Orbital angular momentum has been transferred to optically confined particles from light fields possessing an optical vortex. These experiments have to date been restricted to microparticles in the Mie or Lorentz-Mie regime, that where the particle is comparable to or larger than the wavelength of the trapping light. We demonstrate the first conclusive experimental transfer of orbital angular momentum to metallic nanoparticles in an optical trap created by a vortex light field: the trapping geometry utilizes a blue-detuned laser and confines the particles to the dark region of the vortex beam.
Motivated by both experimental and theoretical activities, we discuss the fate of Kondo screening and possible quantum phase transitions in antiferromagnetically ordered phases of Kondo lattices. While transitions with topological changes of the Fermi surface may occur, we demonstrate that an entirely continuous evolution from itinerant to local-moment antiferromagnetism (i.e. from strong to negligible Kondo screening) is possible as well. This situation is in contrast to that in a non-symmetry-broken situation where a quantum phase transition towards an exotic metallic spin-liquid state necessarily accompanies the disappearance of Kondo screening. We discuss criteria for the existence of topological transitions in the antiferromagnetic phase, as well as implications for theoretical scenarios and for current experiments.
We give a brief overview of the recent advances in nonlinear singular optics that studies the propagation and stability of optical vortices in nonlinear media, with the emphasis on the properties of vortex solitons and rotating azimuthons. In general, self-focusing nonlinearity generates the azimuthal instability of vortex beams, but it can support novel types of stable (or meta-stable) self-trapped beams with a finite angular momentum, such as ring-like necklace beams and soliton clusters. In particular, we describe azimuthons and multi-vortex solitons which provide the generalization of the Laguerre-Gaussian and Hermite-Gaussian optical beams and demonstrate that many of such vortex-carrying beams can be stabilized in the media with nonlocal nonlinear response.
Geometric and topological properties of phase singularity lines in three-dimensional complex scalar wavefields are discussed. In particular, their role as the intersections of the zero contour surfaces of the real and imaginary parts of the field gives numerous insights into 3D vortex topology. In addition, complex scalar wavefields (i.e. solutions of the three-dimensional Helmholtz and paraxial equations) are compared to more general complex scalar fields, including those arising naturally from algebraic geometry.
An experimental demonstration of the mechanical transfer of orbital angular momentum to matter from acoustical vortices in free field is presented. Vortices with topological charges l=+/-1 and l=+/-2 were generated and a torsion pendulum was used to study the angular momentum transfer to hanging disks of several sizes. This allowed us to make a comparative study of the effective acoustical torque in terms of topological charge of the vortex, the disk radius, and its position along the main propagation axis. A theoretical discussion of the generated sound fields is also provided.
The effect of the Gouy phase, which is one of the geometrical phases of photons, is observed through quantum correlation in Laguerre-Gaussian (LG) modes. In an experiment, the relative phase of two different LG modes of measurement basis states is manipulated via the Gouy phase, and the observed coincidence count rates agree well with theoretical predictions. This result suggests that the Gouy phase can be used as a new tool to manipulate multidimensional photonic quantum states.
We consider a setting where every pair of players that undertake a transaction (e.g. exchange goods or information) creates a unit surplus. A transaction can take place only if the players involved have a connection. If the connection is direct the two players split the surplus equally, while if it is indirect then intermediate players also get an equal share of the surplus. Thus, individuals form links with others to create surplus, to gain intermediation rents, and to circumvent others who are trying to become intermediary.Our analysis clarifies the interplay between these forces in the process of strategic network formation. First, we show that, in the absence of capacity constraints on links, it leads to the emergence of a star network where a single agent acts as an intermediary for all transactions and enjoys significantly higher payoffs. Second, we study the implications of capacity constraints in the ability of agents to form links. In this case, distances between players must be long, which induces players who are "far off" to connect in order to avoid paying large intermediation rents. A cycle network then emerges, payoffs being equal across all players. (c) 2007 Elsevier Inc. All rights reserved.
We have demonstrated the direct production of a high-power 1.06 μm vortex mode from a diode-pumped Nd:GdVO4 bounce amplifier with an asymmetric cavity configuration. A maximum vortex output of 12 W was obtained at a pump power of 54 W. The system can also produce 1.3 μm multiple-vortex output.
We studied exciton structures and the Aharonov-Bohm effect in a single carbon nanotube using micro-photoluminescence (PL) spectroscopy under a magnetic field at low temperatures. A single sharp PL peak from the bright exciton state of a single carbon nanotube was observed under zero magnetic field, and the additional PL of dark exciton state appeared below the bright exciton peak under high magnetic fields. It was found that the split between the bright and dark exciton states is several millielectron volts at zero field. The tube diameter dependence of the splitting arises from the intervalley short-range Coulomb interaction.
We present an introductory account of the dynamical and topological aspect for a polarization texture from several aspects. (i) We first give an elementary explanation for a description of polarization in terms of an evolutional equation of the Stokes parameters. This is carried out on the basis of para-axial approximation. (ii) We next consider a field dynamics of the Stokes vectors by using the Lagrangian for the two-component non-linear Schrödinger equation. This results in a form of hydro-dynamical theory of anisotropic fluid. This formulation is also based on the para-axial approximation. (iii) Finally we give a brief sketch for a trial to extend theory to the non-para-axial scheme.
