Project A5

Murali Krishna Ganesa Subramanian, Roman Brannath, Ralph Welsch, Robin Santra, and Markus Drescher

We demonstrate that an external terahertz (THz) field enables the formation of interference between two distinct Auger pathways leading to the same final ionic state. The kinetic energy of Auger electrons ejected from either of two spin-orbit split one-hole states of magnesium cations is recorded. In the presence of the THz field, a clear oscillatory structure in the Auger spectrum emerges, which we find to be in very good agreement with an analytical model based on perturbation theory. For this interference to occur, the THz field has to chirp the energy of both Auger electrons and photoelectrons simultaneously, in order to create states with indistinguishable quantum properties.

Physical Review A 102, 022807 (2020)

L. Young, K. Ueda, M. Gühr, P. H. Bucksbaum, M. Simon, S. Mukamel, N. Rohringer, K. C. Prince, C. Masciovecchio, M. Meyer, A. Rudenko, D. Rolles, C. Bostedt, M. Fuchs, D. A. Reis, R. Santra, H. Kapteyn, M. Murnane, H. Ibrahim, F. Légaré, et. al.
X-ray free-electron lasers (XFELs) and table-top sources of x-rays based upon high harmonic generation (HHG) have revolutionized the field of ultrafast x-ray atomic and molecular physics, largely due to an explosive growth in capabilities in the past decade. XFELs now provide unprecedented intensity (1020 W cm−2) of x-rays at wavelengths down to ~1 Ångstrom, and HHG provides unprecedented time resolution (~50 attoseconds) and a correspondingly large coherent bandwidth at longer wavelengths. For context, timescales can be referenced to the Bohr orbital period in hydrogen atom of 150 attoseconds and the hydrogen-molecule vibrational period of 8 femtoseconds; wavelength scales can be referenced to the chemically significant carbon K-edge at a photon energy of ~280 eV (44 Ångstroms) and the bond length in methane of ~1 Ångstrom. With these modern x-ray sources one now has the ability to focus on individual atoms, even when embedded in a complex molecule, and view electronic and nuclear motion on their intrinsic scales (attoseconds and Ångstroms). These sources have enabled coherent diffractive imaging, where one can image non-crystalline objects in three dimensions on ultrafast timescales, potentially with atomic resolution. The unprecedented intensity available with XFELs has opened new fields of multiphoton and nonlinear x-ray physics where behavior of matter under extreme conditions can be explored. The unprecedented time resolution and pulse synchronization provided by HHG sources has kindled fundamental investigations of time delays in photoionization, charge migration in molecules, and dynamics near conical intersections that are foundational to AMO physics and chemistry. This roadmap coincides with the year when three new XFEL facilities, operating at Ångstrom wavelengths, opened for users (European XFEL, Swiss-FEL and PAL-FEL in Korea) almost doubling the present worldwide number of XFELs, and documents the remarkable progress in HHG capabilities since its discovery roughly 30 years ago, showcasing experiments in AMO physics and other applications. Here we capture the perspectives of 17 leading groups and organize the contributions into four categories: ultrafast molecular dynamics, multidimensional x-ray spectroscopies; high-intensity x-ray phenomena; attosecond x-ray science.
J. Phys. B: At. Mol. Opt. Phys. 51 032003

A. Baumann, S. Bazzi, D. Rompotis, O. Schepp, A. Azima, M. Wieland, D. Popova-Gorelova, O. Vendrell, R. Santra, M. Drescher

We present a joint experimental and theoretical study of the VUV-induced dynamics of H2O and its deuterated isotopologues in the first excited state (˜A1B1) utilizing a VUV-pump VUV-probe scheme combined with ab initio classical trajectory calculations. 16-fs VUV pulses centered at 161 nm created by fifth-order harmonic generation are employed for single-shot pump-probe measurements. Combined with a precise determination of the VUV pulses' temporal profile, they provide the necessary temporal resolution to elucidate sub-10-fs dissociation dynamics in the 1+1 photon ionization time window. Ionization with a single VUV photon complements established strong-field ionization schemes by disclosing the molecular dynamics under perturbative conditions. Kinetic isotope effects derived from the pump-probe experiment are found to be in agreement with our by ab initio classical trajectory calculations, taking into account photoionization cross sections for the ground and first excited state of the water cation.

