arXiv subjects

Dmitry Karlovets

Publications and source records attributed to Dmitry Karlovets.

14 recordsLinked to original sources

arXiv2025

Diffraction by Circular and Triangular Apertures as a Diagnostic Tool of Twisted Matter Waves

We study diffraction of twisted matter waves (electrons and light ions carrying orbital angular momentum $\ell/\hbar=0,\pm1,\pm2,\ldots$ by circular and triangular apertures. Within the scalar Kirchhoff-Fresnel framework, circular apertures preserve cylindrical symmetry and produce ringlike far-field profiles whose radii and widths depend on $|\ell|$ but are insensitive to its sign. In contrast, equilateral triangles break axial symmetry and yield structured patterns that encode both the magnitude and the sign of $\ell$. A transparent Fraunhofer mapping links detector coordinates to the Fourier plane, explaining the $(|\ell|+1)$-lobe rule and the sign-dependent rotation of the pattern. We validate these results for both ideal Bessel beams and localized Laguerre-Gaussian packets, and we cross-check them by split-step Fourier propagation of the time-dependent Schr"odinger equation. From these analyses we extract practical design rules (Fraunhofer distance, lattice pitch, detector sampling) relevant to OAM diagnostics with moderately relativistic electrons with $E_{\rm kin}\sim0.1$ to $5$ MeV and light ions with $E_{\rm kin}\sim0.1$ to $1$ MeV/u. Our results establish triangular diffraction as a simple, passive, and robust method for reading out the OAM content of structured quantum beams.

quant-ph↗

arXiv2024

Coulomb excitation of hydrogen atoms by vortex ion beams

Coulomb excitation of hydrogen atoms by vortex protons is theoretically investigated within the framework of the non--relativistic first--Born approximation and the density matrix approach. Special attention is paid to the magnetic sublevel population of excited atoms and, consequently, to the angular distribution of the fluorescence radiation. We argue that both these properties are sensitive to the projection of the orbital angular momentum (OAM), carried by the projectile ions. In order to illustrate the OAM--effect, detailed calculations have been performed for the $1s \to 2p$ excitation and the subsequent $2p \to 1s$ radiative decay of a hydrogen target, interacting with incident Laguerre--Gaussian vortex protons. The calculation results suggest that Coulomb excitation can be employed for the diagnostics of vortex ion beam at accelerator and storage ring facilities.

physics.atom-ph↗

arXiv2021

Smith-Purcell radiation of a vortex electron

We study Smith-Purcell radiation from a conducting grating generated by a vortex electron with an orbital angular momentum $\ell \hbar$, described as a generalized Laguerre-Gaussian packet, which has an intrinsic magnetic dipole moment and an electric quadrupole moment. By using a multipole expansion of the electromagnetic field of such an electron, we employ a generalized surface-current method, applicable for a wide range of parameters. The radiated energy contains contributions from the charge, from the magnetic moment, and from the electric quadrupole moment, as well as from their interference. The quadrupole contribution grows as the packet spreads while propagating, and it is enhanced for large $\ell$. In contrast to the linear growth of the radiation intensity from the charge with a number of strips $N$, the quadrupole contribution reveals an $N^3$ dependence, which puts a limit on the maximal grating length for which the radiation losses stay small. We study spectral-angular distributions of the Smith-Purcell radiation both analytically and numerically and demonstrate that the electron's vorticity can give rise to detectable effects for non-relativistic and moderately relativistic electrons. On a practical side, preparing the incoming electron's state in a form of a non-Gaussian packet with a quadrupole moment -- such as the vortex electron, an Airy beam, a Schrödinger cat state, and so on -- one can achieve quantum enhancement of the radiation power compared to the classical linear regime. Such an enhancement would be a hallmark of a previously unexplored quantum regime of radiation, in which non-Gaussianity of the packet influences the radiation properties much stronger than the quantum recoil.

quant-ph↗

arXiv2020

Vortex particles in axially symmetric fields and applications of the quantum Busch theorem

