中两维(2D)孤子的形成和演化.基于超流流体力学方程,在准二维和长波近似下,推导描述弱非线性激发带正色散项的Kadomtsev-Petviashvili方程;给出整个BCS-BEC渡越的2D孤子解,以及数值求解孤子在囚禁势中的演化.数值结果显示由于Snake(横向)不稳定性,大振幅的暗孤子会衰变为大量涡旋-反涡旋对,并且这个不稳定性在不同超流区域不同.     

Scanning-tunneling microscope imaging of single-electron solitons in a material with incommensurate charge-density waves

We report on scanning-tunneling microscopy experiments in a charge-density wave (CDW) system allowing visually capturing and studying in detail the individual solitons corresponding to the self-trapping of just one electron. This "Amplitude Soliton" is marked by vanishing of the CDW amplitude and by the π shift of its phase. It might be the realization of the spinon--the long-sought particle (along with the holon) in the study of science of strongly correlated electronic systems. As a distinct feature we also observe one-dimensional Friedel oscillations superimposed on the CDW which develop independently of solitons.     

Exciting rogue waves,breathers, and solitons in coherent atomic media

We propose a scheme that excites rogue waves via electromagnetically induced transparency(EIT), which can also excite breathers and solitons. The system is a resonant Λ-type atomic ensemble. Under EIT conditions, the envelope equation of the probe field can be reduced to several different models, such as the saturable nonlinear Schr?dinger equation(SNLSE), and SNLSE with the trapping potential provided by a far-detuned laser field or a magnetic field. In this scheme, rogue waves can be generated by different initial pulses, such as the Gaussian wave with(or without) the uniform background. The scheme can be used to obtain rogue waves,breathers and solitons. We show the existence regions of rogue waves, breathers, and solitons as the function of the amplitude and width of the initial pulse. The novelty of our paper is that, we not only show rogue waves in the integrable system numerically, but also present the method to generate and control rogue waves in the non-integrable system.     

Self-trapping and Macroscopic Tunnelling of Superfluid Fermi Gases in Multi-well Potentials

We study the tunnelling dynamics of superfluid Fermi gases trapped in multi-well system along the BEC-BCS crossover. Within the hydrodynamical model and by using the multi-mode approximation, the self-trapping dynamics of superfluid Fermi gases in multi-well system are obtained numerically. We find that the self-trapping to diffusion transition strongly depends on the well number. When the well number is less than three, the self-trapped state takes place easier on the BEC side than that on the BCS side. However, when the well number is larger than three, the self-trapped state takes place easier on the BCS side instead of the BEC side. Furthermore, by considering a superfluid of ⁴⁰K atoms, we obtain the zero-mode and π-mode Josephson frequencies of coherent atomic oscillations in double-well system. It is noteworthy that the Josephson mode, especially, the existence of π-mode frequency strongly depends on the atoms number on the BCS side.     

Formation of fundamental solitons in the two-dimensional nonlinear Schrödinger equation with a lattice potential

We consider self-trapping of 2D solitons in the model based on theGross-Pitaevskii/nonlinear Schrödinger equation with the self-attractivecubic nonlinearity and a periodic potential of the optical-lattice (OL)type. It is known that this model may suppress the collapse, giving rise toa family of stable fundamental solitons. Here, we report essential dynamical featuresof self-trapping of the fundamental solitons from input configurations oftwo types, with vorticity 0 or 1. We identify regions in the respectiveparameter spaces corresponding to the formation of the soliton, collapse,and decay. A noteworthy result is the self-trapping of stable fundamentalsolitons in cases when the input norm essentially exceeds the collapsethreshold. We also compare predictions of the dynamical variationalapproximation with direct numerical simulations.     

Sine-Gordon Solitons and Breathers in Rod-like Magnetic Liquid Crystals under External Magnetic Field

To study the nonlinear phenomena in rod-like magnetic liquid crystals (RMLCs), this paper establishes the dynamic model of molecular motion when giving a twisting disturbance to the molecules under external magnetic field. We find the twist of the molecules under magnetic field can be propagated in the form of a traveling wave. The dynamic equation of the molecular twisting we derived satisfies the form of Sine-Gordon equation. We obtain two solutions of the Sine-Gordon equation by theoretical calculation: the kink and anti-kink solitons and breathers. The characteristics of those solitons and breathers are discussed.     

Observation of surface gap solitons in semi-infinite waveguide arrays

We report on the observation of surface gap solitons found to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity. We demonstrate strong self-trapping at the edge of a LiNbO3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.     

Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing

We study breathers and solitons on different backgrounds in optical fiber system, which is governed by generalized coupled Hirota equations with four wave mixing effect. On plane wave background, a transformation between different types of solitons is discovered. Then, on periodic wave background, we find breather-like nonlinear localized waves of which formation mechanism are related to the energy conversion between two components. The energy conversion results from four wave mixing. Furthermore, we prove that this energy conversion is controlled by amplitude and period of backgrounds. Finally, solitons on periodic wave background are also exhibited. These results would enrich our knowledge of nonlinear localized waves' excitation in coupled system with four wave mixing effect.     

Exact transverse solitary and periodic wave solutions in a coupled nonlinear inductor-capacitor network

Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equation are examined and the bifurcations of phase portraits of this equation for various values of the front wave velocity are presented. Using the sineGordon expansion method and classic integration, we obtain exact transverse solutions including breathers, bright solitons,and periodic solutions.     

Propagation of nonlocal optical solitons in lossy media with exponential-decay response

Propagation of optical solitons in lossy nonlocal media with exponential-decay response was investigated theoretically. The analytical solutions of nonlocal solitons and breathers are obtained by variational approach which is applied to a (1 + 1)D nonlocal nonlinear Schrödinger equation. The critical power of soliton and period of breathers are also obtained in the absence of the loss. When the loss is relatively small, the average beam width of breathers has a trend to expand during propagation. The analytical results are confirmed by numerical simulation.     

Emergence of linear wave segments and predictable traits in saturated nonlinear media

We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces.     

Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter γ₃ affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Transition,coexistence, and interaction of vector localized waves arising from higher-order effects

We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system.     

Novel localized wave solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Based on a special transformation that we introduce, the N-soliton solution of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular, by choosing appropriate parameters involved in the N-solitons, two interaction solutions mixed by a bell-shaped soliton and one breather or by a bell-shaped soliton and one lump are constructed from the 3-soliton solution. Five solutions including two breathers, two lumps, and interaction solutions between one breather and two bell-shaped solitons, one breather and one lump, or one lump and two bell-shaped solitons are constructed from the 4-soliton solution. Five interaction solutions mixed by one breather/lump and three bell-shaped solitons, two breathers/lumps and a bell-shaped soliton, as well as mixing with one lump, one breather and a bell-shaped soliton are constructed from the 5-soliton solution. To study the behaviors that the obtained interaction solutions may have, we present some illustrative numerical simulations, which demonstrate that the choice of the parameters has a great impacts on the types of the solutions and their propagation properties. The method proposed can be effectively used to construct localized interaction solutions of many nonlinear evolution equations. The results obtained may help related experts to understand and study the interaction phenomena of nonlinear localized waves during propagations.     

费米气体在光晶格中的自俘获现象及其周期调制

研究了一维光晶格中费米气体从BCS区过渡到unitarity区研究相图及周期调制现象. 通过调节散射长度与耠合系数对相图的影响, 发现在unitarity 区, 从约瑟夫振荡到振荡自俘获及振荡自俘获到自俘获, 存在耦合系数的临界值, 同时得到了临界耦合系数与散射长度的关系. 关键词： 费米气体 自俘获 周期调制     

On the generation of solitons and breathers in the modified Korteweg-de Vries equation

We consider the evolution of an initial disturbance described by the modified Korteweg-de Vries equation with a positive coefficient of the cubic nonlinear term, so that it can support solitons. Our primary aim is to determine the circumstances which can lead to the formation of solitons and/or breathers. We use the associated scattering problem and determine the discrete spectrum, where real eigenvalues describe solitons and complex eigenvalues describe breathers. For analytical convenience we consider various piecewise-constant initial conditions. We show how complex eigenvalues may be generated by bifurcation from either the real axis, or the imaginary axis; in the former case the bifurcation occurs as the unfolding of a double real eigenvalue. A bifurcation from the real axis describes the transition of a soliton pair with opposite polarities into a breather, while the bifurcation from the imaginary axis describes the generation of a breather from the continuous spectrum. Within the class of initial conditions we consider, a disturbance of one polarity, either positive or negative, will only generate solitons, and the number of solitons depends on the total mass. On the other hand, an initial disturbance with both polarities and very small mass will favor the generation of breathers, and the number of breathers then depends on the total energy. Direct numerical simulations of the modified Korteweg-de Vries equation confirms the analytical results, and show in detail the formation of solitons, breathers, and quasistationary coupled soliton pairs. Being based on spectral theory, our analytical results apply to the entire hierarchy of evolution equations connected with the same eigenvalue problem. (c) 2000 American Institute of Physics.