Phys. Rev. A 96, 013428 (2017)

M. Sabbar, H. Timmer, Y. Chen, A. K. Pymer, Z. Loh, S. G. Sayres, S. Pabst, R. Santra, S. R. Leone
Strong-field ionization (SFI) is a key process for accessing real-time quantum dynamics of electrons on the attosecond timescale. The theoretical foundation of SFI was pioneered in the 1960s, and later refined by various analytical models. While asymptotic ionization rates predicted by these models have been tested to be in reasonable agreement for a wide range of laser parameters, predictions for SFI on the sub-laser-cycle timescale are either beyond the scope of the models or show strong qualitative deviations from full quantum-mechanical simulations. Here, using the unprecedented state specificity of attosecond transient absorption spectroscopy, we follow the real-time SFI process of the two valence spin–orbit states of xenon. The results reveal that the irreversible tunnelling contribution is accompanied by a reversible electronic population that exhibits an observable spin–orbit-dependent phase delay. A detailed theoretical analysis attributes this observation to transient ground-state polarization, an unexpected facet of SFI that cannot be captured by existing analytical models that focus exclusively on the production of asymptotic electron/ion yields.
Nature Physics (2017)

A. Karamatskou and R. Santra
The 5p two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation calculations [Wendin et al., J. Opt. Soc. Am. B 4, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the 5p shell only slightly compared to the intrachannel case.
Phys. Rev. A 95, 013415 (2017)

S. Pabst, A. Sytcheva, O. Geffert, R. Santra
We investigate the behavior of several spatial grid methods and complex absorbers for strong-field and attosecond scenarios when using the time-dependent configuration-interaction singles method to solve the multi-electron time-dependent Schrödinger equation for atoms. We compare the pseudospectral grid, finite-element, and finite-element-discrete-variable-representation (DVR) methods with each other and discuss their advantages and disadvantages. Additionally, we study the performances of complex absorbing potential (CAP) and smooth exterior complex scaling (SES) to absorb the outgoing electron. We find that SES performs generally better than CAP for calculating high-harmonic generation spectra and XUV photoelectron spectra. In both of these cases, the DVR and even more the FEM grid representations show more reliable results—especially when using SES. Both absorbers show drawbacks when calculating photoelectron spectra in the strong-field regime.
Phys. Rev. A 94, 033421 (2016)

R. Esteban Goetz, M. Merkel, A. Karamatskou, R. Santra, C. P. Koch
Photoionization with attosecond pulses populates hole states in the photoion. Superpositions of hole states represent ideal candidates for time-dependent spectroscopy, for example via pump-probe studies. The challenge consists in identifying pulses that create coherent superpositions of hole states while satisfying practical constraints. Here, we employ quantum optimal control to maximize the degree of coherence between these hole states. To this end, we introduce a derivative-free optimization method with sequential parametrization update (SPA optimization). We demonstrate the versatility and computational efficiency of SPA optimization for photoionization in argon by maximizing the coherence between the 3s and 3p0 hole states using shaped attosecond pulses. We show that it is possible to maximize the hole coherence while simultaneously prescribing the ratio of the final hole state populations.
Phys. Rev. A 94, 023420 (2016)

R. E. Goetz, A. Karamatskou, R. Santra, C. P. Koch
Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on, e.g., charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can account for specific desired properties in the photoelectron angular distribution alone, in the photoelectron spectrum, or in both. We demonstrate the method for hydrogen and then apply it to argon under strong XUV radiation, maximizing the difference of emission into the upper and lower hemispheres, in order to realize directed electron emission in the XUV regime.
Phys. Rev. A 93, 013413

R. E. Goetz, A. Karamatskou, R. Santra, C. P. Koch

Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on, e.g., charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can account for specific desired properties in the photoelectron angular distribution alone, in the photoelectron spectrum, or in both. We demonstrate the method for hydrogen and then apply it to argon under strong XUV radiation, maximizing the difference of emission into the upper and lower hemispheres, in order to realize directed electron emission in the XUV regime.