The possibilities to accelerate vortex electrons with orbital angular momentum (OAM) to relativistic energies and to produce vortex ions, protons, and other charged particles crucially depend on whether the OAM is conserved during the acceleration and on how phase space of the wave packet evolves. We show that both the OAM and a mean emittance of the packet, the latter obeying the Schrödinger uncertainty relation, are conserved in axially symmetric fields of electric and magnetic lenses, typical for accelerators and electron microscopes, as well as in Penning traps, while a linear approximation of weakly inhomogeneous fields works much better for single packets than for classical beams. We analyze quantum dynamics of the packet's rms radius $\langleρ^2\rangle$, relate this dynamics to a generalized form of the van Cittert-Zernike theorem, applicable at arbitrary distances from a source and for non-Gaussian packets, and adapt the Courant-Snyder formalism to describe the evolution of the wave packet's phase space. The vortex particles can therefore be accelerated, focused, steered, trapped, and even stored in azimuthally symmetric fields and traps, somewhat analogously to the classical angular-momentum-dominated beams. Moreover, we give a quantum version of the Busch theorem, which states how one can produce vortex electrons with a magnetized cathode during either field- or photoemission, as well as vortex ions and protons by using a magnetized stripping foil employed to change a charge state of ions. Spatial coherence of the packets plays a crucial role in these applications and we provide the necessary estimates for particles of different masses.

quant-ph↗

arXiv2020

Quantum mechanical formulation of the Busch theorem

Electron vortex beams offer unique opportunities for the study of chiral or magnetic structures in electron microscopes and of fundamental effects of quantum interference in particle physics. Immersing a cathode in a solenoid field presents a highly efficient and flexible method for the generation of vortex electron beams which is utilized at accelerators, but has not yet been realized in an electron microscope. The conditions for the generation of vortex beams with quantized orbital angular momentum from an immersed cathode in an electron microscope are discussed, and general possibilities of this technique for the production of vortex beams of other charged particles are pointed out.

physics.acc-ph↗

arXiv2019

Dynamical enhancement of nonparaxial effects in the electromagnetic field of a vortex electron

A quantum state of an electron influences its electromagnetic field. If a spatial profile of the electron wave packet is not Gaussian, the particle may acquire additional intrinsic multipole moments, which alter its field, especially at small distances. Here the fields of a vortex electron with orbital angular momentum $\ell$ are obtained in a form of a multipole expansion with an electric quadrupole term kept by using the generalized (non-paraxial) Laguerre-Gaussian beams. The quadrupole contribution arises beyond a paraxial approximation, is linearly enhanced for highly twisted packets with $|\ell| \gg 1$, and can be important for the interactions of twisted beams with bulk matter and artificial structures. Moreover, this term results in an azimuthal asymmetry of the magnetic field in a rest frame of the electron, which appears thanks to the spreading of the packet with time. Thus, somewhat contrary to physical intuition, the spreading may enhance non-paraxial phenomena. For the available electron beams, this asymmetry can in principle be reliably detected, which would be experimental evidence of a non-paraxial effect with the vortex electrons.

quant-ph↗

arXiv2019

On Wigner function of a vortex electron

We derive a relatively simple and Lorentz-invariant expression for a Wigner function of a paraxial vortex electron described as a Laguerre-Gaussian wave packet.

quant-ph↗

arXiv2018

Intrinsic multipole moments of the non-Gaussian wave packets

The charged wave packets with non-Gaussian spatial profiles are shown to possess intrinsic multipole moments. The magnetic dipole moment and the electric quadrupole moment are found for a wide class of the packets, including the vortex electrons with orbital angular momentum $\ell$, the Airy beams, the so-called Schrödinger's cat states, and their generalizations. For the packets with no phase vortices, the electric quadrupole moment is shown to grow quadratically with the packet's width, $|Q_{αβ}| \sim e\cdot σ_{\perp}^2$, while it is also $|\ell|$ times enhanced for the vortex beams. For available beams of electron microscopes, these multipole moments are relatively easily adjusted and can be quite large, which affects the packets' electromagnetic fields and also allows one to develop new diagnostic tools for materials science, atomic and molecular physics, nuclear physics, and so forth.

quant-ph↗

arXiv2018

Relativistic vortex electrons: paraxial versus non-paraxial regimes

A plane-wave approximation in particle physics implies that a width of a massive wave packet $σ_{\perp}$ is much larger than its Compton wavelength $λ_c = \hbar/mc$. For Gaussian beams or for packets with the non-singular phases (say, the Airy beams), corrections to this approximation are attenuated as $λ_c^2/σ_{\perp}^2 \ll 1$ and usually negligible. Here we show that this situation drastically changes for particles with the phase vortices associated with an orbital angular momentum $\ell\hbar$. For highly twisted beams with $|\ell| \gg 1$, the non-paraxial corrections get $|\ell|$ times enhanced and $|\ell|$ can already be as large as $10^3$. We describe the relativistic wave packets, both for vortex bosons and fermions, which transform correctly under the Lorentz boosts, are localized in a 3D space, and represent a non-paraxial generalization of the massive Laguerre-Gaussian beams. We compare such states with their paraxial counterpart paying specific attention to the relativistic effects and to the differences from the twisted photons. In particular, a Gouy phase is found to be Lorentz invariant and it generally depends on time rather than on a distance $z$. By calculating the electron packet's mean invariant mass, magnetic moment, etc., we demonstrate that the non-paraxial corrections can already reach the relative values of $10^{-3}$. These states and the non-paraxial effects can be relevant for the proper description of the spin-orbit phenomena in relativistic vortex beams, of scattering of the focused packets by atomic targets, of collision processes in particle and nuclear physics, and so forth.

