# Jakub BendaCharles University in Prague | CUNI · Institute of Theoretical Physics

Jakub Benda

Doctor of Philosophy

Multiphoton ionization of molecules and RABITT

## About

44

Publications

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252

Citations

Introduction

At the moment I focus on photoionization of molecules with the R-matrix method.
Before, I performed calculation of electron-hydrogen scattering for astrophysical applications with emphasis on higher excitations.
I am also involved in development of a public ECS code (https://sourceforge.net/projects/hecs/), and the UKRmol+ and RMT R-matrix packages (https://www.ukamor.com/).

**Skills and Expertise**

Additional affiliations

Education

October 2010 - September 2012

October 2007 - June 2010

## Publications

Publications (44)

We propose the use of Sturmian basis set for relativistic atomic structure calculations. We describe a numerically stable algebraic calculation of one- and two-particle radial integrals. The method is illustrated on the basis set independent calculation of energies, electric dipole moments, hyperfine integrals and parity non-conserving (PNC) amplit...

We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to c...

We employ the recently developed multi-photon R-matrix method for molecular above-threshold photoionization to obtain second-order ionization amplitudes that govern the interference in RABITT experiments. This allows us to extract RABITT time delays that are in better agreement with non-perturbative time-dependent simulations of this process than t...

Through solution of the multielectron, semi-relativistic, time-dependent Schr\"{o}dinger equation, we show that angular streaking produces strongly spin-polarized electrons in a noble gas. The degree of spin polarization increases with the Keldysh parameter, so that angular streaking -- ordinarily applied to investigate tunneling -- may be repurpos...

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics from gas to condensed phase with attosecond temporal resolution. It has, however, not yet been able to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attose...

We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to c...

Through solution of the multielectron, semirelativistic, time-dependent Schrödinger equation, we show that angular streaking produces strongly spin-polarized electrons in a noble gas. The degree of spin polarization increases with the Keldysh parameter, so that angular streaking—ordinarily applied to investigate tunneling—may be repurposed to gener...

The ab initio “R-matrix with time” method has recently been extended to allow simulation of fully non-perturbative multielectron processes in molecules driven by ultra-short arbitrarily polarized strong laser fields. Here we demonstrate the accuracy and capabilities of the current implementation of the method for two targets: we study single- and m...

We formulate a time-independent method for calculation of multi-photon transition matrix elements based on the ab initio molecular R-matrix method, implemented within the molecular R-matrix suite UKRmol+ [1]. With this method we study the above-threshold ionization of atoms and small molecules, focusing-among other topics-on the absorption of a pho...

Validation results for the molecular R-matrix with time: Two- and four-photon weak- and strong-field ionization of hydrogen. Time delays extracted from a simulated RABBITT experiment. Results are compared to earlier calculations by other authors.

We employ the R matrix with time-dependence method to study attosecond angular streaking of F−. Using this negative ion, free of long-range Coulomb interactions, we elucidate the role of short-range electron correlation effects in an attoclock scheme. Through solution of the multielectron time-dependent Schrödinger equation, we aim to bridge the ga...

We employ the R-matrix with time-dependence method to study attosecond angular streaking of F$^-$. Using this negative ion, free of long-range Coulomb interactions, we elucidate the role of short-range electron correlation effects in an attoclock scheme. Through solution of the multielectron time-dependent Schrodinger equation, we aim to bridge the...

Synopsis
We present results of the first calculations using the variational ab initio molecular R-matrix with time approach. We have calculated two and four-photon ionization cross sections for H 2 and studied the effects of electron correlation and choice of the Gaussian atomic basis sets. Our results are compared with earlier calculations.

Synopsis
We describe and illustrate a number of recent developments of the atomic and molecular ab initio R-matrix suites for both time-dependent calculations of ultrafast laser-induced dynamics and time-independent calculations of photoionization and electron scattering.

Recent experiments [D. Pengel, S. Kerbstadt, L. Englert, T. Bayer, and M. Wollenhaupt, \href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.043426}{{\PRA} {\bf 96} 043426 (2017)}] have measured the photoelectron momentum distribution for three-photon ionization of potassium by counter-rotating circularly polarized 790-nm laser pulses. Th...

Recent experiments [D. Pengel, S. Kerbstadt, L. Englert, T. Bayer, and M. Wollenhaupt, Phys. Rev. A 96 043426 (2017)] have measured the photoelectron momentum distribution for three-photon ionization of potassium by counter-rotating circularly polarized 790-nm laser pulses. The distribution displays spiral vortices, arising from the interference of...

UKRmol+ is a new implementation of the time-independent UK R-matrix electron–molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian — B-spline basis functions to represent the continuum and improved configuration and...

RMT is a programme which solves the time-dependent Schrödinger equation for general, multielectron atoms, ions and molecules interacting with laser light. As such it can be used to model ionization (single-photon, multiphoton and strong-field), recollision (high-harmonic generation, strong-field rescattering) and, more generally, absorption or scat...

Collisions of low energy electrons with molecules are important for understanding many aspects of the environment and technologies. Understanding the processes that occur in these types of collisions can give insights into plasma etching processes, edge effects in fusion plasmas, radiation damage to biological tissues and more. A radical update of...

Validation of the molecular "R-matrix with time" implementation on multi-photon photionization of small molecules.

Application of the molecular "R-matrix with time" to photoionization of small molecules. One-, two- and four-photon cross sections compared to different computational approaches. Study of multi-photon photoionization yield distribution of individual H₂O orbitals.

UKRmol+ is a new implementation of the UK R-matrix electron-molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian -- B-spline basis functions to represent the continuum and improved configuration and Hamiltonian gene...

