Dynamical Electron Vortices in Attosecond Double Photoionization of H$_2$$^*$

\textit{Kinematical} electron matter-wave vortices have been predicted in both single~[1,~2] and double~[3,~4] ionization of He. They have been observed experimentally in multiphoton single ionization of K~[5,~6]. We present in this talk results of a study of a new kind of \textit{dynamical} electron vortices~[7]. Specifically, we study electron momentum vortices in single-photon double ionization of H$_2$ by time-delayed, counter-rotating, elliptically-polarized attosecond pulses propagating either parallel or perpendicular to the molecular axis. For the parallel configuration, \textit{kinematical} vortices occur similar to those found for He~[1-4] and K~[5,~6]. For the perpendicular configuration, we find \textit{dynamical} vortex structures originating from an ellipticity-dependent interplay of $^1\Sigma^+_u$ and $^1\Pi^+_u$ continuum amplitudes. We propose a complete experiment to determine the magnitudes and relative phase of these amplitudes by varying the pulse ellipticities and time delays.\\ \\ $[1]$~J.M. Ngoko Djiokap \textit{et al.}, Phys. Rev. Lett. \textbf{115}, 113004 (2015).\\ $[2]$~J.M. Ngoko Djiokap \textit{et al.}, Phys. Rev. A \textbf{94}, 013408 (2016).\\ $[3]$~J.M. Ngoko Djiokap \textit{et al.}, Phys. Rev. A \textbf{96}, 013405 (2017).\\ $[4]$~J.M. Ngoko Djiokap and A.F. Starace J. Opt. \textbf{19}, 124003 (2017).\\ $[5]$~D. Pengel, S. Kerbstadt, D. Johannmeyer, L. Englert, T. Bayer, and M. Wollenhaupt, Phys. Rev. Lett. \textbf{118}, 053003 (2017).\\ $[6]$~D. Pengel, S. Kerbstadt, L. Englert, T. Bayer, and M. Wollenhaupt, Phys. Rev. A \textbf{96}, 043426 (2017).\\ $[7]$~J.M. Ngoko Djiokap, A.V. Meremianin, N.L. Manakov, L.B. Madsen, S.X. Hu, and A.F. Starace, Phys. Rev. A \textbf{98}, 063407 (2018).\\ \\ $^*$Research supported in part by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Award No. DE-FG03-96ER14646.