Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.
We study spin effects in twisted-electron propagation through the entrance or exit region of an axially symmetric magnetic coil. Starting from the Foldy-Wouthuysen reduction of the Dirac equation, we derive a paraxial spinor equation in which the longitudinally varying solenoidal field produces, in addition to the usual diagonal Zeeman term, a transverse Pauli coupling proportional to the fringe-field gradient. The scalar transverse dynamics is treated exactly by the Ermakov mapping, which absorbs the longitudinally dependent focusing into a metaplectic scaling transformation and reduces the orbital evolution to that of a stationary two-dimensional oscillator. On this background, the transverse Pauli term is treated perturbatively and yields an explicit first-order correction for arbitrary realistic solenoidal profiles. Axial symmetry implies conservation of the total projection of angular momentum, so each spin flip is accompanied by a compensating one-quantum change of orbital angular momentum. In addition, the linear coordinate structure of the perturbation restricts the first-order dynamics to at most two neighboring radial sidebands for each incoming oscillator component. We derive the corresponding transition amplitudes and show how their phases are governed jointly by the Ermakov accumulation and the diagonal spin-orbital rotation. The resulting framework provides a direct way to quantify spin-orbit mixing of twisted electrons in realistic magnetic lenses and solenoidal beam-line elements, and it identifies a route toward controlled spin-OAM conversion in engineered sequences of magnetic-field edges.
Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate moment of inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect, quickly averages to zero in classical ensembles since the flipping period varies significantly upon approaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermal asymmetric nanorotors and show that classically forbidden tunneling gives rise to persistent tennis racket dynamics, in stark contrast to the classical expectation. We characterize this effect, demonstrating that quantum coherent flipping dynamics can persist even in the regime where millions of angular momentum states are occupied. This persistent flipping offers a promising route for observing and exploiting quantum effects in rotational degrees of freedom for molecules and nanoparticles.
We study the material requirements for transferring the total-angular-momentum (TAM) projection of a twisted photon to the orbital angular momentum (OAM) of a photoelectron emitted from an
n-type semiconductor surface. Within a single-valley effective-mass model of surface photoemission, we calculate OAM-resolved spectra for GaAs, InSb,
InAs0.34Sb0.66, and
Hg0.76Cd0.24Te irradiated by twisted photons with Laguerre--Gaussian--like momentum profile. The OAM transfer is characterized by the mean electron OAM, its root-mean-squared width, and the fraction of electrons with OAM-projection equal to the photon TAM-projection. Efficient transfer requires the transverse momentum of the conduction electron to be much smaller than the transverse momentum width of the photon, which favors low temperatures, small conduction-band effective masses, and shallow donor levels. GaAs is less favorable within the present model because of its larger effective mass and deeper donor levels. We also discuss the demanding photon-wave packet parameters, possible extensions to Dirac and Weyl semimetals, and post-emission OAM selection. Although the generation of vortex electrons with a vanishing OAM uncertainty via photoemission seems challenging, we argue that it is still possible to generate single-electron vortex states with a finite OAM dispersion.
Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter
b. Since the total final transverse momentum
P⊥ is no longer fixed, we focus on how the differential cross section depends on
P⊥. We emphasize that non-trivial
P⊥-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter
b plays a key role in many
P⊥-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.