Phys. Rev. A 93, 013413 (2016)

T. Mazza, A. Karamatskou, M. Ilchen, S. Bakhtiarzadeh, A. J. Rafipoor, P. O’Keeffe, T. J. Kelly, N. Walsh, J. T. Costello, M. Meyer, R. Santra

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.

Nature Communications 6, Article no 6799 (2015)

M. Tilley, A. Karamatskou, R. Santra
We investigate the multi-photon process of above-threshold ionization for the light elements hydrogen, carbon, nitrogen, and oxygen in the hard x-ray regime. Numerical challenges are discussed and by comparing Hartree–Fock–Slater calculations with configuration–interaction–singles results we justify the mean-field potential approach in this regime. We present a theoretical prediction of two-photon above-threshold-ionization cross sections for the mentioned elements. Moreover, we study how the importance of above-threshold ionization varies with intensity. We find that for carbon, at x-ray intensities around ${{10}^{23}}\ {\rm W}\;{\rm c}{{{\rm m}}^{-2}}$, two-photon above-threshold ionization of the K-shell electrons is as probable as one-photon ionization of the L-shell electrons.
J. Phys. B: At. Mol. Opt. Phys. 48 12400

Yi-Jen Chen (陳怡蓁), Stefan Pabst, Antonia Karamatskou, Robin Santra
We present a detailed theoretical characterization of the two fundamental collective resonances underlying the xenon giant dipole resonance (GDR). This is achieved consistently by two complementary methods implemented within the framework of the configuration-interaction singles (CIS) theory. The first method accesses the resonance states by diagonalizing the many-electron Hamiltonian using the smooth exterior complex scaling technique. The second method involves a different application of the Gabor analysis to wave-packet dynamics. We identify one resonance at an excitation energy of 74 eV with a lifetime of 27 as and the second at 107eV with a lifetime of 11as. Our work provides a deeper understanding of the nature of the resonances associated with the GDR: a group of close-lying intrachannel resonances splits into two far-separated resonances through interchannel couplings involving the 4d electrons. The CIS approach allows a transparent interpretation of the two resonances as new collective modes. Due to the strong entanglement between the excited electron and the ionic core, the resonance wave functions are not dominated by any single particle-hole state. This gives rise to plasma-like collective oscillations of the 4d shell as a whole.
Phys. Rev. A 91, 032503 (2015)

S. Pabst, R. Santra
Spin–orbit interactions lead to small energy gaps between the outermost p1/2 and p3/2 shells of noble gas atoms. Strong-field pulses tunnel-ionize an electron out of either shell resulting in spin–orbit-driven hole motion. These hole dynamics affect the high-harmonic generation (HHG) yield. However, the spectral shape as well as the angular distribution of the HHG emission is not influenced by spin–orbit coupling. We demonstrate the spin–orbit effect on atomic krypton by solving the multi-electron Schrödinger equation with the time-dependent configuration-interaction singles approach. We also provide pulse parameters where this effect can be identified in experiments through an enhancement in the HHG yield as the wavelength of the strong-field pulse increases.
J. Phys. B: At. Mol. Opt. Phys. 47 124026 (2014)

E. Heinrich-Josties, S. Pabst, R. Santra
We study the state-resolved production of neon ion after resonant photoionization of Ne via the 2s-3p Fano resonance. We find that by tuning the photon energy across the Fano resonance, a surprisingly high control over the alignment of the final 2p hole along the polarization direction can be achieved. In this way, hole alignments can be created that are otherwise very hard to achieve. The mechanism responsible for this hole alignment is the destructive interference of the direct and indirect (via the autoionizing 2s−13p state) ionization pathways of 2p. By changing the photon energy, the strength of the interference varies and 2p hole alignments with ratios up to 19:1 between 2p0 and 2p±1 holes can be created—an effect normally only encountered in tunnel ionization using strong-field ir pulses. The inclusion of spin-orbit interaction does not change the qualitative feature and leads only to a reduction in the alignment by 2/3. Our study is based on a time-dependent configuration-interaction singles approach, which solves the multichannel time-dependent Schrödinger equation.
Phys. Rev. A 89, 043415 (2014)

