Ab-initio theory of photoionization via resonances.

We present an ab initio approach for computing the photoionization spectrum near autoionization resonances in multi-electron systems. While traditional (Hermitian) theories typically require computing the continuum states, which are difficult to obtain with high accuracy, our non-Hermitian approach requires only discrete bound and metastable states, which can be accurately computed with available quantum chemistry tools. We derive a simple formula for the absorption line shape near Fano resonances, which relates the asymmetry of the spectral peaks to the phase of the complex transition dipole moment. Additionally, we present a formula for the ionization spectrum of laser-driven targets and relate the "Autler-Townes" splitting of spectral lines to the existence of exceptional points in the Hamiltonian. We apply our formulas to compute the autoionization spectrum of helium, but our theory is also applicable for nontrivial multi-electron atoms and molecules.

Localised quantum states of atomic and molecular particles physisorbed on carbon-based nanoparticles.

The vibrational states of atomic and molecular particles adsorbed on long linear nanographenes are described using reliable theoretical potentials and appropriate vibrational (lateral) Hamiltonians. Although they rigorously obey the Bloch theorem only for infinite nanographenes, the energy patterns of the probed states closely resemble the usual Bloch bands and gaps. In addition, for any finite nanographene, these patterns are enriched by the presence of "solitary" energy levels and the "resonance" structure of the bands. While typical band states are profoundly delocalised due to a fast tunneling of the adsorbed particle, the "solitary" and "resonance" states exhibit strong localisation, similar to the behaviour of the states of the Wannier-Stark ladders in optical and semiconductor superlattices.

Helium in chirped laser fields as a time-asymmetric atomic switch.

Tuning the laser parameters exceptional points in the spectrum of the dressed laser helium atom are obtained. The weak linearly polarized laser couples the ground state and the doubly excited P-states of helium. We show here that for specific chirped laser pulses that encircle an exceptional point one can get the time-asymmetric phenomenon, where for a negative chirped laser pulse the ground state is transformed into the doubly excited auto-ionization state, while for a positive chirped laser pulse the resonance state is not populated and the neutral helium atoms remains in the ground state as the laser pulse is turned off. Moreover, we show that the results are very sensitive to the closed contour we choose. This time-asymmetric state exchange phenomenon can be considered as a time-asymmetric atomic switch. The optimal time-asymmetric switch is obtained when the closed loop that encircles the exceptional point is large, while for the smallest loops, the time-asymmetric phenomenon does not take place. A systematic way for studying the effect of the chosen closed contour that encircles the exceptional point on the time-asymmetric phenomenon is proposed.

Excitation of helium Rydberg states and doubly excited resonances in strong extreme ultraviolet fields: full-dimensional quantum dynamics using exponentially tempered Gaussian basis sets.

Recently optimized exponentially tempered Gaussian basis sets [P. R. Kapralova-Zdanska and J. Smydke, J. Chem. Phys. 138, 024105 (2013)] are employed in quantitative simulations of helium absorption cross-sections and two-photon excitation yields of doubly excited resonances. Linearly polarized half-infinite and Gaussian laser pulses at wavelengths 38-58 nm and large intensities up to 100 TW/cm(2) are considered. The emphasis is laid on convergence of the results with respect to the quality of the Gaussian basis sets (typically limited by a number of partial waves, density, and spatial extent of the basis functions) as well as to the quality of the basis set of field-free states (typically limited by the maximum rotational quantum number and maximum excitation of the lower electron). Particular attention is paid to stability of the results with respect to varying complex scaling parameter. Moreover, the study of the dynamics is preceded by a thorough check of helium energies and oscillator strengths as they are obtained with the exponentially tempered Gaussian basis sets, being also compared with yet unpublished emission wavelengths measured in electric discharge experiments.

Gaussian basis sets for highly excited and resonance states of helium.

A consistent method for optimizing Gaussian primitives for Rydberg and multiply excited helium states is designed. A novel series for the "exponentially tempered Gaussians" is introduced, which is markedly more efficient than the commonly used series of even tempered Gaussians. The optimization is made computationally feasible due to an approximate calculation of excited states using the effective one-electron Hamiltonian that is defined as Fockian from which the redundant Coulomb and exchange terms are dropped. Finally, ExTG5G and ExTG7F Gaussian basis sets are proposed. They enable calculations of the helium spectrum all the way from the ground state up to the (5, 4)(5) (1)S(e) and (6, 5)(7) (1)S(e) doubly excited resonances, respectively, mostly in the spectroscopic accuracy of 1 cm(-1).

A study of complex scaling transformation using the Wigner representation of wavefunctions.

The complex scaling operator exp(-θ ̂x̂p/ℏ), being a foundation of the complex scaling method for resonances, is studied in the Wigner phase-space representation. It is shown that the complex scaling operator behaves similarly to the squeezing operator, rotating and amplifying Wigner quasi-probability distributions of the respective wavefunctions. It is disclosed that the distorting effect of the complex scaling transformation is correlated with increased numerical errors of computed resonance energies and widths. The behavior of the numerical error is demonstrated for a computation of CO(2+) vibronic resonances.