SPIVOR · Geometrical aspects of spin and vortex dynamics in electromagnetic and matter waves

Geometrical aspects of spin and vortex dynamics in electromagnetic and matter waves

This project addressed the problems of the spin-orbit interaction (SOI) and angular-momentum (AM) phenomena in optics and quantum mechanics. More precisely, the following themes were in the project for the past year: - Vortex-induced dynamics under propagation of electron waves in external fields - Relativistic properties of angular momentum in wave fields - Spin and vortex dynamics in evanescent and surface-plasmon waves. According to these themes, the main problems solved within the project are as follows. Evolution of electron vortex beams in a magnetic field. We examined propagation of electron vortex modes in a longitudinal magnetic field, either uniform or localised in flux tube. This resulted in revisiting of the fundamental Aharonov-Bohm and Landau problems. We have shown that various superpositions of vortex modes exhibit a reach a non-trivial vortex-dependent behaviour, which is in sharp contrast to the uniform cyclotron rotation of classical electrons. Namely, there are three characteristic rotational rates of vortex superpositions depending on the AM value: (i) cyclotron rotation (for positive AM) (ii) Larmor rotation (for zero AM), and (iii) no rotation (for negative AM). These results were verified experimentally owing to the collaboration with a Belgian electron-microscopy group headed by Prof. J. Verbeeck. Relativistic properties of vortex wave beams. We analysed therectically relativistic transformations of vortex beams carrying intrinsic AM. In particular, we have shown that transverse motion and Lorentz transformation of such beam inevitably results in the shift of the center of energy in the orthogonal direction. We called this phenomenon 'relativistic Hall effect'. We revealed close relations between this effect, geometric spin-Hall effects of light, and a 'rolling-shutter deformations' in a photography. We have also generalised usual spatial monochromatic vortex beams to spatio-temporal polychromatic vortices in Minkowski space-time. Spin and vortex dynamics in evanescent and surface plasmon-polariton fields. We predicted and described theoretically a novel type of spin AM of light: A transverse spin of evanescent waves and surface plasmon-polaritons. This spin has intriguing properties which are in sharp contrast to spin of propagating waves (photons). While the spin of photon is directed along its momentum and appears for circularly-polarised waves, the spin of evanescent waves is orthogonal to the wave momentum and appears even for linearly-polarised TE and TM modes. To suggest an experimental setup detecting this transverse spin, we solved the problem of a mechanical action of evanescent fields on Mie scattering particles. Moreover, we examined experimentally spin-Hall effect of light in surface plasmon-polariton beams using quantum weak measurements. This work is based on achievements of the first stage of the project and represents a significant extension of previous studies into new directions. The potential impacts of the project are as follows: On the fundamental level, this project delivers profound theoretical understanding of the SOI and AM effects in vector-optical and scalar-electron waves, unify previously disjointed fundamental problems, and unveil deep interrelations between them. Our studies revealed the intimate connection between spin and orbital angular momenta of light, relativistic position operators, Lorentz transformations, Hall effects, Landau levels, Berry phases, etc. It turns out that only when brought together, these fundamental concepts form a fairly complete picture of the internal degrees of freedom of light and matter waves. Such thorough approach has a universal character and will be naturally applied to quantum systems within the framework of this project. This will deepen the analogy between the light and matter waves at the level of intrinsic geometrodynamical phenomena. On the level of applications, this project investigates conceptually new methods for the employment of the internal degrees of freedom of wave fields for probing and manipulation of various materials and nanostructures. First, the AM vortex states of electrons were shown to be sensitive to magnetic fields and structures. In this manner, local circular dichroism with focused electron vortices in electron microscopes can be employed for probing either magnetic textures or even individual atomic states. Second, the above-mentioned dynamical AM properties of evanescent optical waves allow new methods for manipulation and sorting of nano-particles using near-field and plasmonic systems. We anticipate that efficient probing schemes for chiral and magnetoactive structures can be further developed in the context of optical, plasmon-polariton, and vortex-electron waves.

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