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.     

Rotary solitons in bessel optical lattices

We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, in addition to the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.     

Dynamics of narrow bright solitons in an array of attractive atoms in a Bose-Einstein condensate

We study the dynamics of a narrow bright soliton in a one-dimensional lattice of condensed attractive atoms when the soliton width is comparable to the lattice spacing. If a momentum is imprinted to a stationary state, the soliton can have oscillations around a site or it can undergo a random motion along the array. The motion is very sensitive to the atomic background distribution, and a thermal cloud or quantum field fluctuations can induce a random motion of the soliton.     

Beam evolutions of solitons in strongly nonlocal media with fading optical lattices

We address the impact of imprinted fading optical lattices on the beam evolution of solitons in strongly nonlocal nonlinear media. The results show that the width of the soliton experiences a change with the increasing propagation distance, the critical power for the soliton varies with the lattice fading away, and the soliton breathing is affected by the initial lattice depth and the nonlocality degree.     

A hierarchy of lattice soliton equations and its Darboux transformation

A new discrete spectral problem is introduced and the corresponding hierarchy of the lattice soliton equations are derived by means of the trace identity. We find a new Darboux transformation of the lattice soliton equation, through which the explicit solutions are shown.     

Soliton assisted control of source to drain electron transport along natural channels – crystallographic axes – in two-dimensional triangular crystal lattices

We present computational evidence of the possibility of fast, supersonic or subsonic,nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a formof electron surfing on acoustic waves) along crystallographic axes in two-dimensionalanharmonic crystal lattices. First we study the structural changes a soliton creates inthe lattice and the time lapse of recovery of the lattice. Then we study the behavior ofone electron in the polarization field of one and two solitons with crossing pathways withsuitably monitored delay. We show how an electron surfing on a lattice soliton may switchto surf on the second soliton and hence changing accordingly the direction of its path.Finally we discuss the possibility to control the way an excess electron proceeds from asource at a border of the lattice to a selected drain at another border by followingappropriate straight pathways on crystallographic axes.     

一类两维光学格子中稳定的复合孤子

对两维光学格子中非线性薛定谔方程一类新的稳态解做了数值分析，发现其在传播过程中逐渐衰变为一种稳定的复合孤子，孤子的两分量在传播过程中不断交换能量，总能量守恒. 关键词： 稳态解 两维格子 孤子     

Disorder-induced soliton transmission in nonlinear photonic lattices

We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.     

Elimination of transverse instability in stripe solitons by one-dimensional lattices

We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-dimensional photonic lattice under self-defocusing nonlinearity.     

Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

Soliton dragging by dynamic optical lattices

We report on the phenomenon of controllable soliton dragging by dynamic optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamic lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.     

Packing, unpacking, and steering of multicolor solitons in optical lattices

We discuss potential applications of multicolor solitons supported by periodic lattices imprinted in quadratic nonlinear media. Such lattice solitons can be packed together with appropriate relative phases to form stable soliton trains that can be treated as bit sequences. We describe controllable splitting of the trains into their soliton constituents and the angle- and power-controlled steering and trapping of solitons moving across the lattice into the desired guiding channel.     

Nonlinear phenomenology from quantum mechanics: soliton in a lattice

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.     

Surface defect kink solitons

We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domains and stability properties of defect solitons. Comparing with the uniform semi-infinite lattice, the instability of kink soliton in lattice with a negative defect is significantly suppressed, especially for in-phase soliton. Our results provide an effective way for the realization of stable in-phase kink solitons.     

Interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons (IBSs) and gap soliton trains (GSTs), in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the $\pi$-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The `negative refraction' effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

Dispersionless envelope lattice solitons on a D-dimensional nonlinear lattice

We show by using the real exponential approach that the d-dimensional discrete nonlinear Schrödinger equation has more general dispersionless envelope lattice soliton solutions than the known bright soliton and kink solutions. Depending on the values of the parameters, the new solutions can describe both bright and dark lattice solitons. Especially, we find novel “W”-like envelope lattice solitons.     

Photorefractive solitons embedded in gratings in centrosymmetric crystals

We investigate (1+1D) spatial optical solitons embedded in a fixed-volume grating in centrosymmetric photorefractive crystals. We numerically identify a two-parameter soliton family and deduce both its existence surface and soliton profiles. For shallow gratings, the soliton Fourier spectrum exhibits three lobes located at the reciprocal lattice points -K, 0, and K. Soliton trapping is a consequence of both the self-induced nonlinear waveguide and the grating reflectivity, which prevents the breakaway of the lateral components. To provide a preliminary evaluation of soliton stability, we also investigate the propagation of slightly perturbed soliton profiles.     

Particle structure analysis of soliton sectors in massive lattice field theories

We discuss the particle structure in the soliton sectors of massive lattice field theories by means of convergent cluster expansions. In several models we prove that the soliton field operator with lowest charge couples the vacuum to a stable one-particle state, in a suitable region of the coupling parameter space. Both local and stringlike solitons are analyzed. We also show that the mass of the local soliton equals the surface tension.     

Observation of in-band lattice solitons

We report the first experimental and theoretical demonstrations of in-band (or embedded) lattice solitons. Such solitons appear in trains, and their propagation constants reside inside the first Bloch band of a square lattice, different from all previously observed solitons. We show that these solitons bifurcate from Bloch modes at the interior high-symmetry X points within the first band, where normal and anomalous diffractions coexist along two orthogonal directions. At high powers, the in-band soliton can move into the first band gap and turn into a gap soliton.     

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.