Atomic Physics 2018

A large number of effects influence the photo-emission delays seen in RABITT spectrograms on scales of 10 attoseconds and more. Two dominant effects are scattering during emission and electron correlation. In both processes system-specific properties are intertwined with the IR probe pulse. Scattering - if considered single electron - is the simpler of the two cases, provided the potential can be plausibly modeled. Correlation in the initial state and during scattering can have further dramatic impact. As a further point, RABITT was conceived as a perturbative method, but the validity range for perturbation theory is found to be quite narrow. The points above will be illustrated on various examples, mostly by increasingly realistic numerical solutions for the popular CO2 molecule.

Refractive lenses and prisms are indispensable tools used to control the properties of light beams at visible, infrared and ultraviolet wavelengths. It is therefore desirable to develop XUV refractive lenses, which is, however, hindered by the strong absorption in this spectral region. Here we demonstrate control over the refraction of XUV pulses using a gas jet with a density gradient across the XUV beam profile. In a first set of experiments, a gas-phase prism is demonstrated that leads to deflection of broadband attosecond pulse trains according to the frequency-dependent refractive index in the XUV regime. The observed deflection of XUV radiation is particularly large in the vicinity of atomic resonances. In a second set of experiments, we exploit this deflection to demonstrate a gas-phase XUV refractive lens, which allows us to focus narrowband HHG pulses. The focal length can be controlled by varying the gas type and the gas pressure. In comparison to reflective mirrors that are used to focus XUV pulses, our gas-phase lens provides further advantages, as it preserves the XUV propagation direction and is immune to damage. In combination with a Fresnel zone plate, XUV refractive lenses may be used to focus attosecond pulses to nanometer spot sizes.

The semiclassical initial value formalism to solve the time-dependent Schroedinger equation using classical trajectories will be reviewed. Special focus will be laid on the multi-trajectory Herman-Kluk method [1] and Heller's thawed Gaussians [2]. The connection of the two methods by a Gaussian integration will be stressed. Applications of the semiclassical formalism to the dynamics of interacting electrons will then be presented. Firstly, we use the classical dynamics of two interacting electrons in a harmonic confinement (quantum dot) to extract semiclassical spectra [3]. Secondly, we show that the difference between singlet and triplet initial state dynamics in electron-electron scattering is captured by the semiclassical Herman-Kluk initial value approach [4], in contrast to the thawed Gaussian as well as a classical Wigner approach. Finally, we turn to the dynamics of electrons in external fields and review the semiclassical treatment of localization by half-cycle pulse driving [5] and the dominant interaction Hamiltonian approach to high-order harmonic generation [6,7]. References: [1] M. Herman and E. Kluk, Chem. Phys. 91, 27 (1984) [2] E. J. Heller, J. Chem. Phys. 62, 1544 (1975) [3] F. Grossmann and T. Kramer, J. Phys. A 44, 445309 (2011) [4] F. Grossmann, M. Buchholz, E. Pollak and M. Nest, Phys. Rev. A 89, 032104 (2014) [5] S. Yoshida, F. Grossmann, E. Persson and J. Burgdoerfer, Phys. Rev. A 69, 043410 (2004) [6] C. Zagoya, C.-M. Goletz, F. Grossmann, and J.-M. Rost, Phys. Rev. A 85, 041401(R) (2012) [7] C. Zagoya, C.-M. Goletz, F. Grossmann, and J.-M. Rost, New Journal of Phys. 14, 093050 (2012)

Several years ago, we developed a formulation of the time-dependent Schrodinger equation (TDSE) using complex-valued classical trajectories. The method has a number of appealing features: 1) it has a simple and rigorous derivation from the TDSE with a precisely formulated approximation; 2) it treats classically allowed and classically forbidden processes on the same footing; 3) it allows the introduction of arbitrary time-dependent external fields into the dynamics seamlessly and rigorously. This talk will begin with a review of the method and then focus on recent applications including nonadiabatic dynamics, optical exciation, wavepacket revivals and strong field tunneling ionization and high harmonic generation. [1] Y. Goldfarb, I. Degani and D.J. Tannor, J. Chem. Phys. 125, 231103 (2006). [2] N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517-8 (2012). [4] W. Koch and D. J. Tannor, Chem. Phys. Lett. 683, 306 (2017). [5] W. Koch and D. J. Tannor, manuscript in preparation.

