Observation of Rabi dynamics with a short-wavelength free-electron laser.

Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field1. They are ubiquitous in physics with applications in different areas such as photonics2, nano-electronics3, electron microscopy4 and quantum information5. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interactions within the rotating-wave approximation6. Although intense nanometre-wavelength light sources have been available for more than a decade7-9, Rabi dynamics at such short wavelengths has not been directly observed. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser10 can drive Rabi dynamics between the ground state and an excited state in helium atoms. The measured photoelectron signal reveals an Autler-Townes doublet and an avoided crossing, phenomena that are both fundamental to coherent atom-field interactions11. Using an analytical model derived from perturbation theory on top of the Rabi model, we find that the ultrafast build-up of the doublet structure carries the signature of a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond12 and few-femtosecond13 extreme-ultraviolet pulses, our results unfold opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.

Optimal photoelectron circular dichroism of a model chiral system.

We optimize the internuclear geometry and electronic structure of a model chiral system to achieve a maximal photoelectron circular dichroism (PECD) in its one-photon ionization by circularly polarized light. The electronic structure calculations are performed by the single center method, while the optimization is done using quantum alchemy employing a Taylor series expansion. Thereby, the effect of bond lengths and uncompensated charge distributions on the chiral response of the model is investigated theoretically in some detail. It is demonstrated that manipulating a chiral asymmetry of the ionic potential may enhance the dichroic parameter (i.e., the PECD) of the randomly oriented model system well beyond ß1 = 25%. Furthermore, we demonstrate that quantum alchemy is applicable to PECD despite the unusually strong coupling of spatial and electronic degrees of freedom and discuss the relative impact of the individual degrees of freedom in this model system. We define the necessary conditions for the computational design of PECD for real (non-model) chiral molecules using our approach.

Theoretical study of spin polarization in multiphoton ionization of Xe.

Spin polarization in the multiphoton above-threshold ionization of 5p3/2- and 5p1/2-electrons of Xe with intense 395nm, circularly polarized laser pulses, is investigated theoretically. For this purpose, we solve the time-dependent Schrödinger equation on the basis of spherical spinors. We, thus, simultaneously propagate the spin-up and spin-down single-active-electron wave packets, driven by the laser pulses in the ionic potential, which includes the spin-orbit interaction explicitly. The present theoretical results are in good agreement with the recent experimental results [D. Trabert et al., Phys. Rev. Lett. 120, 043202 (2018)].

Interatomic and Intermolecular Coulombic Decay.

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

Influence of the emission site on the photoelectron circular dichroism in trifluoromethyloxirane.

We report a joint experimental and theoretical study of the differential photoelectron circular dichroism (PECD) in inner-shell photoionization of uniaxially oriented trifluoromethyloxirane. By adjusting the photon energy of the circularly polarized synchrotron radiation, we address 1s-photoionization of the oxygen, different carbon, and all fluorine atoms. The photon energies were chosen such that in all cases electrons with a similar kinetic energy of about 11 eV are emitted. Employing coincident detection of electrons and fragment ions, we concentrate on identical molecular fragmentation channels for all of the electron-emitter scenarios. Thereby, we systematically examine the influence of the emission site of the photoelectron wave on the differential PECD. We observe large differences in the PECD signals. The present experimental results are supported by corresponding relaxed-core Hartree-Fock calculations.

A new route for enantio-sensitive structure determination by photoelectron scattering on molecules in the gas phase.

X-Ray as well as electron diffraction are powerful tools for structure determination of molecules. Studies on randomly oriented molecules in the gas phase address cases in which molecular crystals cannot be generated or the interaction-free molecular structure is to be addressed. Such studies usually yield partial geometrical information, such as interatomic distances. Here, we present a complementary approach, which allows obtaining insight into the structure, handedness, and even detailed geometrical features of molecules in the gas phase. Our approach combines Coulomb explosion imaging, the information that is encoded in the molecular-frame diffraction pattern of core-shell photoelectrons and ab initio computations. Using a loop-like analysis scheme, we are able to deduce specific molecular coordinates with sensitivity even to the handedness of chiral molecules and the positions of individual atoms, e.g., protons.

