Quantum mechanically, photoionization can be fully described by the complex photoionization amplitudes that describe the transition between the ground state and the continuum state. Knowledge of the value of the phase of these amplitudes has been a central interest in photoionization studies and newly developing attosecond science, since the phase can reveal important information about phenomena such as electron correlation. We present a new attosecond-precision interferometric method of angle-resolved measurement for the phase of the photoionization amplitudes, using two phase-locked extreme ultraviolet pulses of frequency $\omega$ and $2\omega$, from a free-electron laser. Phase differences $\mathrm{\Delta }\tilde{\eta }$ between one- and two-photon ionization channels, averaged over multiple wave packets, are extracted for neon $2p$ electrons as a function of the emission angle at photoelectron energies 7.9, 10.2, and 16.6 eV. $\mathrm{\Delta }\tilde{\eta }$ is nearly constant for emission parallel to the electric vector but increases at 10.2 eV for emission perpendicular to the electric vector. We model our observations with both perturbation and ab initio theory and find excellent agreement. In the existing method for attosecond measurement, reconstruction of attosecond beating by interference of two-photon transitions (RABBITT), a phase difference between two-photon pathways involving absorption and emission of an infrared photon is extracted. Our method can be used for extraction of a phase difference between single-photon and two-photon pathways and provides a new tool for attosecond science, which is complementary to RABBITT.

Coherent control of the photoelectron angular distribution (PAD) in ionization by a bichromatic circularly polarized field is theoretically studied in neon in the photon energy range 16–20 eV. The breakdown of the PAD axial symmetry with respect to the light propagation direction is analyzed. The coherent control of the PAD manifests itself through: (1) a change from a one-lobe to a three-lobe shape, respectively, for co- and counter-rotating harmonics, (2) a variation of the polar asymmetry with the light frequency, and (3) a rotation of the PAD around the direction of the beam depending on the relative phase between the harmonics. Tuning the lowest harmonic at the $2p^{5}3s$ or $2p^{5}4s$ intermediate excited states strongly influences the PAD. In contrast to atomic hydrogen and the alkali atoms, the cases of equal and opposite helicity are not related in neon. Features of a conjugate polarization setup, when one harmonic is linearly polarized while the other one is circularly polarized, are also discussed.

Attosecond photoelectron interferometry based on the combination of an attosecond pulse train and a synchronized infrared field is a fundamental technique for the temporal characterization of attosecond waveforms and for the investigation of electron dynamics in the photoionization process. In this approach, the comb of extreme ultraviolet harmonics typically lies above the ionization threshold of the target under investigation, thus releasing a photoelectron by single-photon absorption. The interaction of the outgoing photoelectron with the infrared pulse results in the absorption or emission of infrared photons, thereby creating additional peaks in the photoelectron spectrum, referred to as sidebands. While, in the absence of resonances in the first ionization step, the phases imparted on the photoionization process evolve smoothly with the photon energy, the presence of intermediate resonances imprints a large additional phase on the outgoing photoelectron wave packet. In this paper, using a comb of harmonics below and above the ionization threshold of neon, we investigate the effect of intermediate bound excited states on attosecond photoelectron interferometry. We show that the phase of the oscillations of the sidebands and their angular distributions are strongly affected by such resonances. By slightly tuning the photon energies of the extreme ultraviolet harmonics, we show how the contributions of selected resonances can be enhanced or suppressed.

A fundamental phenomenon of coherent control is investigated theoretically using the example of neon photoionization by the bichromatic field of a free-electron laser. A system exposed to coherent fields with commensurable frequencies loses some symmetry, which manifests itself in the angular distribution and spin polarization of the electron emission. We predict several such effects, for example, the violation of symmetry with respect to the plane perpendicular to the polarization vector of the second harmonic and the appearance of new components of spin polarization. Furthermore, we predict a very efficient control of spin polarization via manipulation of the phase between the harmonics. Experimental observation of these effects is accessible with modern free-electron lasers operating in the extreme ultraviolet wavelength regime.

Modern free-electron lasers generate a highly intense polarized radiation which initiates a sequence of ionization and decay events. Their probability depends on the polarization of each involved state as a function of time. Its complete account is limited by the fact that a state can be formed in various ways. Here we present an equivalent of rate equations for population that completely accounts for polarization of radiation formulated in terms of statistical tensors. To illustrate our approach we theoretically consider the sequential photoionization of krypton by an intense extreme ultraviolet femtosecond pulse for photon energies below the $3d$-shell excitation threshold. The calculations of the ion yields, photoelectron spectra, and ionic polarization for various photon fluences are presented and the role of the polarization is discussed.

We investigate features of electron emission from atoms in the field of the fundamental and second harmonic of a laser in conditions relevant to those realized in free-electron lasers. General expressions for the angular anisotropy and photoelectron spin polarization are obtained. These expressions are used for describing of the ionization of the valence shell of inert gas atoms and illustrated by calculations for neon. The possibility of control over the electron emission characteristics by varying the relative phase between harmonic (i.e., realization of one of the forms of the coherent control) is considered.