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We explore the process of orbital angular momentum (OAM) transfer from a twisted light beam to an electron in atomic ionization within the first Born approximation. The characteristics of the ejected electron are studied regardless of the detection scheme. We find that the outgoing electron possesses a definite projection of OAM when a single atom is located on the propagation axis of the photon, whereas the size of the electron wave packet is solely determined by the energy of the photon rather than by its transverse coherence length. Shifting the position of the atom yields a finite dispersion of the electron OAM. We also study a more experimentally feasible scenario -- a localized finite-sized atomic target -- and develop representative approaches to describing coherent and incoherent regimes of photoionization., Comment: 9 pages, 4 figures

We study spontaneous emission of a photon during the transitions between relativistic Landau states of an electron in a constant magnetic field that can reach the Schwinger value of $H_c = 4.4 \times 10^9$ T. In contrast to the conventional method in which detection of both the final electron and the photon is implied in a certain basis, here we derive the photon state as it evolves from the process itself. It is shown that the emitted photon state represents a twisted Bessel beam propagating along the field axis with a total angular momentum (TAM) projection onto this axis $\ell-\ell'$ where $\ell$ and $\ell'$ are the TAM of the initial electron and of the final one, respectively. Thus, the majority of the emitted photons turn out to be twisted with $\ell-\ell' \gtrsim 1$, even when the magnetic field reaches the critical value of $H\sim H_c$. The transitions without a change of the electron angular momentum, $\ell'=\ell$, are possible, yet much less probable. We also compare our findings with those for a spinless charged particle and demonstrate their good agreement for the transitions without change of the electron spin projection even in the critical fields, while the spin-flip transitions are generally suppressed. In addition, we argue that whereas the ambiguous choice of an electron spin operator affects the differential probability of emission, this problem can partially be circumvented for the photon evolved state because it is the electron TAM rather than the spin alone that defines the TAM of the emitted twisted photon., Comment: 20 pages, 8 figures

Although the widely used stationary Landau states describe electrons with a definite orbital angular momentum (OAM) in a magnetic field, it is the lesser known nonstationary Laguerre-Gaussian (NSLG) states that appropriately characterize vortex electrons after their transfer from free space to the field. The reason is boundary conditions lead to oscillations of the r.m.s. radius (the transverse coherence length) of the electron packet that has entered a solenoid. We comprehensively investigate properties of the NSLG states and establish their connections with the Landau states. For instance, we show that the transverse coherence length of an electron in the field usually oscillates around a value greatly exceeding the Landau state coherence length. We also discuss sensitivity of the NSLG states to a small misalignment between the propagation axis of a free electron and the field direction, which is inevitable in a real experiment. It is shown that for any state-of-the-art parameters, the corrections to the observables are negligible, and the electron OAM stays robust to a small tilt of the propagation axis. Finally, we draw analogies between a quantum wave packet and a classical beam of many particles in phase space, calculating the mean emittance of the NSLG states, which acts as a measure of their quantum nature., Comment: 17 pages, 10 figures

We argue that it is generally nonstationary Laguerre-Gaussian states (NSLG) rather than the Landau ones that appropriately describe electrons with orbital angular momentum both in their dynamics at a hard-edge boundary between a solenoid and vacuum and inside the magnetic field. It is shown that the r.m.s. radius of the NSLG state oscillates in time and its period-averaged value can significantly exceed the r.m.s. radius of the Landau state, even far from the boundary. We propose to study the unconventional features of quantum dynamics inside a solenoid in several experimental scenarios with vortex electrons described by the NSLG states. Relevance for processes in scanning and transmission electron microscopes, as well as for particle accelerators with relativistic beams is emphasized., Comment: 6 pages, 2 figures

The problem of elastic scattering of electron Airy beams on potential fields is considered for a hydrogen atom in the ground state and for Yukawa potential. It is demonstrated that the angular dependence of the scattering probability density is in general azimuthally asymmetric. When the position of the atom happens to coincide with one the minima of the probability density of the Airy beam the asymmetric pattern is represented by four separated peaks. We show that this behaviour is very sensitive to the precision with which the relative position of the atom and the minima is defined and study how uncertainty in the position measured in terms of the transverse size of the wave-packet affects observation of azimuthal asymmetry. Finally, we consider a spatially localized target and discuss the difficulties of observing the azimuthal asymmetry for targets with sizes that exceed the critical value determined by the beam parameters and the position of the target center., Comment: 10 pages, 7 figiures

