Pair interactions of heavy vortices in quantum fluids

The dynamics of quantum vortex pairs carrying heavy doping matter trapped inside their cores is studied. The nonlinear classical matter field formalism is used to build a universal mathematical model of a heavy vortex applicable to different types of quantum mixtures. It is shown how the usual vortex dynamics typical for undoped pairs qualitatively changes when heavy dopants are used: heavy vortices with opposite topological charges (chiralities) attract each other, while vortices with the same charge are repelled. The force responsible for such behavior appears as a result of superposition of vortices velocity fields in the presence of doping substance and can be considered as a special realization of the Magnus effect. The force is evaluated quantitatively and its inverse proportionality to the distance is demonstrated. The mechanism described in this paper gives an example of how a light nonlinear classical field may realize repulsive and attractive interactions between embedded heavy impurities.     

Long-range nonlocal flow of vortices in narrow superconducting channels

We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of intervortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice (VL), even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.     

色味连锁夸克物质中的涡旋

夸克物质在不同的温度和重子数密度下表现出丰富的相结构。高密低温情况下,夸克物质的基态是色味连锁相。介绍了金兹堡-朗道理论以及色味连锁夸克物质中的各种涡旋态（特别是准超流涡旋）,并讨论了磁场和自转对准超流涡旋的的影响。由于致密星核心内部有可能形成准超流涡旋,这一结果对致密星体的研究具有现实意义。如果将温度、夸克质量等因素考虑在内,研究夸克物质中涡旋结构的性质将为诸如致密星物理实验等相关的领域提供新的视角。The quark matter exhibits a rich phase structure at different temperatures and baryon number densities. At high baryon density and low temperature, the color-flavor locked phase is believed to be the ground state of the quark matter. We present an introduction to various vortices in the color-flavor locked quark matter, especially for the semi-superfluid vortices, and their research method (Ginzburg-Landau method). The influence of magnetic field and rotation on properties of these vortices is discussed. Due to the possibility of forming a semi-superfluid vortex in the core of the dense star, this result is of practical significance in the study of dense stars. If considering other factors, such as temperature and quark mass, study of the vortex structure properties in the quark matter could provide new perspectives for related fields, for instance dense star physics.     

Do vortices entangle?

We propose an experiment for directly constructing and locally probing topologically entangled states of superconducting vortices which can be performed with present-day technology. Calculations using an elastic string vortex model indicate that as the pitch (the winding angle divided by the vertical distance) increases, the vortices approach each other. At values of the pitch higher than a maximum value the entangled state becomes unstable to collapse via a singularity of the model. We provide predicted experimental signatures for both vortex entanglement and vortex cutting. The local probe we propose can also be used to explore a wide range of other quantities.     

Viscoelastic effects on asymmetric two‐dimensional vortex patterns in a strongly coupled dusty plasma

Strongly coupled dusty plasma medium is often described as a viscoelastic fluid that retains its memory. In a flowing dusty plasma medium, vortices of different sizes appear when the flow does not remain laminar. The vortices also merge to transfer energy between different scales. In the present work, we study the effect of viscoelasticity and compressibility over a localized vortex structure and multiple rotational vortices in a strongly coupled viscoelastic dusty plasma medium. In case of single rotating vortex flow, a transverse wave is generated from the localized vortex source and the evolution time of generated waves is found to be reduced due to finite viscoelasticity and compressibility of the medium. It is found that the viscoelasticity suppresses the dispersion of vorticity. In the presence of multiple vortices, we find, the vortex mergers get highly affected in the presence of memory effect of the fluid, and thus the dynamics of the medium gets completely altered compared to a non‐viscoelastic fluid. For a compressible fluid, viscoelasticity dampens the energy in the sonic waves generated in the medium. Thus a highly viscoelastic and compressible fluid, in some cases, behaves similarly to an incompressible viscoelastic fluid. The wave‐front like rings propagate in elliptical orbits keeping the footprint of the earlier position of the point‐vortex. The rings collide with each other even within the patch vortex region forming regions of high vorticity at the point of intersection and pass through each other.     

