Two dimensional vortex lattices from pure wavefront tilts

A new method of generation of two dimensional vortex lattices is described. In this method, different parts of the wavefront are given different local tilts to realize vortex lattice in the propagated field. These linear phase variations corresponding to tilts in different locations of the wavefront are created using a spatial light modulator (SLM). The diffracted field from the SLM is found to contain vortex lattice and the presence of these vortices is confirmed experimentally. Computational results are also provided.     

Spectroscopy of magnetic excitations in magnetic superconductors using vortex motion

In magnetic superconductors a moving vortex lattice is accompanied by an ac magnetic field which leads to the generation of spin waves. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I-V characteristics at voltages at which the washboard frequency of the vortex lattice matches the spin wave frequency omegaS(g), where g are the reciprocal vortex lattice vectors. We show that if the washboard frequency lies above the magnetic gap, measurement of the I-V characteristics provides a new method to obtain information on the spectrum of magnetic excitations in borocarbides and cuprate layered magnetic superconductors.     

Vortices in Bose-Einstein condensates: A review of the experimental results

Rotating dilute Bose-Einstein condensates (BEC) of alkali atoms offer a testing ground for theories of vortices in weakly interacting superfluids. In a rotating super-fluid, quantised vortices, with a vorticity h/m, form above a critical velocity. Such vortices have been generated in BEC of alkali atoms by different techniques such as (a) wave function engineering of a two-component BEC, (b) decay of solitons, (c) rotation of a thermal cloud before cooling it below the condensation temperature, (d) stirring with an ‘optical’ spoon, (e) rotating a deformation in the anisotropic trap in which the condensate is trapped and (f) by creating Berry phase by adiabatically reversing the axial magnetic field. Since the core of a vortex is a fraction of a micrometer in diameter, it cannot be directly imaged optically. The condensate with vortices is allowed to ballistically expand till the size increases by one order before the vortices are imaged. Surface wave spectroscopy and the change in aspect ratio of a rotating cloud are the other techniques used. Studies have been made on the creation and dynamics of single vortex and on systems with more than a hundred vortices. Results have been obtained on vortex nucleation, stability of vortex structures, nature of the vortex lattice and defects in such a lattice. Important results are: (a) evidence exists that vortex nucleation takes place by a surface mode instability; but this is not the only mechanism; (b) the vortex lattice is perfectly triangular right up to the edge; (c) in the initial stages of rotation of the cloud a tangled web of vortices is seen; it takes a few hundred milliseconds before the vortices arrange themselves in a lattice; this time appears to be independent of temperature; (d) the decay of vortices appears to arise from the transfer of energy to the rotating thermal component and is dependent on temperature; (e) defects in the lattices such as dislocations and grain boundaries are seen; (f) transverse oscillations (Tkachenko modes) of the vortex lattice have been observed; and (g) giant vortices have been produced. These will be discussed.     

Vortices in superconducting bulk, films and SQUIDs

The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).     

Experimental Simulation of the Generation of a Vortex Flow on a Water Surface by a Wave Cascade

The generation of a vortex flow by waves on a water surface, which simulate an energy cascade in a system of gravity waves at frequencies of 3, 4, 5, and 6 Hz, has been studied experimentally. It has been found that pumping is accompanied by the propagation of waves on the surface at different angles to the fundamental mode and by a nonlinear interaction between waves resulting in the generation of new harmonics. It has been shown that large-scale flows are formed by modes of the lowest frequency of 3 Hz intersecting at acute angles. The energy distribution of the vortex motion can be described by a power-law function of the wavenumber and is independent of the energy distribution in a system of surface waves. The energy coming to large-scale vortex flows directly from the wave system is transferred to small scales. A direct rather than inverse energy flux is established in the system of vortices.     

Vortex chains induced by anisotropic spin-orbit coupling and magnetic field in spin-2 Bose-Einstein condensates

We investigate the anisotropic spin-orbit coupled spin-2 Bose-Einstein condensates with Ioffe-Pritchard magnetic field. With nonzero magnetic field, anisotropic spin-orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin-orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Vortex deconfinement in the XY model with a magnetic field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.     

Transfer and storage of vortex states in light and matter waves

We theoretically explore the transfer of vortex states between atomic Bose-Einstein condensates and optical pulses using ultraslow and stopped light techniques. We find shining a coupling laser on a rotating two-component ground state condensate with a vortex lattice generates a probe laser field with optical vortices. We also find that optical vortex states can be robustly stored in the atomic superfluids for times, in Rb-87 condensates, limited only by the ground state coherence time.     