A. Karamatskou, S. Pabst, Y.-J. Chen, R. Santra
We present an extension of the time-dependent configuration-interaction singles (TDCIS) method to the computation of the electron kinetic-energy spectrum in photoionization processes. Especially for strong and long ionizing light pulses, the detection of the photoelectron poses a computational challenge because propagating the outgoing photoelectron wave packet requires large grid sizes. Two different methods that allow for the extraction of the asymptotic photoelectron momentum are compared regarding their methodological and computational performance. The first method follows the scheme of Tong et al. [X. M. Tong, K. Hino, and N. Toshima, Phys. Rev. A 74, 031405(R) (2006)], where the photoelectron wave function is absorbed by a real splitting function. The second method following that presented by Tao and Scrinzi [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012)], measures the flux of the electron wave packet through a surface at a fixed radius. With both methods the full angle- and energy-resolved photoelectron spectrum is obtained. Combined with the TDCIS scheme, it is possible to analyze the dynamics of the outgoing electron in a channel-resolved way and, additionally, to study the dynamics of the bound electrons in the parent ion. As an application, one-photon and above-threshold ionization of argon following strong XUV irradiation are studied via energy- and angle-resolved photoelectron spectra.
Phys. Rev. A 89, 033415 (2014)

D. Krebs, S. Pabst, R. Santra
Atoms constitute relatively simple many-body systems, making them suitable objects for developing an understanding of basic aspects of many-body physics. Photoabsorption spectroscopy is a prominent method to study the electronic structure of atoms and the inherent many-body interactions. In this article, the impact of many-body effects on well-known spectroscopic features, such as Rydberg series, Fano resonances, Cooper minima, and giant resonances, is studied and related many-body phenomena in other fields are outlined. To calculate photoabsorption cross sections, the time-dependent configuration interaction singles (TDCIS) model is employed. The conceptual clearness of TDCIS in combination with the compactness of atomic systems allows for a pedagogical introduction to many-body phenomena.
Am. J. Phys. 82, 113 (2014)

S. Pabst, R. Santra
We resolve an open question about the origin of the giant enhancement in the high-harmonic generation spectrum of atomic xenon around 100 eV. By solving the many-body time-dependent Schrödinger equation with all 4d, 5s, and 5p orbitals active, we truly demonstrate the enhancement results from the collective many-body excitation induced by the returning photoelectron via two-body interchannel interactions. Without the many-body interactions, which promote a 4d electron into the 5p vacancy created by strong-field ionization, no collective excitation and no enhancement in the high-harmonic generation spectrum exist.
Phys. Rev. Lett. 111, 233005 (2013)

S. Pabst
Time-resolved investigations of ultrafast electronic and molecular dynamics were not possible until recently. The typical time scale of these processes is in the picosecond to attosecond realm. The tremendous technological progress in recent years made it possible to generate ultrashort pulses, which can be used to trigger, to watch, and to control atomic and molecular motion. This tutorial focuses on experimental and theoretical advances which are used to study the dynamics of electrons and molecules in the presence of ultrashort pulses. In the first part, the rotational dynamics of molecules, which happens on picosecond and femtosecond time scales, is reviewed. Well-aligned molecules are particularly suitable for angle-dependent investigations like x-ray diffraction or strong-field ionization experiments. In the second part, the ionization dynamics of atoms is studied. The characteristic time scale lies, here, in the attosecond to few-femtosecond regime. Although a one-particle picture has been successfully applied to many processes, many-body effects do constantly occur. After a broad overview of the main mechanisms and the most common tools in attosecond physics, examples of many-body dynamics in the attosecond world (e.g., in high-harmonic generation and attosecond transient absorption spectroscopy) are discussed.
Eur. Phys. J. Special Topics 221, 1-71 (2013)