I will discuss our experiments on the observation of pronounced channel closings in atomic and molecular excitation in strong laser fields. Besides the rigorous theoretical explanation of atomic excitation by time dependent Schrödinger equation calculations, we adopted the frustrated tunneling model and the SFA approach to gain insight in the excitation process. We were finally able to reconcile the multiphoton and frequency pictures [1]. In contrast to the atomic case experimental and theoretical results on strong field molecular excitation are scarce. First experimental data on strong-field excited homo-nuclear molecules will be presented and will be compared with theoretical results from the group of A. Saenz [2]. [1] H. Zimmermann, S. Patchkovskii, M. Ivanov, and U. Eichmann Phys. Rev. Lett. 118, 013003 ( 2017) [2] S. Meise, U. Eichmann, A Saenz et al., to be published

Enhanced ionization, i.e. a strongly increased ionization probability found for specific internuclear separations, is one of the most paradigmatic molecular strong-field effects. This phenomenon has been investigated experimentally and theoretically for a number of molecules, especially the hydrogen molecular ion and neutral hydrogen molecules. Recently, strong experimental evidence was even found that enhanced ionization can even occur simultaneously, i.e. more than one carbon-hydrogen bond may break in corresponding organic molecules. Besides this plethora of studies, only few investigations have been devoted to heteronuclear systems. Motivated by a combined experimental and theoretical study on HeH+ in ultrashort intense laser pulses, we have now performed fully correlated calculations of this molecule in intense laser pulses by solving the corresponding time-dependent Schrödinger equation in full dimensionality for fixed, but varying internuclear separation. A pronounced influence of the carrier-envelope phase of the laser is found that can lead to a variation of the products by a factor 50 or more! The detailed analysis reveals an interesting electron dynamics that will be presented and discussed in this talk.

Recently, in the tunneling regime of strong field ionization an unexpected Coulomb field eect has been identified by numerical solution of time-dependent Schr¨odinger equation in photoelectron spectra in the upper energy range of the direct electrons. We investigate the mechanism of the Coulomb effect employing a classical theory with Monte Carlo simulations of trajectories, and a quantum theory based on the generalized eikonal approximation for the continuum electron. The effect is shown to have a classical nature and is due to momentum space bunching of photoelectrons released not far from the peak of the laser field. Moreover, our analysis reveals specific features of the angular distribution of high energy direct electrons which can be employed for molecular imaging. For the H+2 molecule as an example we show the signatures of the molecule orientation and the molecular structure in the investigated angular distribution.

Using the phase space path-integral formalism we derive an expression for the momentum space matrix element of the exact time-evolution operator of an atom in the presence of a strong laser field [1]. We present it in the form of a perturbative expansion in the effective interaction of the electron with the rest of the atom. Zeroth-order term of this expansion corresponds to the well-known strong-field approximation (SFA). In this talk we concentrate on the first-order correction to the SFA in the case of the above-threshold ionization process [2]. The corresponding T-matrix element, which determines the differential ionization rate for the process which includes rescattering of the liberated electron wave packet off the parent atomic core, is expressed in the form of a five-dimensional integral over the ionization time, intermediate (3D) electron momentum, and the rescattering time. This integral is solved using the saddle-point method [3]. Solutions of the saddle-point equations are classified by the multi-index $(\nu,\mu)$ for forward-scattering quantum orbits and by the multi-index $(\alpha,\beta,m)$ for backward-scattering quantum orbits. Backward-scattering solutions are responsible for the high-energy electrons (having the cutoff energy $\approx 10U_p$ for a linearly polarized laser field; $U_p$ is the electron ponderomotive energy), while the forward-scattering solutions are responsible for the low-energy electrons (well-known low-energy structures with energies $\le 0.1U_p$). We will present the corresponding quantum-orbits which are obtained projecting the complex electron trajectories into the real plane (ionization and rescattering times are complex due to the quantum nature of the tunneling process and so are the electron trajectories obtained introducing these solutions into the Newton equation of the electron motion). Particular emphasis will be on the intermediate electron energy region $\sim 1U_p$, where both the forward- and backward-scattering solutions, characterized by large imaginary parts of the corresponding times, contribute. We will introduce the concept of complex-time quantum orbits in order to better explain physical meaning of these solutions [3]. The above-described method can be applied to different high-order strong-field induced processes, including high-order harmonic generation, nonsequential double ionization, and high-order above-threshold detachment, as well as to laser-assisted strong-field processes such as x-ray-atom scattering, electron-atom scattering, electron-ion radiative recombination etc. (see [4,5] and references therein). Finally, we will derive the semiclassical approximation for strong-field processes by expanding the momentum-space matrix element of the exact time-evolution operator in powers of small fluctuations around the classical trajectories. In this case the atomic potential influences the electron trajectories and, in addition to the trajectories which exist in the case when the electron is driven by the laser field alone, new trajectories appear. We will illustrate this using example of the laser-assisted potential scattering process [1]. [1] D. B. Milošević, "Semiclassical approximation for strong-laser-field processes", Phys. Rev. A 96, 023413 (2017). [2] D. B. Milošević, "Phase space path-integral formulation of the above-threshold ionization", J. Math Phys. 54, 042101 (2013). [3] D. B. Milošević, "Forward- and backward-scattering quantum orbits in above-threshold ionization", Phys. Rev. A 90, 063414 (2014). [4] D. B. Milošević, D. Bauer, and W. Becker, "Quantum-orbit theory of high-order atomic processes in intense laser fields", J. Mod. Opt. 53, 125 (2006). [5] D. B. Milošević, "Strong-field approximation and quantum orbits", Ch. VII, pp. 199-221, in D. Bauer (ed.), Computational strong-field quantum dynamics: Intense Light-Matter Interactions (De Gruyter Textbook), (Walter de Gruyter GmbH, Berlin, 2016).

