Vortex rings and solitary waves in trapped Bose–Einstein condensates

We discuss nonlinear excitations in an atomic Bose–Einstein condensate which is trapped in a harmonic potential. We focus on axially symmetric solitary waves propagating along a cylindrical condensate. A quasi one-dimensional dark soliton is the only nonlinear mode for a condensate with weak interactions. For sufficiently strong interactions of experimental interest solitary waves are hybrids of one-dimensional dark solitons and three-dimensional vortex rings. The energy-momentum dispersion of these solitary waves exhibits characteristics similar to a mode proposed sometime ago by Lieb in a strictly 1D model, as well as some rotonlike features. We subsequently discuss interactions between solitary waves. Head-on collisions between dark solitons are elastic. Slow vortex rings collide elastically but faster ones form intermediate structures during collisions before they lose energy to the background fluid. Solitary waves and their interactions have been observed in experiments. However, some of their intriguing features still remain to be experimentally identified.     

Tunable complex photonic chiral lattices by reconfigurable optical phase engineering

We present a novel single-step fabrication approach, based on optical phase engineering, for tunable complex photonic chiral lattices of diverse geometries in a large area. By means of engineered reconfigurable phase patterns, we computationally simulate as well as experimentally investigate these complex structures. We show the generation of both periodic right- and left-handed chiral structures as well as photonic transversely quasi-crystallographic chiral structures. These complex chiral lattices are also demonstrated in a photorefractive material, and the lattice formation is analyzed by plane-wave-guided imaging as well as diffraction pattern imaging. Furthermore, complex photonic chiral structures with engineered tunable relative phase shifts between adjacent spiral units realizable in a single step are explored and analyzed.     

Collective multivortex states in periodic arrays of traps

We examine the vortex states in a 2D superconductor interacting with a square array of pinning sites. As a function of increasing pinning size or strength we find a series of novel phases including multivortex and composite superlattice states such as aligned dimer and trimer configurations at individual pinning sites. Interactions of the vortices give rise to an orientational ordering of the internal vortex structures in each pinning site. We also show that these vortex states can give rise to a multistage melting behavior.     

Generation of helical Ince-Gaussian beams with a liquid-crystal display

We generate helical Ince-Gaussian (HIG) beams by using complex amplitude and phase masks encoded onto a liquid-crystal display (LCD). These beams display an intensity pattern consisting of elliptic rings, whose number and ellipticity can be controlled, and a phase exhibiting a number of in-line vortices, each with a unitary topological charge. We show experimental results that display the properties of these elliptic dark hollow beams. We introduce a novel interference technique for generating the object and reference beams by using a single LCD and show the vortex interference patterns. We expect that these HIG beams will be useful in optical trapping applications.     

Large-eddy simulations and vortex structures of turbulent jets in crossflow

Using the method of large-eddy simulation, the 3-dimensional turbulent jets in crossflow with stream-wise and transverse arrangements of nozzle are simulated, emphasizing on the dynamical process of generation and evolution of vortex structures in these flows. The results show that the basic vortex structures in literatures, such as the counter-rotating vortex pair, leading-edge vortices, lee-side vortices, hanging vortices, kidney vortices and anti-kidney vortices, are not independent physical substances, but local structures of the basic vortex structure of turbulent jets in crossflow-the 3-D stretching vortex rings originating from the orifice of the nozzle, which is discovered in this study. Therefore, the most important large-scale structures of turbulent jets in crossflow are unified to the 3-D vortex rings which stretch and twist in stream-wise and swing in transverse directions. We also found that the shedding frequencies of vortex rings are much lower than the one corresponding to the appearance of leading-edge and lee-side vortices in the turbulent jets.     

Watching dark solitons decay into vortex rings in a Bose-Einstein condensate

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.     

