Special reduction formulae for bipolar harmonics with higher ranks of internal spherical functions are derived, which will be useful in problems involving multiple expansions in spherical functions. Together with irreducible tensor operator techniques these results provide a new and effective approach, which enables one to extract the geometrical and dynamical factors from the cross sections of atomic processes with polarized particles with an accurate account of all the polarization effects. The angular distribution of polarized electrons and the circular dichroism in photoionization of polarized atoms with an arbitrary angular momentum are presented in an invariant vector form. A specific circular dichroism, which is caused by the correlation of electron and atom orientations, is discussed. The angular distribution of escaping electrons in double photoionization of unpolarized atom is presented in a simple form. A convenient parametrization is proposed for describing the dependence of the photoprocess cross sections on the polarization state of the photon beam.

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Multistart spiral vortex patterns are predicted for the electron momentum distributions in the polarization plane following ionization of the helium atom by two time-delayed circularly polarized ultrashort laser pulses. For two ultraviolet (UV) pulses having the same frequency (such that two photons are required for ionization), single-color two-photon interferometry with corotating or counter-rotating time-delayed pulses is found to lead respectively to zero-start or four-start spiral vortex patterns in the ionized electron momentum distributions in the polarization plane. In contrast, two-color one-photon plus two-photon interferometry with time-delayed corotating or counter-rotating UV pulses is found to lead respectively to one-start or three-start spiral vortex patterns. These predicted multistart electron vortex patterns are found to be sensitive to the carrier frequencies, handedness, time delay, and relative phase of the two pulses. Our numerical predictions are obtained by solving the six-dimensional two-electron time-dependent Schrödinger equation (TDSE). They are explained analytically using perturbation theory (PT). Comparison of our TDSE and PT results for single-color two-photon processes probes the role played by the time-delay-dependent ionization cross channels in which one photon is absorbed from each pulse. Control of these cross channels by means of the parameters of the fields and the ionized electron detection geometries is discussed.

Manakov, N. L.; Hu, S. X.; Madsen, L. B.; and Starace, Anthony F., "Kinematical vortices in double photoionization of helium by attosecond pulses" (2017 Two-armed helical vortex structures are predicted in the two-electron momentum distributions produced in double photoionization (DPI) of the He atom by a pair of time-delayed elliptically polarized attosecond pulses with opposite helicities. These predictions are based upon both a first-order perturbation theory analysis and numerical solutions of the two-electron, time-dependent Schrödinger equation in six spatial dimensions. The helical vortex structures originate from Ramsey interference of a pair of ionized two-electron wave packets, each having a total angular momentum of unity, and appear in the sixfold differential DPI probability distribution for any energy partitioning between the two electrons. The vortex structures are exquisitely sensitive to the time delay between the two pulses, their relative phase, their ellipticity, and their handedness; moreover, they occur in a variety of electron detection geometries. However, the vortex structures only occur when the angular separation β = cos −1 (p 1 ·p 2 ) between the electron momenta p 1 and p 2 is held fixed. The vortex structures can also be observed in the fourfold differential DPI probability distribution obtained by averaging the sixfold differential probability over the emission angles of one electron. Such kinematical vortices are a general phenomenon that may occur in any ionization process, initiated by two time-delayed short pulses with opposite ellipticities, for particular detection geometries.

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