Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

Matter-wave solitons in the presence of collisional inhomogeneities: Perturbation theory and the impact of derivative terms

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.     

Quantum reflection of bright matter-wave solitons

We propose the use of bright matter-wave solitons formed from Bose-Einstein condensates with attractive interactions to probe and study quantum reflection from a solid surface at normal incidence. We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical modelling shows that the robust, self-trapped nature of bright solitons leads to a clean reflection from the surface, limiting the disruption of the density profile and permitting accurate measurements of the reflection probability.     

Matter-wave interference in Bose-Einstein condensates: A dispersive hydrodynamic perspective

The interference pattern generated by the merging interaction of two Bose-Einstein condensates reveals the coherent, quantum wave nature of matter. An asymptotic analysis of the nonlinear Schrödinger equation in the small dispersion (semiclassical) limit, experimental results, and three-dimensional numerical simulations show that this interference pattern can be interpreted as a modulated soliton train generated by the interaction of two rarefaction waves propagating through the vacuum. The soliton train is shown to emerge from a linear, trigonometric interference pattern and is found by use of the Whitham modulation theory for nonlinear waves. This dispersive hydrodynamic perspective offers a new viewpoint on the mechanism driving matter-wave interference.     

Motion of a Bose-Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose-Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross-Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potentiaI in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.     

Multiplex velocity selection for precision matter-wave interferometry

We describe a novel velocity-selection technique for measuring dispersive phase shifts in matter-wave interferometers. Where conventional velocity-selection techniques simply reduce the width of the initial velocity distribution, here, the velocity distribution is chopped into a series of narrow peaks such that the velocity dependence of the phase shifts will result in a rephasing of the interference for certain strengths of applied potential. This technique overcomes limitations due to wide and poorly known velocity distributions and thus allows a better determination of the applied interaction with complete independence from the initial velocity distribution of the beam.Dedicated to H. Walther on the occasion of his 60th birthday     

Slowly moving matter-wave gap soliton propagation in weak random optical lattices

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the effective-particle theory, the effects of the randomness on gap solitons are obtained and the trajectories of gap solitons are well predicted. Moreover, the general laws that describe the movement depending on the weak randomness are obtained. We find that with an increase of the random strength, the ensemble-average velocity reduces slowly and the reflection probability becomes larger. The theoretical results based on the effective-particle theory are confirmed by the numerical simulations based on the Gross-Pitaevskii equation.     

Matter-wave bright solitons: Internal atomic recombination and external feeding

We consider matter-wave bright solitons in the presence of three-body atomic recombination, an axial periodic modulation and a feeding term, and use a variational method to derive conditions to have dynamically stabilized solitons due to compensation between the dissipation and alimentation of atoms from external sources. We critically examine how the BEC soliton is affected by the imbalance between the internal atom loss and external feeding. We pay special attention to study the influence of these terms on the soliton dynamics in optical lattice potentials that cause periodic modulation.     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.     

Friction and diffusion of matter-wave bright solitons

We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.     

Nonautonomous solitons of Bose-Einstein condensation in a linear potential with an arbitrary time-dependence

In the presence of a linear potential with an arbitrary time-dependence, Hirota method is developed carefully for applying into the effective mean-field model of quasi-one-dimensional Bose-Einstein condensation with repulsive interaction. We obtain the exact nonautonomous soliton solution (NSS) analytically. These solutions show that the time-dependent potential can affect the velocity of NSS. In some special cases the velocity has the character of both increase and oscillation with time. A detail analysis for the asymptotic behaviour of solutions shows that the collision of two NSSs is elastic.     

Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Dynamics of kicked matter-wave solitons in an optical lattice

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.     

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.     

Controlled Manipulation with a Bose--Einstein Condensates N-Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

A model of the perturbed complex Toda chain （PCTC） to describe the dynamics of a Bose-Einstein condensate （BEC） N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.     

Exact transmission state of a Bose-Einstein condensate in a near-harmonic trap

We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution.     

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.     

Matter wave soliton collisions in the quasi one-dimensional potential

We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi 1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find criterion for possible collapse. This information is then used to investigate the dynamics of the two soliton collision. In this dynamics we identify three regimes according to the relation between nonlinear interaction and the excitation energy: elastic collision, excitation and collapse regime. We show that surprisingly accurate predictions can be obtained from variational analysis.     

Hidden features of the soliton adaptation law to external potentials: Optical and matter-wave 3D nonautonomous soliton bullets

We show that the law of the soliton adaptation to varying-in-time external potentials indicates conclusively the way for solitonlike bullets generation in three-dimensional nonautonomous nonlinear and dispersive systems. It turns out that the generation of matter-wave soliton bullets can be realized if periodic variations of non-linearity and confining sign-reversal varying-in-time harmonic oscillator potential are opposite in phases so that peaks of nonlinearity inside the atomic cloud coincide in time with repulsive character of trapping potential during reversal periodic transformations from cigar-shaped to ball-shaped trapping structures. In nonlinear optical applications, periodic graded-index nonlinear structures with alternating waveguiding and antiwaveguiding segments can be used to simulate complicated processes of matter-wave soliton bullets generation.