Tunable optical vortex arrays using spontaneous periodic pattern formation in nematic liquid crystal cells

Controllable liquid crystal (LC) defects can provide an effective approach to creating tunable optical vortices. We develop a method to create tunable matter vortex arrays in an LC cell, in which +1 and −1 defects are periodically arranged in a square grid lattice. Spontaneous formation of the periodic defect array is achieved using a spontaneous standing pressure wave without using any patterned electrode or patterned alignment layer. The +1 and −1 defects in the array can induce optical vortices with opposite handedness, and the matter vortex array produces a periodic optical vortex array with orbital angular momenta of −2ℏ and +2ℏ in the same grid lattice. Because the pitch of the grid can be controlled, the method can provide a useful pathway to producing tunable optical vortex arrays for various applications such as advanced optical communication and quantum computation.     

Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system “as a whole” and show that the evolution of the vorticity profile is due to resonances between different orbits of the point vortices. The evolution stops when the profile of angular velocity becomes monotonic even if the system has not reached the statistical equilibrium state (Boltzmann distribution). In that case, the system remains blocked in a quasi stationary state with a non standard distribution. We also study the relaxation of a test vortex in a steady bath of field vortices. The relaxation of the test vortex is described by a Fokker-Planck equation involving a diffusion term and a drift term. The diffusion coefficient, which is proportional to the density of field vortices and inversely proportional to the shear, usually decreases rapidly with the distance. The drift is proportional to the gradient of the density profile of the field vortices and is connected to the diffusion coefficient by a generalized Einstein relation. We study the evolution of the tail of the distribution function of the test vortex and show that it has a front structure. We also study how the temporal auto-correlation function of the position of the test vortex decreases with time and find that it usually exhibits an algebraic behavior with an exponent that we compute analytically. We mention analogies with other systems with long-range interactions.     

具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构研究

通过虚时演化方法研究了具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构.结果发现:面内四极磁场和旋转双重作用可导致中央Mermin-Ho涡旋的产生;随着磁场梯度增强,Mermin-Ho涡旋周围环绕的涡旋趋向对称化排布;在四极磁场下,密度相互作用和自旋交换相互作用作为体系的调控参数,可以控制Mermin-Ho涡旋周围的涡旋数目;该体系自旋结构中存在双曲型meron和half-skyrmion两种拓扑结构.     

Large scale dissipation and filament instability in two-dimensional turbulence

Coherent vortices in two-dimensional turbulence induce far-field effects that stabilize vorticity filaments and inhibit the generation of new vortices. We show that the large-scale energy sink often included in numerical simulations of statistically stationary two-dimensional turbulence reduces the stabilizing role of the vortices, leading to filament instability and to continuous formation of new coherent vortices. This counterintuitive effect sheds new light on the mechanisms responsible for vortex formation in forced-dissipated two-dimensional turbulence, and it has significant impact on the temporal evolution of the vortex population in freely decaying turbulence. The time dependence of vortex statistics in the presence of a large-scale energy sink can be approximately described by a modified version of the scaling theory developed for small-scale dissipation.     

Non-monotonic driven vortex noise in HTSC

We present noise measurements on YBCO thin films in different conditions of magnetic field and driving current. Noise spectra for non-driven and driven cases (in the flux-creep region) evidence deep differences in vortex dynamics between these two regimes. For the driven case, the effect of applying magnetic field is a reduction in noise, which can be explained by the increase in the fraction of vortices that undergo flux-flow. For the non-driven case, magnetic field has no significative influence on noise, probably due to the absence of Lorentz force that causes coherent movement of vortices. For all magnetic fields studied in this work (0-154 mT) the effect of increasing current is an increase of noise, which is in contrast to the results from other authors. This behavior can be explained by an increase of current induced vortex-antivortex annihilation events. We propose that driven noise has a non-monotonic behavior due to the competition between annihilation events and driving force which causes opposite effects on noise.     