Photoelectron circular dichroism of a model chiral anion.

Photoelectron circular dichroism (PECD) in the one-photon detachment of a model chiral anionic system is studied theoretically by the single center method. The computed chiral asymmetry, characterized by the dichroic parameter ß1 of up to about ±3%, is in good accord with the first experimental observations of the effect in photodetachment of amino acid anions [P. Krüger and K. M. Weitzel, Angew. Chem., Int. Ed. 60, 17861 (2021)]. Our findings confirm a general assumption that the magnitude of PECD is governed by the ability of an outgoing photoelectron wave packet to accumulate characteristic chiral asymmetry from the short-range part of the molecular potential.

Photoelectron circular dichroism of O 1s-photoelectrons of uniaxially oriented trifluoromethyloxirane: energy dependence and sensitivity to molecular configuration.

The photoelectron circular dichroism (PECD) of the O 1s-photoelectrons of trifluoromethyloxirane (TFMOx) is studied experimentally and theoretically for different photoelectron kinetic energies. The experiments were performed employing circularly polarized synchrotron radiation and coincident electron and fragment ion detection using cold target recoil ion momentum spectroscopy. The corresponding calculations were performed by means of the single center method within the relaxed-core Hartree-Fock approximation. We concentrate on the energy dependence of the differential PECD of uniaxially oriented TFMOx molecules, which is accessible through the employed coincident detection. We also compare the results for the differential PECD of TFMOx to those obtained for the equivalent fragmentation channel and similar photoelectron kinetic energy of methyloxirane (MOx), studied in our previous work. Thereby, we investigate the influence of the substitution of the methyl group by the trifluoromethyl group at the chiral center on the molecular chiral response. Finally, the presently obtained angular distribution parameters are compared to those available in the literature.

Observation of Photoion Backward Emission in Photoionization of He and N_{2}.

We experimentally investigate the effects of the linear photon momentum on the momentum distributions of photoions and photoelectrons generated in one-photon ionization in an energy range of 300 eV≤E_{γ}≤40 keV. Our results show that for each ionization event the photon momentum is imparted onto the photoion, which is essentially the system's center of mass. Nevertheless, the mean value of the ion momentum distribution along the light propagation direction is backward-directed by -3/5 times the photon momentum. These results experimentally confirm a 90-year-old prediction.

Double Core-Hole Generation in O_{2} Molecules Using an X-Ray Free-Electron Laser: Molecular-Frame Photoelectron Angular Distributions.

We report on a multiparticle coincidence experiment performed at the European X-ray Free-Electron Laser at the Small Quantum Systems instrument using a COLTRIMS reaction microscope. By measuring two ions and two electrons in coincidence, we investigate double core-hole generation in O_{2} molecules in the gas phase. Single-site and two-site double core holes have been identified and their molecular-frame electron angular distributions have been obtained for a breakup of the oxygen molecule into two doubly charged ions. The measured distributions are compared to results of calculations performed within the frozen- and relaxed-core Hartree-Fock approximations.

Photoelectron circular dichroism in the multiphoton ionization by short laser pulses. III. Photoionization of fenchone in different regimes.

Photoelectron circular dichroism (PECD) in different regimes of multiphoton ionization of fenchone is studied theoretically using the time-dependent single center method. In particular, we investigate the chiral response to the one-color multiphoton or strong-field ionization by circularly polarized 400 nm and 814 nm optical laser pulses or 1850 nm infrared pulse. In addition, the broadband ionization by short coherent circularly polarized 413-1240 nm spanning pulse is considered. Finally, the two-color ionization by the phase-locked 400 nm and 800 nm pulses, which are linearly polarized in mutually orthogonal directions, is investigated. The present computational results on the one-color multiphoton ionization of fenchone are in agreement with the available experimental data. For the ionization of fenchone by broadband and bichromatic pulses, the present theoretical study predicts substantial multiphoton PECDs.

