ИСТИНА

In a coherent control scheme, a quantum system is driven from an initial to a specific final state via different pathways with corresponding interfering transition amplitudes. Control of the outcome of the reaction is achieved by changing the phase between the amplitudes. In atomic ionization, coherent control is generally accomplished by using coherent light sources. Varying the phase between the electromagnetic waves, for example, between two different harmonics, leads to the control of the photoemission flux. Up to recently such processes were available only in the optical range and even used to extract relative amplitudes for photoionization into channels with different parity. In 2016 such a scheme was realized with femtosecond VUV pulses from free-electron laser (FEL) FERMI (Trieste, Italy), thereby opening a new avenue in nonlinear optics in the XUV frequency regime. The talk concentrates on a few examples of controlling the angular distribution of the photoemission generated by intense bichromatic XUV radiation, consisting of the fundamental (nonlinear second-order ionization process) and its second harmonic (linear ionization process). The interference of the two ionization paths manifests itself through a counterintuitive symmetry violation in the angular distribution of the photo-emission: for linearly polarized radiation the symmetry with respect to the plane perpendicular to the polarization vector is broken, while for circularly polarized light the axial symmetry with respect to the photon beam is violated. The degree of this asymmetry depends on the strength of the fundamental and the harmonics. It shows an oscillatory behavior as function of the relative phase of the harmonics and, in certain cases, can provide important information regarding the phases of the harmonics generated by FELs. Specific effects on the asymmetry are predicted for the case when the fundamental scans an intermediate resonance, i.e. one of the ionization paths is a two-photon resonant transition. In the resonance region, an analytic parameterization of the asymmetry can be derived as function of the photon energy within the lowest nonvanishing order of perturbation theory. Selected illustrative examples include hydrogen and neon atoms with calculations performed in perturbation theory as well as by solving the time-dependent Schödinger equation.