Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

Effect of a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method,we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates.It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity,while at the position of the localized impurity the soliton can be quasitrapped by the impurity.Additionally,we find that the strength of the localized impurity has an important effect on the dark soliton dynamics.With increasing strength of the localized impurity,the amplitude of the dark soliton becomes bigger,while its width is narrower,and the soliton propagates slower.     

Interaction of a nuclear spin with a soliton gas

We investigate the dynamics of a nuclear spin which is weakly coupled to a one-dimensional, thermalized, low-density gas of sine-Gordon solitons. Longitudinal (T₁) and transverse (T₂) relaxation times and the dynamic frequency shift are computed.     

Effect of the dark soliton crystal temperature on the deflection of the bright soliton in a separate bright–dark screening soliton pair

We investigate theoretically the dark soliton crystal temperature effect on the deflection of the bright one in a bright–dark soliton pair which is formed in a serial non-photovoltaic photorefractive crystal circuit. Our numerical results show that the spatial shift of the bright soliton changes with the temperature of the dark one crystal and varying the temperature of the dark soliton crystal can influence the deflection strongly. The temperature dependence of the deflection process is further studied by perturbation technique and the results are found to be good agreement with that obtained by numerical method. Relevant examples are provided.     

Interaction of an optical soliton with a dispersive wave

Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching conditions.     

Propagation of a dark soliton in a disordered Bose-Einstein condensate

We consider the propagation of a dark soliton in a quasi-1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well-defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.     

Quantum reflection of a Bose-Einstein condensate with a dark soliton from a step potential

We study dynamical behaviors of a Bose-Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability R_s. Variation of the reflection probability with respect to the orientation angle θ of the dark soliton can be well described by a cosine function R_s~cos[λ(θ-π/2)], where λ is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitive width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.     

Trapping a dark soliton pulse within a nano ring resonator

We propose the interesting results that a dark soliton pulse can be localized within a nonlinear nano-waveguide. The system consists of nonlinear micro and nano ring resonators, whereas the dark soliton can be input into the system and trapped within the nano-waveguide. A dark soliton pulse is input into a ring resonator and chopped to be the smaller pulses. The required pulse is filtered and amplified, which can be controlled and localized within the nano-waveguide. The localized bright soliton is also reviewed and discussed.     

Effect of dark soliton on the spectral evolution of bright soliton in a silicon-on-insulator waveguide

The spectral evolution of bright soliton in a silicon-on-insulator optical waveguide is numerically simulated using the split-step Fourier method. The power and input chirp of the dark soliton and the second-order dispersion are varied to investigate the effect of dark soliton on the spectrum of bright soliton. The simulations prove that the dark soliton modifies the spectral shape of the bright soliton. Further, the variation in the power of dark soliton affects the splitting of bright soliton. Furthermore, the chirped dark soliton can improve the spectral width and flatness. The variation in the dispersion of dark soliton modifies the phase matching of the bright soliton and the dispersive wave emission, thereby affecting the spectral evolution.     

Parallel guiding of signal beams by a ring dark soliton

Guiding of multiple signal beams in an induced all-optical cable is studied theoretically. A balance relation is derived for the interaction geometry and undistorted propagation of bright elliptical signal beams nested in a single ring dark soliton. The numerical analyses show a remarkable misalignment stability of the parallel guiding scheme.     

Analysis of dark soliton generation in the microcavity with mode-interaction

Mode-interaction plays an important role in the dark soliton generation in the microcavity. It is beneficial to the excitation of dark solitons, but also facilitates a variety of dark soliton states. Based on the non-normalized Lugiato-Lefever equation, the evolution of dark soliton in the microcavity with mode-interaction is investigated. By means of mode-interaction, the initial continuous wave(CW) field evolves into a dark soliton gradually, and the spectrum expands from a single mode to a broadband comb. After changing the mode-interaction parameters, the original modes which result in dual circular dark solitons inside the microcavity, are separated from the resonant mode by 2 free spectral ranges(FSR). When the initial field is another feasible pattern of weak white Gaussian noise, the large frequency detuning leads to the amplification of the optical power in the microcavity, and the mode-interaction becomes stronger. Then, multiple dark solitons, which correspond to the spectra with multi-FSR, can be excited by selecting appropriate mode-interaction parameters. In addition, by turning the mode-interaction parameters, the dark soliton number can be regulated, and the comb tooth interval in the spectrum also changes accordingly. Theoretical analysis results are significant for studying the dark soliton in the microcavity with mode-interaction.     

Other incarnations of the Gross-Pitaevskii dark soliton

We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. As a consequence of this, the GPE soliton gets related to the magnetic soliton in an easy-plane ferromagnet, where it describes the square of the in-plane magnetization of the system. These relationships are shown to be useful in understanding various characteristics of solitons in these distinct many-body systems.     