Phases of atom-molecule vortex matter

We study ground state vortex configurations in a rotating atom-molecule Bose-Einstein condensate. It is found that the coherent coupling between the atomic and molecular condensates can render a pairing of atomic and molecular vortices into a composite structure that resembles a carbon dioxide molecule. Structural phase transitions of vortex lattices are also explored through different physical parameters including the rotational frequency of the system.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

Dynamic vortex-antivortex interaction in a single cross-tie wall

A fascinating property of micromagnetism comes from the possibility to control the domain and vortex configuration through the sample shape and size. For instance, in a rectangular platelet a configuration containing a stable combination of vortices and an antivortex can be created. Such a single cross-tie wall can be understood as being a coupled micromagnetic system with three static solitons. Here we report on its magnetization dynamics including the vortex-antivortex interactions. The spectrum of eigenmodes is investigated as well as the effect of different vortex core orientations. We show that the vortex dynamics can be used to identify the core configuration, which is not directly accessible to x-ray microscopy because of its limited spatial resolution.     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Vortices in a Rotating Spin-Orbit-Coupled Bose-Einstein Condensate under Extreme Elongation in a Harmonic Plus Quartic Trap

We consider the ground-state properties of a rotating spin-orbit-coupled Bose-Einstein condensate under extreme elongation in a harmonic plus quartic potential. The effects of spin-orbit coupling and rotation on the ground-state vortex structures are investigated. In the absence of spin-orbit coupling, new nucleated vortices gradually form vortex lines and annular vortex structures with the increase of the rotation frequency. In the presence of spin-orbit coupling, part of the vortices arrange in a line and form a stable vortex chain, and the remanent vortices coexist in pairs aside such vortex chain. More specially, the remanent vortices of each component repel each other and form vortex pair for isotropic spin-orbit coupling, while attract each other and locate in the same positions for anisotropic spin-orbit coupling.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

Magnetic vortex gyration mediated by point-contact position

Micromagnetic simulation is employed to study the gyration motion of magnetic vortices in distinct permalloy nanodisks driven by a spin-polarized current. The critical current density for magnetic vortex gyration, eigenfrequency, trajectory, velocity and the time for a magnetic vortex to obtain the steady gyration are analyzed. Simulation results reveal that the magnetic vortices in larger and thinner nanodisks can achieve a lower-frequency gyration at a lower current density in a shorter time. However, the magnetic vortices in thicker nanodisks need a higher current density and longer time to attain steady gyration but with a higher eigenfrequency. We also find that the point-contact position exerts different influences on these parameters in different nanodisks, which contributes to the control of the magnetic vortex gyration. The conclusions of this paper can serve as a theoretical basis for designing nano-oscillators and microwave frequency modulators.     

Superfluidlike motion of vortices in light condensates

We demonstrate, through numerical simulations, the generation of stable vortex lattices in light condensates. This can be achieved by propagating several concentric laser beams with nested vortices of different topological charges in an optical material with a cubic-quintic nonlinearity. We have considered several initial conditions, and in all the cases the net topological charges of the resulting lattice is equal to the topological charge of the initial outer vortex. The lattice exhibits rotation similar to vortex motion in superfluids. These vortex arrays could be used to implement all-optical photonic crystal fibers. Our results also apply to Bose-Einstein condensates in the presence of three-body elastic interactions.     

非相对论Chern-Simons多涡旋解的拓扑结构(英文)

运用规范势分解理论研究了Jackiw Pi模型中的自对偶方程, 得到一个新的自对偶方程, 发现了Chern Simons多涡旋解与拓扑荷之间的联系。为了研究Jackiw Pi模型多涡旋解的拓扑性质, 构造了一个新的静态自对偶Chern Simons多涡旋解,每个涡旋由5个实参数描述。 2个实参量用来描述涡旋的位置, 2个实参量用来描述涡旋的尺度和相位, 还有一个实参量描述涡旋的荷。 为了研究拓扑数对涡旋形状的影响, 给出了具有不同拓扑数的多涡旋解。 另外还研究了该涡旋解的磁通量的拓扑量子化。     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.