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Synopsis Intense, circularly polarized extreme-ultraviolet (XUV) and near-infrared (NIR) laser pulses are combined to double-ionize atomic helium via the oriented intermediate He+ (3p) resonance state. A strong and NIR-intensity dependent circular dichroism is accounted to a helicity dependent AC-Stark shift.

The linear polarization of x-rays, emitted from highly-charged ions, has been studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock method. Emphasis was placed especially on two-photon cascades that proceed via intermediate overlapping resonances. For such two-step cascades, we here explore how the level-splitting of the resonances affects the linear polarization of the x-rays, and whether modifications in the degree of polarization may help determine small level-splittings in multiply- and highly-charged ions, if carefully analyzed along isoelectronic sequences. Detailed calculations are carried out for the 1s2p2 Ji = 3/2 → 1s2s2p J = 1/2, 3/2 + γ1 → 1s22s Jf = 1/2 + γ1 + γ2 radiative cascade of lithium-like W71+ ions. For this cascade, a quite remarkable increase of the (degree of) linear polarization is found for the second-step γ2 photons, if the level-splitting becomes smaller than Δω 0.2 a.u. ≈ 5.4 eV. Accurate polarization measurements of x-rays may therefore be also utilized in the future to ascertain small level-splittings in multiply- and highly-charged ions.

The sequential two-photon double ionization has been analyzed for the 4d electrons of atomic xenon in the region of the giant resonance and beyond (70–200 eV), for which intense FEL radiation is available at the free electron laser FLASH. The 4d vacancies in xenon couple strongly to the autoionization continuum with lifetimes of only a few fs, and their Auger decay thus competes with the subsequent (second-and higher-step) photoionization in typical FEL pulses.

A theoretical description of the sequential three-photon triple atomic ionization is given within a model of stepwise ionization with emphasis on the angular distributions and angular correlations of the emitted electrons. The theory is applied to the photoionization of neon atom at 90.5 eV, corresponding to the experiment performed at the Free electron LASer in Hamburg (FLASH) by A. Rouzee et al (Phys. Rev. A 83 031401(R) (2011)).

Theory of the sequential two-photon double ionization of atoms in the XUV wavelength region is discussed in the context of recent experiments with the free-electron laser. Angular distributions and angular correlations of photoelectrons are analyzed within the statistical tensor formalism and examples are given for sequential two-photon double ionization of noble gases.