We describe the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of ℏ, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate (BEC) 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. We use this technique to generate circular flow of a BEC confined in a toriodal shaped trap. We measure that the flow of atoms persists for up to 10 seconds, which we interpret as the first evidence of persistent currents in a superfluid Bose gas.

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Quantum turbulence is recently one of the most important topics in low temperature physics. Physics of quantum turbulence and quantized vortices have been studied chiefly in superfluid helium. The realization of atomic Bose-Einstein condensation has allowed us to study quantized vortives in the fascinating systems too. Generally there are two kinds of cooperative phenomena comprised of quantized vortices, from the research history of superfluid helium. Lots of studies in atomic Bose-Einstein condensates (BECs) are devoted mainly to the issues of vortex lattices under rotation. However, another important state on quantized vortices, namely quantum turbulence, has been never studied in atomic BECs. In this work, we address for the first time quantum turbulence in atomic BECs theoretically and numerically. After reviewing shortly the recent developments on quantum turbulecne, 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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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