An optical vortex incident on a birefringent crystal unfolds into a complex topological structure of lines of circular polarization (C-lines) and surfaces of linear polarization (L-surfaces). The incident beam splits into two orthogonally polarized beams of ordinary and extraordinary polarization. Extraordinary refraction causes a shift of the extraordinarily polarized beam even under normal incidence. This shift together with the different phase velocities of both beams is the origin of an intriguing pattern of polarization singularities. We measure spatially resolved the full set of Stokes parameters after the beam passed the crystal to determine experimentally the spatial structure of the polarization singularities in three dimensions, two spatial directions (x,y) and one (Λ) corresponding to the relative phase retardation between ordinary and extraordinary beam. The observed unfolding of the initial phase singularity is the most generic case of the generation of polarization singularities in uniaxial or biaxial birefringent crystals. It can be describe in a very general way in terms of Stokes parameters where the polarization singularities arise naturally from the zeros of the Stokes parameters.
The topological structures of the generic smooth functions on a smooth manifold belong to the small quantity of the most fundamental objects of study both in pure and applied mathematics. The problem of their study has been formulated by A. Cayley in 1868, who required the classification of the possible configurations of the horizontal lines on the topographical maps of mountain regions, and created the first elements of what is called today ‘Morse Theory’ and ‘Catastrophes Theory’. In the paper we describe this problem, and in particular describe the classification of Morse functions on the 2 sphere and on the torus.
The homeostatic framework has dominated our understanding of cellular physiology. We question whether homeostasis alone adequately explains microbial responses to environmental stimuli, and explore the capacity of intracellular networks for predictive behavior in a fashion similar to metazoan nervous systems. We show that in silico biochemical networks, evolving randomly under precisely defined complex habitats, capture the dynamical, multidimensional structure of diverse environments by forming internal representations that allow prediction of environmental change. We provide evidence for such anticipatory behavior by revealing striking correlations of Escherichia coli transcriptional responses to temperature and oxygen perturbations- precisely mirroring the covariation of these parameters upon transitions between the outside world and the mammalian gastrointestinal tract. We further show that these internal correlations reflect a true associative learning paradigm, because they show rapid decoupling upon exposure to novel environments.
Natural habitats of some microorganisms may fluctuate erratically, whereas others, which are more predictable, offer the opportunity to prepare in advance for the next environmental change. In analogy to classical Pavlovian conditioning, microorganisms may have evolved to anticipate environmental stimuli by adapting to their temporal order of appearance. Here we present evidence for environmental change anticipation in two model microorganisms, Escherichia coli and Saccharomyces cerevisiae . We show that anticipation is an adaptive trait, because pre-exposure to the stimulus that typically appears early in the ecology improves the organism’s fitness when encountered with a second stimulus. Additionally, we observe loss of the conditioned response in E. coli strains that were repeatedly exposed in a laboratory evolution experiment only to the first stimulus. Focusing on the molecular level reveals that the natural temporal order of stimuli is embedded in the wiring of the regulatory network—early stimuli pre-induce genes that would be needed for later ones, yet later stimuli only induce genes needed to cope with them. Our work indicates that environmental anticipation is an adaptive trait that was repeatedly selected for during evolution and thus may be ubiquitous in biology.
Generally there are two kinds of cooperative phenomena comprised of quantized vortices. One is a vortex lattice under rotation, and the other is a vortex tangle (quantum turbulence) made by some flow. Both have been studied in the field of superfluid helium through the long research history. On the other hand, the research of atomic Bose-Einstein condensates (BECs) has been limited to the former case, namely a vortex lattice. In this work, we address for the first time quantum turbulence in atomic BECs theoretically and numerically. We propose how to make quantum turbulence in a trapped BEC by combining rotation around two axes, and confirm the Kolmogorov spectra by the Gross-Pitaevskii model.
We developed super-resolution microscopy using the fluorescence depletion process. To verify the principle of this microscopy, we measured fluorescence images of micro-beads, i.e the point-spread function (PSF). It was found that the FWHM of PSF becomes smaller than 110 nm. The results show that proposed microscopy can provide a sufficient spatial resolution to overcome the diffraction limit. In microscopy, the Laguerre-Gaussian beam with a zero center singularity plays an important role and determines performance of microscopy. We introduce our proposed technique, including formation about a Laguerre-Gaussian beam tightly focused by a high-NA microscope objective lens.
We study the proximity effect between an $s$-wave superconductor and the surface states of a strong topological insulator. The resulting two-dimensional state resembles a spinless ${p}_{x}+i{p}_{y}$ superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.
We investigate the spacetime of a slowly rotating black hole in Chern-Simons modified gravity. The frame-dragging effect under the Chern-Simon gravity gives a similar feature to that of galaxy rotation curves.
We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of h, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons. We subsequently use our technique to induce rotation of the condensate confined in an asymmetric, ring-shaped hybrid optical and magnetic trap. We observe the cloud rotating for up to 13 seconds, due to the superfluid character of the condensate.
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here, we use scaling theory to quantify the degree of correlations in the particular case of networks with a power-law degree distribution. These networks are classified in terms of their correlation properties, revealing additional information on their structure. For instance, the studied social networks and the Internet at the router level are clustered around the line of random networks, implying a strongly connected core of hubs. On the contrary, some biological networks and the WWW exhibit strong anticorrelations. The present approach can be used to study robustness or diffusion, where we find that anticorrelations tend to accelerate the diffusion process.