Control of surface plasmon excitation via the scattering of light by a nanoparticle

We analyze the scattering of vortex pairs (the particular case of 2D dark solitons) by a single quantum vortex in a Bose–Einstein condensate with repulsive interaction between atoms. For this purpose, an asymptotic theory describing the dynamics of such 2D soliton-like formations in an arbitrary smoothly nonuniform flow of a ultracold Bose gas is developed. Disregarding the radiation loss associated with acoustic wave emission, we demonstrate that vortex–antivortex pairs can be put in correspondence with quasiparticles, and their behavior can be described by canonical Hamilton equations. For these equations, we determine the integrals of motion that can be used to classify various regimes of scattering of vortex pairs by a single quantum vortex. Theoretical constructions are confirmed by numerical calculations performed directly in terms of the Gross–Pitaevskii equation. We propose a method for estimating the radiation loss in a collision of a soliton-like formation with a phase singularity. It is shown by direct numerical simulation that under certain conditions, the interaction of vortex pairs with a core of a single quantum vortex is accompanied by quite intense acoustic wave emission; as a result, the conditions for applicability of the asymptotic theory developed here are violated. In particular, it is visually demonstrated by a specific example how radiation losses lead to a transformation of a vortex–antivortex pair into a vortex-free 2D dark soliton (i.e., to the annihilation of phase singularities).     

Spectral properties of waves in superlattices with 2D and 3D inhomogeneities

We investigate the dynamic susceptibility and one-dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough-nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inhomogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was discovered earlier [15] upon an increase in root-mean-square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio-spectroscopic and optical methods for identifying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.     

Evolution of the vortex structures and turbulent spots at the late-stage of transitional boundary layers

The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and dark spots structure observed by experiment research, has been confirmed by our computational results. The formation mechanisms of these structures have been explored. It is revealed that the new vortex structures, the ring-like vortex chain and induced disturbance velocities play a dominant role in the generation of turbulent spots.     

Appearance of fractional vortex dipoles by using spiral linear zone plate

We present a novel technique based on linear zone plate (LZP) by which linear singularities regarded as fractional vortex dipoles are efficiently generated. Our approach requires applying spiral phase to a LZP, so fractional vortex dipoles are then acquired. By also implementing transverse phase shift to the spiral LZP, we are able to equally divide the number of the produced dark beams carrying mixed phase dislocations into two transverse separate parts. As a result, by varying a so called the controlling parameter the lateral positions of the focused fractional vortex dipoles are changed. Since we are able to generate dark beams in different and specific linear positions, therefore we suggest these features will be of great interest in one-dimensional optical trapping. All results are completely verified by experimental works.     

Study of interactions between liquid vortices and bubbles by simultaneous particle image velocimetry and laser-induced fluorescence tracking

Extensive experimental research has been conducted using the particle image velocimetry (PIV), laser-induced fluorescence (LIF) imaging and backlit photographic recordings to study the complex interactions between coherent vortex structures created in the shear layer of jets and the bubbles. Triggering of the naturally-developing instabilities of the shear layer by a thin, pulsed annular flow surrounding the jets allowed the creation of large, orderly structures with controllable frequency and phase. Synchronization of the triggering with data acquisition permitted phase averaging of the data and revealed several interesting phenomena. In particular, the evolution of large vortices and bubble fields could be tracked and the interactions could be studied. The horizontal and vertical velocity components of the liquid and bubble fields and the vertical velocity of both the vortex and bubble rings that were created were measured by the PIV. LIF and image recordings have been combined to visualize bubble trapping inside large eddy structures.     

Holographic flow visualization as a tool for studying three-dimensional coherent structures and instabilities

Holography is capable of three-dimensional (3D) representation of spatial objects such as fluid interfaces and particle ensembles. Based on this, we adapt it into a 3D flow visualization tool called Holographic Flow Visualization (HFV). This technique provides a novel means of studying spatially and temporally evolving complex fluid flow structures marked by a disperse phase or interfaces of different fluids. This paper demonstrates that HFV is a straightforward technique, especially when the In-line Recording Off-axis Viewing (IROV) configuration is used. The technique can be applied either as a stand-alone experimental tool for studying scalar-based coherent structures, flow instabilities, interactions of different fluids driven by fluid dynamics, interfacial phenomena, or as a precursor to volumetric 3D velocity vector field measurement of complex transient flow dynamics. Experimental results in several complex fluid flows and flames demonstrate the effectiveness of HFV. Different methods are used to mark flow structures undergoing different instabilities: 1) a vortex ring grown out of a drop of polymer suspension falling in water, 2) cascade of a bag-shaped drop of milk in water, and 3) internal flow structures of a jet diffusion flame.     

