Multi-arm spiral electron vortices in multiphoton ionization by circularly polarized pulses

Single ionization of helium by single-color two-photon absorption or two-color one-photon/two-photon absorption from two time-delayed circularly-polarized ultraviolet pulses are shown to produce ionized-electron momentum distributions in the polarization plane having respectively \emph{even}-arm (\emph{zero}- and \emph{four}-start) or \emph{odd}-arm (\emph{one}- and \emph{three}-start) spiral vortex structures. Results are obtained by both \emph{ab initio} numerical solution of the six-dimensional two-electron time-dependent Schr\"{o}dinger equation\footnote{J.M. Ngoko Djiokap \emph{et al.}, Phys.~Rev.~Lett. \textbf{115}, 113004 (2015).} and by perturbation theory. The \emph{multi}-arm patterns are sensitive to the carrier frequencies, handedness, time-delay, and relative phase of the two pulses, allowing control of electron angular distributions. \emph{Even}-arm spiral vortices have been observed in optics.\footnote{M. Harris \emph{et al.}, Opt. Commun. \textbf{106}, 161 (1994).} Thus, our \emph{even}-arm spiral electron vortices are a dramatic example of wave-particle duality. Moreover, our \emph{odd}-arm electron matter-wave vortices are consistent with recent findings~\footnote{C. A. Mancuso\emph{et al.}, Phys. Rev. A \textbf{91}, 031402(R) (2015).} in strong-field physics.