Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism $|{\mathrm{\Delta }}_{\mathrm{ED}}|=1$ always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.

The nonresonant, two-photon, one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the $K$-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section; for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold; for the case of Ne, for example, the cross section drops there by a factor of three.

Photoelectron angular distributions following the nonresonant two-photon $K$-shell ionization of neutral atoms are studied theoretically. Using the independent particle approximation and relativistic second-order perturbation theory, the contributions of screening and relativistic effects to the photoelectron angular distribution are evaluated. A simple nonrelativistic expression is presented for the angle-differential cross section in dipole approximation for two-photon ionization by elliptically polarized photons, and its limitations are analyzed numerically. Moreover, we show that screening effects of the inactive electrons can significantly affect the photoelectron distributions and can also lead to a strong elliptical dichroism. Numerical results are presented for the case of two-photon $K$-shell ionization of neutral Ne, Ge, Xe, and U atoms.

Nonsequential two-photon ionization of inner-shell $np$ subshell of neutral atoms by circularly polarized light is investigated. Detection of subsequent fluorescence as a signature of the process is proposed and the dependence of fluorescence degree of polarization on incident photon beam energy is studied. It is generally expected that the degree of polarization remains approximately constant, except when the beam energy is tuned to an intermediate $n^{\prime }s$ resonance. However, strong unexpected change in the polarization degree is discovered for nonsequential two-photon ionization at specific incident beam energy due to a zero contribution of the otherwise dominant ionization channel. Polarization degree of the fluorescence depends less on the beam parameters, and its measurements at this specific beam energy, whose position is very sensitive to the details of the employed theory, are highly desirable for evaluation of theoretical calculations of nonlinear ionization at hitherto unreachable accuracy.

We have conceived and built the HILITE (High-Intensity Laser-Ion Trap Experiment) Penning-trap setup for the production, confinement and preparation of pure ensembles of highly charged ions in a defined quantum state as a target for various high-intensity lasers. This enables a broad suite of laser-ion interaction studies at high photon energies and/or intensities, such as non-linear photo-ionisation studies. The setup has now been used to perform experiments at one such laser facility, namely the FLASH Free-Electron Laser at DESY in Hamburg, Germany. We describe the experimental possibilities of the apparatus, the results of the first measurements and future experiments at other laser facilities.

In multiphoton ionization of atoms, elliptical dichroism may arise in the photoelectron angular distributions due to the interference of the possible ionization pathways. We here consider the interaction of atoms with an elliptically polarized biharmonic ($\omega + 2\omega$) field which simultaneously allows one- and two-photon ionization of the atoms. The interference between these two ionization pathways introduces contributions to the elliptical dichroism in addition to the dichroism that arises from the two-photon ionization alone. We show that these additional dichroism contributions can lead to a stronger dichroism in comparison to the one arising from two-photon ionization only. We present a relativistic analysis of the corresponding photoelectron angular distributions and discuss individual contributions to the dichroic phenomena. Detailed computations have been performed for biharmonic ionization of neutral helium atoms.