Controlling Dynamics of Postcollision Interaction.

A general scheme to get insight and to control postcollision interaction (PCI) by means of sequential double ionization with two high-frequency pulses is discussed. In particular, we propose to consider PCI of a slow photoelectron released by the pump pulse from a neutral atom with a fast photoelectron released by the time-delayed probe pulse from the created ion. This scheme is exemplified by the ab initio calculations performed for the prototypical helium atom. In order to visualize PCI effects in real time and real space, the corresponding time-dependent Schrödinger equation is solved by propagating two-electron wave packets in terms of essential stationary eigenstates of the unperturbed Hamiltonian. It is demonstrated that the exchange of energy between the slow and fast photoelectron wave packets in continuum, as well as the recapture of threshold photoelectrons owing to the PCI, can be controlled by the properties of the ionizing pulses and the time delay between them.

Photoelectron Circular Dichroism with Two Overlapping Laser Pulses of Carrier Frequencies ω and 2ω Linearly Polarized in Two Mutually Orthogonal Directions.

Using a model methanelike chiral system, we theoretically demonstrate a possibility to access photoelectron circular dichroism (PECD) by a single experiment with two overlapping laser pulses of carrier frequencies ω and 2ω, which are linearly polarized in two mutually orthogonal directions. Depending on the relative phase, the resulting electric field can be tailored to have two different rotational directions in the upper and lower hemispheres along the polarization of the ω pulse. We predict a strong forward-backward asymmetry in the emission of photoelectrons from randomly oriented samples, which has an opposite sign in the upper and lower hemispheres. The predicted PECD effect is phase and enantiomer sensitive, providing new insight in this fascinating fundamental phenomenon. The effect can be optimized by varying relative intensities of the pulses.

Photoelectron circular dichroism in the multiphoton ionization by short laser pulses. II. Three- and four-photon ionization of fenchone and camphor.

Angle-resolved multiphoton ionization of fenchone and camphor by short intense laser pulses is computed by the time-dependent single center method. Thereby, the photoelectron circular dichroism (PECD) in the three-photon resonance enhanced ionization and four-photon above-threshold ionization of these molecules is investigated in detail. The computational results are in satisfactory agreement with the available experimental data, measured for randomly oriented fenchone and camphor molecules at different wavelengths of the exciting pulses. We predict a significant enhancement of the multiphoton PECD for uniaxially oriented fenchone and camphor.

Circular Dichroism in Fluorescence Emission Following the C 1s→π* Excitation and Resonant Auger Decay of Carbon Monoxide.

Dichroism in angle-resolved spectra of circularly polarized fluorescence from freely-rotating CO molecules was studied experimentally and theoretically. For this purpose, carbon monoxide in the gas phase was exposed to circularly polarized soft X-ray synchrotron radiation. The photon energy was tuned across the C 1s→π* resonant excitation, which decayed via the participator Auger transition into the CO⁺ A ²Π state. The dichroic parameter ß1 of the subsequent CO⁺ (A ²Π → X ²Σ⁺) visible fluorescence was measured by photon-induced fluorescence spectroscopy. Present experimental results are explained with the ab initio electronic structure and dynamics calculations performed by the single center method. Our results confirm the possibility to perform partial wave analysis of the emitted photoelectrons in closed-shell molecules.

Photoelectron circular dichroism in the multiphoton ionization by short laser pulses. I. Propagation of single-active-electron wave packets in chiral pseudo-potentials.