In spite of the fact that there are different techniques in the creation of the high-quality liquid crystals (LCs) alignment by means of various surfaces, the azimuthal and polar anchoring energies as well as the pre-tilt angle are important parameters to all of them. Here, the modified by a certain manner aligning layers, previously formed by nonlinear laser lithography (NLL), having high-quality nano-periodic grooves on Ti surfaces, recently proposed for LC alignment was studied. The change of the scanning speed of NLL in the process of nano-structured Ti surfaces and their further modification by means of ITO-coating, and deposition of polyimide film has enabled different aligning layers, whose main characteristics, namely azimuthal and polar anchoring energies, were measured. For the modified aligning layers, the dependencies of the twist and pre-tilt angles for LC cells filled by nematic E7 ({\Delta}{\epsilon} > 0) and MLC-6609 ({\Delta}{\epsilon} < 0) were obtained. Also the contact angle for droplets of isotropic liquid (glycerol), and nematic LCs was measured for the various values of the scanning speed during the laser processing., Comment: 49 pages, 18 figures

Modelling all possible life cycles of a company in a highly competitive economic environment gives a significant advantage to the owner in his business investment activities. This article proposes and analyses a dynamic model of a company's life cycle with known action costs and transition probabilities, that can be affected by an outside influence. For this task, the Markov model was utilized. The proposed model is illustrated on a task of determining an advertising policy for a car dealership, that would increase the stock equity of a company. The result demonstrates the usefulness of a model for use in determining future actions of a company. We also review multiple models of the influence of outside factors on a company's total capitalization.

Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo (QMC) simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom (charge and flux) to achieve a nonstoquastic Hamiltonian. Such coupling can enhance performance of QA processors, extend the range of quantum simulations. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a YY interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters., Comment: 15 pages, 12 figures

It is well known that the alignment of liquid crystals can be realized by rubbing or photoalignment technologies. Recently nonlinear laser lithography was introduced as a fast, relatively low-cost method for large area nano-grating fabrication based on laser-induced periodic surface structuring. In this letter for the first time the usage of the nonlinear laser lithography as a perspective method of the alignment of nematics was presented. By nonlinear laser lithography, microgrooves with about 1 {\mu}m period were formed on Ti layer. The microstructured Ti layer was coated with oxidianiline-polyimide film with annealing of the polymer followed without any further processing. Aligning properties of microstructured Ti layers were examined with combined twist LC cell. The dependencies of the twist angle of LC cells and azimuthal anchoring energy of layers on scanning speed and power of laser beam during processing of the Ti layer were the focus of our studies as well. The maximum azimuthal anchoring energy, obtained for pure microstructured Ti layer, is comparable with photoalignment technology. It was found that the deposition of polyimide film on microstructured Ti layer leads to the gain effect of the azimuthal anchoring energy. Also, AFM study of aligning surfaces was carried out., Comment: 16 pages, 4 figures

Silicon is an excellent material for microelectronics and integrated photonics with untapped potential for mid-IR optics. Despite broad recognition of the importance of the third dimension, current lithography methods do not allow fabrication of photonic devices and functional microelements directly inside silicon chips. Even relatively simple curved geometries cannot be realized with techniques like reactive ion etching. Embedded optical elements, like in glass, electronic devices and better electronic-photonic integration are lacking. Here, we demonstrate laser-based fabrication of complex 3D structures deep inside silicon using 1 micrometer-sized dots and rod-like structures of adjustable length as basic building blocks. The laser-modified Si has a different optical index than unmodified parts, which enables numerous photonic devices. Optionally, these parts are chemically etched to produce desired 3D shapes. We exemplify a plethora of subsurface, i.e., "in-chip" microstructures for microfluidic cooling of chips, vias, MEMS, photovoltaic applications and photonic devices that match or surpass the corresponding state-of-the-art device performances.