Collisions of low energy electrons with molecules are important for understanding many aspects of the environment and technologies. Understanding the processes that occur in these types of collisions can give insights into plasma etching processes, edge effects in fusion plasmas, radiation damage to biological tissues and more. A radical update of...

RMT is a program which solves the time-dependent Schrodinger equation for general, multielectron atoms, ions and molecules interacting with laser light. As such it can be used to model ionization (single-photon, multi-photon and strong-field), recollision (high-harmonic generation, strong-field rescattering), and more generally absorption or scatte...

Relativistic quantum electrodynamics, QED, is a theory unifying quantum mechanics, special theory of relativity, and classical electrodynamics.

In this chapter, we focus on hydrogen-like atoms and their spectral structure in great depth. We show that the spectrum consists of a gross structure resulting from the electrostatic interaction between an electron and the nucleus, a fine structure arising from the spin-orbit interaction, and a hyperfine structure stemming from the spin-spin intera...

In the previous chapters, we thoroughly investigated the simplest atom of all—the hydrogen atom. We have found that, owing to the existence of a sufficient number of integrals of motion, one can solve its energy spectrum exactly. Unfortunately, one cannot determine exactly the spectrum of helium nor of any of the heavier atoms. Nevertheless, we kno...

In this chapter, we introduce the fundamental principles of quantum mechanics. We commence by discussing the famous Stern-Gerlach experiments for a particle with the spin 1∕2 as several key quantum mechanical phenomena may be well understood thereof. Using these very experiments as an example, we then illustrate how the basic principles are incorpo...

However light and elegant the mathematical apparatus of quantum mechanics appears, we can solve exactly only very few physically interesting problems with it. Therefore, we need to opt for appropriate approximations when facing the remaining vast majority of quantum-mechanical problems. In this chapter, we will introduce two basic approaches—the va...

In this chapter, we introduce the basic principles and applications of quantum electrodynamics while describing the motion of a particle within the nonrelativistic approximation. We start by showing how classical electrodynamics may be cast into the Hamilton formalism, the subsequent transition from classical to quantum electrodynamics being then s...

In this chapter, we focus on a topic usually called the application of algebraic methods or Lie algebras within quantum mechanics. We have already demonstrated that one can determine very efficiently the spectrum of the harmonic oscillator owing to the closure of the set of three operators, namely the Hamiltonian \(\hat{\mathsf{H}}\) and the ladder...

This book highlights the power and elegance of algebraic methods of solving problems in quantum mechanics. It shows that symmetries not only provide elegant solutions to problems that can be solved exactly, but also substantially simplify problems that must be solved approximately.
Furthermore, the book provides an elementary exposition of quantum...

This thesis focuses on calculations of the cross sections and other scattering
quantities that characterize the outcome of collisions of electrons with hydrogen atoms.
For the chosen energy range and atomic transitions the scattering process is solved within
the non-relativistic quantum mechanics by discretization of the Schrödinger equation in
the...

In this article we present converged datasets containing scattering data for collisions of electrons on the atomic hydrogen for total energies below the n=4 excitation threshold. The data have been obtained from an ab initio solution of the two-electron Schrödinger equation in the B-spline basis with the exterior complex scaling boundary condition...

For total energies below the ionization threshold it is possible to dramatically reduce the computational burden of the solution of the electron-atom scattering problem based on grid methods combined with the exterior complex scaling. As in the R-matrix method, the problem can be split into the inner and outer problem, where the outer problem consi...

Textbook on basics of quantum physics and electrodynamics.

We provide an updated version of the program hex-ecs originally presented in Comput. Phys. Commun. 185 (2014) 2903–2912. The original version used an iterative method preconditioned by the incomplete LU factorization (ILU), which–though very stable and predictable–requires a large amount of working memory. In the new version we implemented a “separ...

We introduce and demonstrate a new high performance image reconstruction method for super-resolution structured illumination microscopy based on maximum a posteriori probability estimation (MAP-SIM). Imaging performance is demonstrated on a variety of fluorescent samples of different thickness, labeling density and noise levels. The method provides...

While collisions of electrons with hydrogen atoms pose a well studied and in some sense closed problem, there is still no free computer code ready for “production use”, that would enable applied researchers to generate necessary data for arbitrary impact energies and scattering transitions directly if absent in on-line scattering databases. This is...

Being motivated by the applied researchers’ persisting need for accurate scattering data for the collisions of electrons with hydrogen atoms, we developed a computer package-Hex-that is designed to provide trustworthy results for all basic discrete and continuous processes within non-relativistic framework. The package consists of several computati...

Most information of the dynamics of events on the Sun comes from direct observations. For a correct evaluation and interpretation of the observed data, also the low-level quantum information on the collisions of free electrons with hydrogen atoms is necessary, including the collision rates and/or raw cross sections. In this article we present a par...

Poster for the DAMOP 2012 conference in Orange County, CA.

## Projects

Projects (4)

Development of a computationally efficient stationary method based on the R-matrix approach for multi-photon (perturbative) ionisation of atoms and molecules and its application to RABITT and similar processes.

1.3 version release featuring (September 2022):
- reintroduction of SCOP method
- estimates for ionisation fragmentation in absence of experimental data
- add isotope option
- outsourcing jobs to HPC
- automation of parameter variation
- latest UKRmol+

Development of software for the accurate description of atoms and
molecular systems in intense, ultra-short light fields with arbitrary polarisation. This involves generalising and interfacing two world-leading suites of codes: the R-matrix with time-dependence codes (RMT) for ultra-fast atomic dynamics and the UKRmol+ suite for electron/positron scattering and photoionisation processes in
molecules.