A theoretical method to study the angle-resolved multiphoton ionization of polyatomic molecules is developed. It is based on the time-dependent formulation of the Single Center (TDSC) method and consists in the propagation of single-active-electron wave packets in the effective molecular potentials in the presence of intense laser pulses. For this purpose, the time-dependent Schrödinger equation for one electron, moving in a molecular field and interacting with an arbitrary laser pulse, is solved in spherical coordinates by an efficient numerical approach. As a test, the method is applied to the one- and two-photon ionizations of a model methane-like chiral system by circularly polarized short intense high-frequency laser pulses. Thereby, we analyze the photoelectron circular dichroism (PECD) in the momentum distribution. The considered model application illustrates the capability of the TDSC method to study multiphoton PECD in fixed-in-space and randomly oriented chiral molecules.

Generation of entanglement using a short-wavelength seeded free-electron laser.

Quantum entanglement between the degrees of freedom encountered in the classical world is challenging to observe due to the surrounding environment. To elucidate this issue, we investigate the entanglement generated over ultrafast timescales in a bipartite quantum system comprising two massive particles: a free-moving photoelectron, which expands to a mesoscopic length scale, and a light-dressed atomic ion, which represents a hybrid state of light and matter. Although the photoelectron spectra are measured classically, the entanglement allows us to reveal information about the dressed-state dynamics of the ion and the femtosecond extreme ultraviolet pulses delivered by a seeded free-electron laser. The observed generation of entanglement is interpreted using the time-dependent von Neumann entropy. Our results unveil the potential for using short-wavelength coherent light pulses from free-electron lasers to generate entangled photoelectron and ion systems for studying spooky action at a distance.

Light-induced conical intersections in polyatomic molecules: general theory, strategies of exploitation, and application.

When the carrier frequency of a laser pulse fits to the energy difference between two electronic states of a molecule, the potential energy surfaces of these states dressed by the field become energetically close and the states can couple strongly to each other. Recently, it has been predicted that for diatomic molecules these surfaces may exhibit a conical intersection induced by the laser light in the space of the nuclear internal and external coordinates. Here, we report a general theory of the light-induced conical intersections emerging in polyatomic molecules where additional internal degrees of freedom are involved in the dynamics. Freely rotating and also fixed-in-space arbitrary polyatomic molecules exposed to differently polarized optical laser pulses of resonant carrier frequency are considered. Detailed analysis of the theory shows how the light-induced conical intersections can be controlled by molecular orientation and by the carrier frequency, polarization, strength, and duration of the laser pulse. This opens the possibility to also control the ensuing non-adiabatic dynamics. Different strategies of exploitation of the light-induced conical intersections are proposed. The present theory is exemplified by utilizing the light-induced conical intersections to control photodissociation of the second electronically excited state S2 of the fixed-in-space cis-methyl nitrite CH3ONO.

Dynamic interference of photoelectrons produced by high-frequency laser pulses.

The ionization of an atom by a high-frequency intense laser pulse, where the energy of a single photon is sufficient to ionize the system, is investigated from first principles. It is shown that as a consequence of an ac Stark effect in the continuum, the energy of the photoelectron follows the envelope of the laser pulse. This is demonstrated to result in strong dynamic interference of the photoelectrons of the same kinetic energy emitted at different times. Numerically exact computations on the hydrogen atom demonstrate that the dynamic interference spectacularly modifies the photoionization process and is prominently manifested in the photoelectron spectrum by the appearance of a distinct multipeak pattern. The general theory is well approximated by explicit analytical expressions that allow for a transparent understanding of the discovered phenomena and for making predictions on the dependence of the measured spectrum on the pulse.

Electron Dynamics and Correlations During High-Order Harmonic Generation in Be.

We investigate theoretically the high-order harmonic generation in beryllium atom irradiated by a short 1850 nm linearly polarized laser pulse in the intermediate strong-field ionization regime with the Keldysh parameter of 0.85. To this end, the respective time-dependent Schrödinger equation is solved by the time-dependent restricted-active-space configuration-interaction (TD-RASCI) method. By systematically increasing the active space of included configurations, we demonstrate an individual effect of different physical processes evoked by the pulse, which, all together, significantly enrich and extend the computed high-order harmonic generation spectrum.