A. Karamatskou, S. Pabst, R. Santra
If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-called adiabatic representation. This representation is commonly used in various fields of physics. For electronically bound states, the adiabatic representation yields discrete potential-energy curves that are connected by nonadiabatic transitions. When applying the adiabatic representation to optical strong-field ionization, a conceptual challenge is that the eigenstates of the instantaneous Hamiltonian form a continuum; i.e., there are no discrete adiabatic states. This difficulty can be overcome by applying an analytic-continuation technique. In this way, we obtain a rigorous classification of adiabatic states and a clear characterization of (non)adiabatic and (non)diabatic ionization dynamics. Moreover, we distinguish two different regimes within tunneling ionization and explain the dependence of the ionization probability on the pulse envelope.
Phys. Rev. A 87, 043422 (2013)

A. Wirth, R. Santra, E. Goulielmakis
The chemical properties of atoms, molecules and of more complex systems such as clusters, nanoparticles or condensed matter systems are determined by valence electrons. Real-time control of these properties requires the capability of tracing as well as of driving valence electrons on their native temporal scale of motion, that is, within tens to thousands of attoseconds. Here we detail the technique of attosecond transient absorption spectroscopy. It combines the extreme sensitivity of core-level spectroscopy with the unprecedented temporal resolution offered by the tools of attosecond technology. We use the technique to demonstrate real-time tracing and complete characterization of coherent electron motion triggered by single, double or multiple ionization of atoms exposed to intense, few-cycle pulses. Our work opens the door to high fidelity, time-domain studies and control of electron dynamics in the microcosm.
Chemical Physics 414 (2013) 149–159

A. Wirth, R. Santra, E. Goulielmakis
The chemical properties of atoms, molecules and of more complex systems such as clusters, nanoparticles or condensed matter systems are determined by valence electrons. Real-time control of these properties requires the capability of tracing as well as of driving valence electrons on their native temporal scale of motion, that is, within tens to thousands of attoseconds. Here we detail the technique of attosecond transient absorption spectroscopy. It combines the extreme sensitivity of core-level spectroscopy with the unprecedented temporal resolution offered by the tools of attosecond technology. We use the technique to demonstrate real-time tracing and complete characterization of coherent electron motion triggered by single, double or multiple ionization of atoms exposed to intense, few-cycle pulses. Our work opens the door to high fidelity, time-domain studies and control of electron dynamics in the microcosm.
Chemical Physics 414 (2013) 149–159

S. Pabst, A. Sytcheva, A. Moulet, A. Wirth, E. Goulielmakis, R. Santra
We present a fully ab initio calculations for attosecond transient absorption spectroscopy of atomic krypton with overlapping pump and probe pulses. Within the time-dependent configuration interaction singles (TDCIS) approach, we describe the pump step (strong-field ionization using a near-infrared pulse) as well as the probe step (resonant electron excitation using an extreme-ultraviolet pulse) from first principles. We extend our TDCIS model and account for the spin-orbit splitting of the occupied orbitals. We discuss the spectral features seen in a recent attosecond transient absorption experiment [ A. Wirth et al. Science 334 195 (2011)]. Our results support the concept that the transient absorption signal can be directly related to the instantaneous hole population even during the ionizing pump pulse. Furthermore, we find strong deformations in the absorption lines when the overlap of pump and probe pulses is maximum. These deformations can be described by relative phase shifts in the oscillating ionic dipole. We discuss possible mechanisms contributing to these phase shifts. Our finding suggests that the nonperturbative laser dressing of the entire N-electron wave function is the main contributor.
Phys. Rev. A 86, 063411 (2012)

S. Pabst, L. Greenman, D. A. Mazziotti, R. Santra
We investigate the relevance of multiple-orbital and multipole effects during high-harmonic generation (HHG). The time-dependent configuration interaction singles (TDCIS) approach is used to study the impact of the detailed description of the residual electron-ion interaction on the HHG spectrum. We find that the shape and position of the Cooper minimum in the HHG spectrum of argon changes significantly whether or not interchannel interactions are taken into account. The HHG yield can be underestimated by up to 2 orders of magnitude in the energy region of 30–50 eV. We show that the argument of low ionization probability is not sufficient to justify ignoring multiple-orbital contributions. Additionally, we find the HHG yield is sensitive to the nonspherical multipole character of the electron-ion interaction.
Phys. Rev. A 85, 023411 (2012)