Pairing of solitons in two-dimensional S=1 magnets

We study a general model of isotropic two-dimensional spin-1 magnet, which is relevant for the physics of ultracold atoms with hyperfine S=1 spins in an optical lattice at odd filling. We demonstrate a novel mechanism of soliton pairing occurring in the vicinity of a special point with an enhanced SU(3) symmetry: upon perturbing the SU(3) symmetry, solitons with odd CP2 topological charge are confined into pairs that remain stable objects.     

Ground states, solitons and spin textures in spin-1 Bose-Einstein condensates

We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.     

Vector valley Hall edge solitons in the photonic lattice with type-II Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics. They maintain their profiles during propagation, due to the joint action of lattice potential and nonlinearity, and at the same time are immune to defects or disorders, thanks to the topological protection. In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays, in which the time-reversal symmetry is effectively broken. Very recently, topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved. However, these were scalar solitary structures. Here, for the first time, we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones, which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice. This comes about because the valley Hall edge state can possess both negative and positive dispersions, which allows the mixing of two different edge states into a vector soliton. Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime, but also enlighten relevant research based on the lattices with type-II Dirac cones.     

Polarization vortex spatial optical solitons in Bessel optical lattices

We investigate the formation of polarization vortex spatial optical solitons in optical lattice induced by a non-diffracting Bessel beam. The properties of these solitons in zeroth-order and first-order Bessel lattices with focusing and defocusing Kerr nonlinearity are discussed. It is found that these solitons have some analogies with phase vortex solitons carrying single positive or negative topological charge in these lattices. Besides, these polarization vortex solitons have complicated dynamical characteristic and can be stabilized in some parameter region.     

The indecomposable representation of SO0(2, 2) on the one-particle space of the massless field in 1 + 1 dimension

In the continuum O(3) sigma model in two spatial dimensions, there are topological solitons whose size can be stabilized by adding Skyrme and potential terms. This Letter describes a lattice version, namely a natural way of modifying the 2D Heisenberg model to achieve topological stability on the lattice.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Dark-bright discrete solitons: A numerical study of existence, stability and dynamics

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed.     

Surface solitons supported by one-dimensional composite Bessel optical lattices

We address the existence of surface solitons at an interface in a defocusing cubic medium with an imprinted one-dimensional （1D） composite Bessel optical lattice. This setting is composed of two Bessel lattices with different orders and different modulation depths, separated beside both sides of an interface. Stability analysis and numerical propagation simulations prove that solitons supported by the model are dynamically stable in the entire domain of their existence. The order of lattice determines the shape of soliton, and the amplitude of soliton depends on the lattice modulation depth. The experimental realization of the scheme is also proposed. Our results may provide another effective way of controlling the shapes of surface solitons and thus their evolutions by introducing a new freedom degree.     

Topological solitons in active optical cavities: Fundamental properties and possible applications

Fundamental properties of topological spatial solitons existing in active cavities with high (above 100) Fresnel numbers, laser and/or parametric amplification, and saturated absorber were numerically and experimentally studied. Writing and erasing of bi- and tristable laser solitons (fundamental solitons [1, 2] and vortex solitons [3]) using an external control light pulse were considered in various regions of the laser cross section. The existence of optical domain walls (separated phase domains which are in antiphase) in the form of expanding spiral waves and the localized domain soliton rotating about the Neel defect (in this connection, we called it the “Neel soliton”) in active cavities with mixed laser and parametric amplification was shown in a numerical experiment for the first time. We proposed potential possibilities of using topological solitons in optical data processing, storage, and transmission.     

Spin-charge separated solitons in a topological band insulator

In this Letter we construct a simple, controllable, two-dimensional model based on a topological band insulator. It has many attractive properties. (1) We obtain spin-charge separated solitons that are associated with dynamic pi fluxes. (2) These solitons obey Bose statistics and their condensation triggers a phase transition from a spin Hall insulator to an easy-plane ferromagnet. (3) It suggests an alternative way to classify the Z2 topological band insulator without resorting to the sample boundary.     

Deffect free energies in lattice gauge theories with matter fields

We introduce and analyze different defect free energies in lattice gauge theories with matter fields. We investigate in which way the behaviour of these defect free energies characterizes different phase (and different regimes not separated by bulk phase boundaries) of such theories. Our main analytical results concern the ₂ model, but some of our concepts and method extend to a fairly general class of models, including non-abelian lattice gauge theories.We also estimate masses of topological solitons (vortices and magnetic monopoles) in terms of defect free energies of line defects.     

光晶格势阱中二元凝聚体的矢量孤子的振荡和分裂

考虑外部囚禁势阱为光晶格势阱,研究了二元玻色-爱因斯坦凝聚体中亮-亮孤子的动力学行为.结果表明,亮-亮孤子的运动方向和振荡行为可以分别通过调节光晶格势阱的晶格常数和势阱深度来控制.进一步地,亮-亮孤子还可以被局域在光晶格势阱中,并且随着势阱深度的增加,局域孤子会产生分裂行为.     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

Soliton quantization in lattice field theories

Quantization of solitons in terms of Euclidean region functional integrals is developed, and Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The quantization method is applied to several lattice field theories with solitons, and the particle structure in the soliton sectors of such theories is analyzed. A construction of magnetic monopoles in the four-dimensional, compactU(1)-model, in the QED phase, is indicated as well.     

Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice

We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.     

Soliton topology versus discrete symmetry in optical lattices

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general "charge rule" using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing on the case of Bessel lattices allows us to derive also an overall stability rule for the allowed vortex solitons.     

Edge-soliton-mediated vortex-core reversal dynamics

We report an additional reversal mechanism of magnetic vortex cores in nanodot elements driven by currents flowing perpendicular to the sample plane, occurring via dynamic transformations between two coupled edge solitons and bulk vortex solitons. This mechanism differs completely from the well-known switching process mediated by the creation and annihilation of vortex-antivortex pairs in terms of the associated topological solitons, energies, and spin-wave emissions. Strongly localized out-of-plane gyrotropic fields induced by the fast motion of the coupled edge solitons enable a magnetization dip that plays a crucial role in the formation of the reversed core magnetization. This work provides a deeper physical insight into the dynamic transformations of magnetic topological solitons in nanoelements.     

Topological dragging of solitons

We put forward properties of solitons supported by optical lattices featuring topological dislocations and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are even found to form soliton traps, and the properties of such solitons are shown to crucially depend on the trap topology. The uncovered phenomenon opens a new concept for soliton control and manipulation, e.g., in disk-shaped Bose-Einstein condensates.     

The nontrivial states in one-dimensional nonlinear bichromatic superlattices

We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of the lattice with their chemical potential located in the linear gap regime and are sensitive to the phase parameter of the superlattice potential. We further demonstrate that the topological property of the nonlinear Bloch bands can be characterized by topological Chern numbers defined in the extended two-dimensional parameter space. In addition, we discuss that the composition relations between the nolinear Bloch waves and gap solitions for the nonlinear superlattices. The stabilities of edge solitons are also studied.