Interaction of a moving dipole with a soliton in the KdV equation

The Korteweg-de Vries equation with the perturbing term εδ'(x −Vt) (a point-like dipole), which models disturbances produced by a small body moving in a liquid layer, is considered. In the case V<0, when the moving dipole emits a quasi-linear monochromatic wave, perturbation of the emission spectrum due to collision of the dipole with a free soliton is investigated. It is demonstrated that prior to the collision (at ft → − ∞) the resultant spectrum's width is exponentially small in ∣t∣, while after the collision (at t → + ∞) the width is ∾t⁻¹. Then it is demonstrated that in the case V>0 (a non-emitting dipole) a soliton may be pinned by the moving dipole. In the adiabatic approximation, the pinned state is stable provided ε < 0. In this case a pair of solitons may also be pinned by the dipole, but that pinned state is unstable. Other types of solitary pinned profiles and their stability are discussed. Oscillations of a soliton near the adiabatically stable pinned state are accompanied by emission of quasi-linear waves. The emission intensity is calculated in a general form, and it is demonstrated that the oscillation are subject to radiative instability due to the fact that the energy of the system is not positive definite. The same model is considered with the Bürgers' dissipative term. The dissipation may compensate the radiative instability and render the pinned state of a soliton completely stable. Besides, it is demonstrated that the Bürgers' term gives rise to multisoliton pinned profiles. A maximum possible number of solitons in the profile is found.     

Nonautonomous dark soliton solutions in two-component Bose–Einstein condensates with a linear time-dependent potential

We report the analytical nonantonomous soliton solutions （NSSs） for two-component Bose-Einstein condensates with the presence of a time-dependent potential. These solutions show that the time-dependent potential can affect the velocity of NSS. The velocity shows the characteristic of both increasing and oscillation with time. A detailed analysis for the asymptotic behavior of NSSs demonstrates that the collision of two NSSs of each component is elastic.     

Vortex interaction and the two-dimensional dark soliton

We study vortex interaction and a two-dimensional dark soliton in the two-dimensional Gross-Pitaevskii equation. A vortex-antivortex pair propagates with a constant velocity when the initial distance is large. But complicated behaviors appear when the initial distance of two vortices becomes smaller. If the initial distance is sufficiently small, a two-dimensional dark solution is created as a result of the pair annihilation. The two-dimensional dark soliton has an anisotropic structure and propagates in a certain direction. The two-dimensional dark soliton is stable against head-on collision.     

Linear response function around a localized impurity in a superconductor

Imaging the effects of an impurity like Zn in high-T_c superconductors [Nature 61 (2000) 746] has rekindled interest in defect problems in the superconducting phase. This has prompted us here to re-examine the early work of March and Murray [Phys. Rev. 120 (1960) 830] on the linear response function in an initially translationally invariant Fermi gas. In particular, we present corresponding results for a superconductor at zero temperature, both in the s- and in the d-wave case, and mention their direct physical relevance in the case when the impurity potential is highly localized.     

Complete and orthonormal eigenfunctions of excitations to a one-dimensional dark soliton

We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose-Einstein condensates.     

凝聚体中亮孤子和暗孤子的交替演化

利用Darboux变换法，解析地研究了局限于恒定不变外部势阱中的玻色-爱因斯坦凝聚体的非线性动力学性质.结果发现凝聚体中的粒子之间的相互作用强度对其非线性动力学特征有重要的影响.当玻色子之间的相互排斥作用相当强时，凝聚体中只会存在亮孤子；而玻色子之间的相互排斥作用相当弱(小于临界值)时，凝聚体中会出现亮孤子和暗孤子交替演化. 关键词： 玻色-爱因斯坦凝聚 Darboux变换 孤子     

Spatiotemporal evolution of continuous-wave field and dark soliton formation in a microcavity with normal dispersion

Stable dark soliton and dark pulse formation in normally dispersive and red-detuned microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation. The soliton essence is proved by fitting the calculated field intensity profile with the analytical formula of a dark soliton. Meanwhile, we find that a dark soliton can be generated either from the nonlinear evolution of an optical shock wave or narrowing of a locally broad dark pulse with smoother fronts. Explicit analytical expression is obtained to describe the oscillatory fronts of the optical shock wave. Furthermore,from the calculation results, we show that for smaller frequency detunings, e.g., α 3, in addition to the dark soliton formation, a single dark pulse with an oscillatory dip can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination. The existence region together with various field intensity profiles and the corresponding spectra of single dark pulse are demonstrated.     

Multitweezers generation using dark soliton pulses and applications

Multi-dark soliton pulses have been successfully generated by using forward and backward pumping of the S-band erbium doped fiber in the fiber optic loop, where the Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between pump fields with Stokes field through acoustic wave. Results obtained have shown that the dark soliton trains can be generated and configured as the multi-optical tweezers. The advantage is that the generated tweezers are in the form of dynamic tweezers, where they can transmit/transport via the soliton communication link. The single dark soliton is also experimentally generated by using the different fiber optic scheme. We have also theoretically shown that the dynamic tweezers can be controlled and tuned, which is available for trapping and transportation in the communication link via a wavelength router. The quantum states of the transported atoms/molecules by the dynamic tweezers can be performed by using the quantum processing unit incorporating in the system.