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Pairs of entangled vortex photons can promise new prospects of application in quantum computing and cryptography. We investigate the possibility of generating such states via two-level atom emission stimulated by a single photon wave packet with a definite total angular momentum (TAM). The entangled pair produced in this process possesses well-defined mean TAM with the TAM variation being much smaller than $\hbar$. On top of that, the variation exponentially decreases with the increase in TAM of the incident photon. Our model allows one to track the time evolution of the state of the entangled pair. An experimentally feasible scenario is assumed, in which the incident photon interacts with a spatially confined atomic target. We conclude that induced emission can be used as a source of entangled vortex photons with applications in atomic physics experiments, quantum optics, and quantum information sciences. more...

The Landau states of electrons with orbital angular momentum in magnetic fields are important in the quantum theories of metals and of synchrotron radiation at storage rings, in relativistic astrophysics of neutron stars, and in many other areas. In realistic scenarios, electrons are often born inside the field or injected from a field-free region, requiring nonstationary quantum states to account for boundary or initial conditions. This study presents nonstationary Laguerre-Gaussian (NSLG) states in a longitudinal magnetic field, characterizing vortex electrons after their transfer from vacuum to the field. Comparisons with Landau states and calculations of observables such as mean energy and r.m.s. radius show that the r.m.s. radius of the electron packet in the NSLG state oscillates in time around a significantly larger value than that of the Landau state. This quantum effect of oscillations is due to boundary conditions and can potentially be observed in various problems, particularly when using magnetic lenses of electron microscopes and linear accelerators. Analogies are drawn between a quantum wave packet and a classical beam of many particles in phase space, including the calculation of mean emittance of the NSLG state as a measure of their quantum nature., Comment: 39 pages, 9 figures more...

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 more...

We present a detailed analysis of the capture and acceleration of a non-relativistic charged vortex particle (electron, positron, proton, etc.) with an orbital angular momentum in a field of an axisymmetric electromagnetic lens, typical for a linear accelerator. We account for the acceleration as well as for the inhomogeneity of both electric and magnetic fields that may arise from some real-life imperfections. We establish conditions when the wave packet can be captured and successfully transported through the lens. We describe the transition process and explain how a free Laguerre-Gaussian packet could be captured into the Landau state of the lens preserving its structure for all moments in time. Several representative examples are provided to illustrate developed formalism., Comment: 14 pages, 5 figures more...

Physics of structured waves is currently limited to relatively small particle energies as the available generation techniques are only applicable to the soft $X$-ray twisted photons, to the beams of electron microscopes, to cold neutrons, or non-relativistic atoms. The highly energetic vortex particles with an orbital angular momentum would come in handy for a number of experiments in atomic physics, nuclear, hadronic, and accelerator physics, and to generate them one needs to develop alternative methods, applicable for ultrarelativistic energies and for composite particles. Here, we show that the vortex states of in principle arbitrary particles can be generated during photon emission in helical undulators, via Cherenkov radiation, in collisions of charged particles with intense laser beams, in such scattering or annihilation processes as $e\mu \to e\mu, ep \to ep, e^-e^+ \to p\bar{p}$, and so forth. The key element in obtaining them is the postselection protocol due to entanglement between a pair of final particles and it is largely not the process itself. The state of a final particle -- be it a $\gamma$-ray, a hadron, a nucleus, or an ion -- becomes twisted if the azimuthal angle of the other particle momentum is measured with a large error or is not measured at all. As a result, requirements to the beam transverse coherence can be greatly relaxed, which enables the generation of highly energetic vortex beams at accelerators and synchrotron radiation facilities, thus making them a new tool for hadronic and spin studies. more...

The hard X-ray twisted photons and relativistic massive particles with orbital angular momentum -- vortex electrons, muons, protons, etc. -- have many potential applications in high-energy and nuclear physics. However, such states can be obtained so far mainly via diffraction techniques, not applicable for relativistic energies. Here we show that the vortex states of different particles, including hadrons, ions, and nuclei, can be generated in a large class of processes with two final particles simply by altering a postselection protocol. Thanks to entanglement and to the uncertainty relations, an evolved state of a final particle becomes twisted if the momentum azimuthal angle of the other particle is measured with a large uncertainty. We give several examples, including Cherenkov and undulator radiation, particle collisions with intense laser beams, $e\mu \to e\mu, ep \to ep$. This technique can be adapted for ultrarelativistic lepton and hadron beams of linear colliders, and it can also facilitate the development of sources of X-ray and $\gamma$-range twisted photons at storage rings and free-electron lasers., Comment: 11 pages, 2 figures more...