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.     

Compound plasmonic vortex generation based on spiral nanoslits

In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre–Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for several examples confirm the effectiveness of the design principle. The discussions about the interference of vortex fields definite the generation condition for the structured vortex. This work provides a design methodology for generating new vortices using spiral nanoslits and the advanced radially structured plasmonic vortices is helpful for broadening the applications of vortex fields.     

Vortex stretching as a mechanism for quantum kinetic energy decay

A pair of perturbed antiparallel quantum vortices, simulated using the three-dimensional Gross-Pitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K(?ψ) being converted into interaction energy E(I) and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons, and the creation of an approximately -5/3 kinetic energy spectrum at high wave numbers. All of the wave generation and reconnection steps follow from interactions between the two original vortices. A four vortex example is given to demonstrate that some of these steps might be general.     

Magnetic-field effects on the size of vortices below the surface of NbSe2 detected using low energy beta-NMR

A low energy radioactive beam of polarized 8Li has been used to observe the vortex lattice near the surface of superconducting NbSe2. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved beta-detected NMR. Below Tc, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.     

Visualization of two-dimensional vortex flows in thin oscillating liquid films

A possibility of visualizing flows using random inhomogeneities of film thicknesses of different colors as particles for visualization is shown on an example of a vortex flow structure in an oscillating thin liquid film. Formation of vortex flows in a thin liquid film containing surface-active substances is investigated in experiments. The film is fixed horizontally along the edges of the cell vibrating in the vertical direction. Spatially homogeneous oscillations of the liquid film can excite different types of waves that generate two-dimensional vortex flows due to nonlinearity. We present results of experimental investigation of the structure of vortex flows in a thin film (0.5–10 μm) with rectangular boundaries. It has been revealed that, if the horizontal size of an inhomogeneous region is much smaller than the size of vortices, the inhomogeneities are transported by vortices and their interference pattern can be used for visualization of vortex flows.     

Attraction between pancake vortices in the crossing lattices of layered superconductors

The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancake vortices, forming the AVs and JVs, produces the deformation of the AV line. It is demonstrated that, as a result of this deformation, a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chain formation. The vortex structure in the weak perpendicular magnetic field is the vortex chain phase, where only a small part of JVs is occupied by AVs.     

Vortex states of a superconducting film from a magnetic dot array

Using Ginzburg-Landau theory, we find novel configurations of vortices in superconducting thin films subject to the magnetic field of a magnetic dot array, with dipole moments oriented perpendicular to the film. Sufficiently strong magnets cause the formation of vortex-antivortex pairs. In most cases, the vortices are confined to dot regions, while the antivortices can form a rich variety of lattice states. We propose an experiment in which the perpendicular component of the dot dipole moments can be tuned using an in-plane magnetic field. We show that in such an experiment the vortex-antivortex pair density shows broad plateaus as a function of the dipole strength. Many of the plateaus correspond to vortex configurations that break dot lattice symmetries. In some of these states, the vortex cores are strongly distorted. Possible experimental consequences are mentioned.     

Flux vortices and transport currents in type II superconductors

This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical defects. The theoretical models are compared critically with experimental measurements of pinning forces and other related phenomena, such as flux creep, low amplitude vortex oscillations and vortex lattice defect effects. Finally, the implications for technological materials are assessed.     

Effect of a constant magnetic field on echo signals in high-temperature superconductor powders

The generation of acoustic and vortex oscillations in high-temperature superconductor (HTSC) powders excited by radiofrequency (rf) pulses was analyzed in detail in our earlier publications. The rf magnetic field stimulates oscillations of magnetic vortices on the surface of an HTSC grain, which are transformed into lattice vibrations via the pinning centers at the surface, thus inducing a propagating acoustic wave. The allowance for second-order nonlinearity in the gradient of deviation of the crystal lattice from its equilibrium position in the equation for the acoustic wave leads to a dependence of the natural frequency of crystal lattice vibrations on the amplitude and duration of pulses exciting these vibrations. Such a dependence is responsible for echo signals that can be detected experimentally. The proposed model makes it possible to interpret most experimental results for BiPbSrCaCuO superconducting samples. We consider the effect of a constant magnetic field on the amplitude and the echo signal decay time. We observed a clearly manifested peak that was not described by other authors. The model proposed here provides an obvious explanation for this peak.