Creation and annihilation of phase singularities in a focal field

It is well known that uniform illumination of a lens leads to a focal field with a pattern of dark Airy rings in the focal plane, whereas this is not the case for Gaussian illumination. We show theoretically and experimentally that in the transition between the two cases the Airy rings, being phase singularities, reorganize themselves by means of a creation-annihilation process leading to new dark rings outside the focal plane.     

Observation of hybrid soliton vortex-ring structures in Bose-Einstein condensates

We present the experimental discovery of compound structures comprising solitons and vortex rings in Bose-Einstein condensates. We examine both their creation via soliton-vortex collisions and their subsequent development, which is largely governed by the dynamics of interacting vortex rings. A theoretical model in three-dimensional cylindrical symmetry is also presented.     

A crossed focused vortex beam with application to cold molecules

We report the generation of a crossed, focused, optical vortex beam by using a pair of hybrid holograms, which combine the vortex phase and lens phase onto a spatial light modulator. We study the intensity distributions of the vortex beam in free propagation space, and the relationship of its dark spot size with the incident Gaussian beam's waist, the lens's focal length, and its orbital angular momentum. Our results show that the crossed, focused, vortex beam's dark spot size can be as small as 16.3μm and adjustable by the quantum number of the orbital angular momentum, and can be used to increase the density of trapped molecules. Furthermore, we calculate the optical potential of the blue-detuned, crossed vortex beam for MgF molecules. It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling, as the intensity gradient of such vortex beam is extremely high near the focal point.     

Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation

Optical dark traps such as Laguerre-Gaussian beams, modulated optical vortices, and high-order Bessel beams have been used in the micromanipulation of microparticles. Such optical traps are highly versatile, as they are able to trap both high- and low-index microparticles as well as to set them into rotation by use of the orbital angular momentum of light. Holography has been widely used to modulate the shape of an optical vortex for new optical traps. We show that, by designing the shape of a spiral phase plate and using electron-beam lithography for fabrication, one can modulate the amplitude and the phase of an optical vortex with respect to the specific shape of the spiral phase plate as required. Furthermore, to the best of our knowledge this is the first report of transferring orbital angular momentum from a spiral phase plate to an absorptive microparticle in an experiment. Hence, with this technique, optical dark traps can easily be designed and fabricated.     

Vortex streets in a cavity with higher-order standing waves

Recently a laser analog of vortex generation behind an obstacle in a flow was demonstrated. Vortex generation occurs when tilted waves of different transverse structures are simultaneously excited in a laser. We have generalized this phenomenon to higher-order standing waves. Here typical phenomena expected for optical vortices, such as the excitation and disappearance of single vortices out of and into dark lines and dark areas, as well as vortex-pair creation and annihilation become apparent.     

三维介观超导环涡旋态的研究

通过数值求解非线性金兹堡-朗道(G-L)方程组,研究了三维介观超导环中的涡旋态。发现了在细环中只能存在巨涡旋态,以及存在顺磁、抗磁迈斯纳效应和间隙性超导现象。在粗环中,发现了多涡旋态和巨涡旋态共存的混合态。相应讨论有助于理解介观超导环中涡旋态相变。     

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.     

Rotating matter waves in Bose-Einstein condensates

In this paper we consider analytically and numerically the dynamics of waves in two-dimensional, magnetically trapped Bose-Einstein condensates in the weak interaction limit. In particular, we consider the existence and stability of azimuthally modulated structures such as rings, multi-poles, soliton necklaces, and vortex necklaces. We show how such structures can be constructed from the linear limit through Lyapunov-Schmidt techniques and continued to the weakly nonlinear regime. Subsequently, we examine their stability, and find that among the above solutions the only one which is always stable is the vortex necklace. The analysis is given for both attractive and repulsive interactions among the condensate atoms. Finally, the analysis is corroborated by numerical bifurcation results, as well as by numerical evolution results that showcase the manifestation of the relevant instabilities.