Ab-initio theory of photoionization via resonances

Abstract

We present an ab-initio approach for computing the photoionization spectrum near autoionization resonances in multielectron 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 lineshape 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 non-trivial multi-electron atoms and molecules.We present an ab-initio approach for computing the photoionization spectrum near autoionization (AI) resonances in multi-electron systems. Recent developments in attosecondlaser technology enable probing and controlling photoionization processes, and lead to a renewed interest in ionization and related phenomena, such as high-harmonic generation and strong-field electronic dynamics 1-5 . These experimental capabilities call for ab-initio theories, which can relate the electronic structure of the sampled medium to the measured ionization spectrum. However, most existing theories require the calculation of the continuum states 6,7 (above the ionization threshold), which are difficult to obtain with high accuracy with traditional methods 8,9 . In this work, we use non-Hermitian quantum mechanics (NHQM) 10 in order to avoid the need of computing continuum states. Our theory produces a simple formula for the "Fano asymmetry parameter" [Eq. (8)], which expresses the asymmetry of the peaks in the ionization spectrum near AI resonances 11 , and a formula for the photoionization spectrum of laser-driven systems [Eq. (10)]. We relate the Autler-Townes 12 splitting of ionization spectral peaks to the existence of exceptional points 13 (EPs)-special degenerate resonances where multiple AI states share the same energy and wavefunction. We demonstrate the predictions of our theory for helium using ab-initio electronic-structure data from Ref. 14,15. By using advanced non-Hermitian quantum-chemistry algorithms 16,17 , our theory can also be applied for larger atoms and molecules.In NHQM, the time-independent Schrödinger equation is solved with outgoing boundary conditions and the resulting energy spectrum is discrete, containing real-energy bound states and complex-energy metastable states 10 . This situation is very different from traditional Hermitian quantum mechanics (HQM), where metastable (autoionizing) states are described as real-energy bound states embedded in a continuum of free states 11 . Moreover, in HQM, the transition dipole moment is real, while in NHQM, it is ge...

Complex Energies and Transition-Dipoles for the Uracil anion Shape-type Resonances from stabilization curves via Padé

“…Herein we also report the transition dipoles between the resonance states, these can be used, for example, to calculate the photoionization spectra and the Fano asymmetry parameter. 42 Thus, the information presented herein enables future investigation of uracil and the mechanisms involving DEA. Below, we shortly discuss a mechanism that may minimize radiation damage to biological systems, such as uracil, and illustrates the need for calculating complex energies as well as transition dipoles.…”

Complex Energies and Transition-Dipoles for the Uracil anion Shape-type Resonances from stabilization curves via Padé

“…This data can be used, for example, to calculate the photoionization spectra and the Fano asymmetry parameter. 42 Thus, the information presented in this work enables future investigation of uracil and the mechanisms involving DEA.…”

The RVP Method—From Real Ab-Initio Calculations to Complex Energies and Transition Dipoles

“…The state labels in the first column corresponds to the labels in Figure 6. The reference values refer to a very accurate results obtained by complex scaling (CS) and full configuration interaction (FCI) with a very large (ExTG5G) basis set [36,75]. The RVP transition dipoles are calculated using two type of truncated ExTG5G basis sets, where Basis-I is larger than Basis-II.…”

“…The reference values in Table 2 corresponds to very accurate theoretical values obtained by a CS/ FCI with a very large ExTG5G basis set, see Refs. [36,75] for details. These values can be regarded as exact since ExTG5G is highly-extended and optimised even for treating highly excited helium Rydberg states.…”