quant-ph↗

arXiv2018

Non-paraxial relativistic wave packets with orbital angular momentum

One of the reasons for the tremendous success of a plane-wave approximation in particle physics is that the non-paraxial corrections to such observables as energy, magnetic moment, scattering cross section, and so on are attenuated as $λ_c^2/σ_{\perp}^2 \ll 1$ where $σ_{\perp}$ is a beam width and $λ_c = \hbar/mc$ is a Compton wavelength. This amounts to less than $10^{-14}$ for modern electron accelerators and less than $10^{-6}$ for electron microscopes. Here we show that these corrections are $|\ell|$ times enhanced for vortex particles with high orbital angular momenta $|\ell|\hbar$, which can already be as large as $10^3\hbar$. We put forward the relativistic wave packets, both for vortex bosons and fermions, which transform correctly under the Lorentz boosts, are localized in a 3D space, and represent a non-paraxial generalization of the Laguerre-Gaussian beams. We demonstrate that it is $\sqrt{|\ell|}\, λ_c \gg λ_c$ that defines a paraxial scale for such packets, in contrast to those with a non-singular phase (say, the Airy beams). With current technology, the non-paraxial corrections can reach the relative values of $10^{-3}$, yield a proportional increase of an invariant mass of the electron packet, describe a spin-orbit coupling as well as the quantum coherence phenomena in particle and atomic collisions.

quant-ph↗

arXiv2017

Quantum scattering beyond the plane-wave approximation

While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.

quant-ph↗

arXiv2016

Scattering of wave packets with phases

A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet $σ_p/\langle p\rangle$ as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum $t$ are discussed.

hep-ph↗

arXiv2011

Radiative polarization of electrons in a strong laser wave

We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulae for the cross section given by D.\,Yu. Ivanov et al [Eur.\ Phys.\ J. C \textbf{36}, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy $γ= E/mc^2 \lesssim 10$ and only for a non-head-on collision geometry. In these conditions polarization degree may achieve the values up to 65%, but the effective polarization time is found to be larger than 1\,s even for a high power optical or infrared laser with intensity parameter $ξ= |{\bf E}| m c^2/E_c \hbar ω\sim 0.1$ ($E_c = m^2 c^3/e \hbar$). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers which provide the high polarization degree represent neither helicity nor transverse polarization, that makes the use of them inconvenient in practice.

physics.acc-ph↗

arXiv2011

On the theory of polarization radiation generated in the media with sharp boundaries

Polarization radiation arising when a charged particle moves uniformly in vacuum nearby the media possessing a finite permittivity $ε(ω) = ε^{\prime} + i ε^{\prime \prime}$ and sharp boundaries is considered. The method is developed in which polarization radiation is represented as a field of the current density induced in matter by the field of the moving charge. Solution is found for a problem of radiation arising when the particle moves along the axis of the cylindrical channel inside a thin screen of a finite radius and a finite permittivity. Depending on parameters of the problem, the solution obtained describes different types of polarization radiation: Cherenkov, transition, and diffraction radiations. In particular, when the channel radius approaches zero and external radius of the screen tends to infinity the expression found for radiated energy coincides with Pafomov solution for transition radiation in a slab. In another special case of ideal conductivity, the result obtained coincides with the one for diffraction radiation generated by the particle in the round hole in the thin screen. Solution is found for a problem of radiation generated when the charge moves nearby a rectangular screen possessing a finite permittivity. The expression derived describes diffraction and Cherenkov mechanisms of radiation and takes into account the multiple reflections of radiation inside the screen. Solution is also found for a problem of radiation generated when the particle moves nearby a thin grating consisting of a finite number of rectangular strips possessing a finite permittivity and separated with vacuum gaps (Smith-Purcell radiation). In the special case of an ideally conducting grating, the formula derived for radiated energy coincides with the one of the well-known surface current model.

physics.class-ph↗