The time-dependent Schrödinger equation for a quantum-mechanical system can be obtained from the time-independent Schrödinger equation of the system together with its clock, when two conditions are fulfilled: The system has to depend conditionally on the configuration of the clock, and, for the clock, a classical limit has to be taken. Based on the Exact Factorization of a wavefunction into a marginal and a conditional wavefunction, it is also possible to obtain an equation of motion for the system that depends on a fully quantum-mechanical clock. In this talk, the continuity equation corresponding to this clock-dependent Schrödinger equation is discussed. As an illustration of the clock-dependent continuity equation, a simple model for electron transfer is investigated and the nuclear configuration is interpreted as a quantum clock for the electronic motion. It is found that whenever the Born-Oppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons. Additionally, implications of the clock-dependent Schrödinger equation for the simulation of a quantum dynamics are mentioned and the possibility of obtaining Bohmian trajectories for the clock-dependent Schrödinger equation, as well as their meaning, are discussed.

The outcome of photo-induced processes in matter is determined by the complex interplay between electronic excitations and the subsequent changes in structure. These ultrafast dynamics have eluded our understanding mainly due to the inability of existing tool in connecting both processes in real-time. Here we present a decisive step forward by employing attosecond pulses covering the water window (284-543 eV) for x-ray absorption fine-structure spectroscopy in graphite. This powerful approach allows simultaneous access to both electronic and structural information with sub-fs resolution, and is equally applicable to gas-, liquid- or condensed-phase matter.

Advances in the generation and shaping of spatially structured photonic fields both in the near and far field render possible the control of the duration, the phase, and the polarization state of the field distributions. While light-matter interaction with spatially homogeneous optical fields is well established, the distinctive features of the interaction of quantum matter with vector beams, meaning fields with non-trivial topology of polarization state, are still to be explored in full detail. The talk presents an analysis of the response of atomic and nanoscopic quantum structures to irradiation by cylindrical laser vector beams with shaped polarization. It is found that radially polarized vector beams drive radially breathing charge-density oscillations via electric-type quantum transitions. Azimuthally polarized vector beams do not affect the charge at all but trigger, via a magnetic vector potential a dynamic Aharonov–Bohm effect, meaning a vector-potential driven oscillating magnetic moment. No unidirectional currents are generated. Atoms driven by a radially polarized vector beams exhibit angular momentum conserving quadrupole transitions tunable by a static magnetic field, while when excited with azimuthally polarized beam different final-state magnetic sublevels can be accessed. Simulations will be shown illustrating how the topology of the photon fields affects the trajectories of propagating particle waves.

Photoelectron holography is a very powerful tool for imaging dynamic changes in matter with never-imagined precision [1]. Electrons undergoing above threshold ionization (ATI) may take many paths to the detector, some of which will interact strongly with the core and other that will not. Thus, like in light holography, the interference between these different trajectories can be used to image the ion. Whilst a myriad of holographic patterns have been identified over the years, their interpretation is either based on simplified classical models that neglect the residual binding potential, or on the strong field approximation (SFA), which approximates the continuum by field-dressed plane waves. However, experimental results have shown that there are features in ATI photoelectron angular distributions (PADs) that can only be described by including the effect of the Coulomb potential [2]. Thus, for a complete description of electron holography an alternative model is required. In the present work, we study the influence of the Coulomb potential on photoelectron holography by applying a novel orbit-based approach beyond the SFA, based on a path-integral method: the Coulomb quantum-orbit strong field approximation (CQSFA) [3,4,5]. Using the CQSFA we are able to reproduce most if not all interference features observed in ATI PADs. This includes the fan-like pattern resulting from interference between direct electrons, which is reinterpreted as a holographic pattern formed by direct and forward deflected trajectories, the spider-like structure due to two interfering types of forward-scattered orbits, and side-lobes present on the $p_{f||}$ axis, which are in part linked to the spider but are also present due to Coulomb distortion of single electron orbits [4]. A comparison of the CQSFA ATI PADs with those calculated using the time-dependent Schrödinger equation (TDSE) shows good agreement. Furthermore, we find a plethora of overlooked interference patterns [4,6], which include alternative fan- and spider-like structures that arise from considering orbits from different laser half cycles and interference patterns that arise from a previously neglected backscattered electron trajectory. Additionally, we derive a range of analytic conditions that incorporate the effect of the Coulomb potential, which allow for better interpretation of holographic interference patterns and provide information about several features, such as outer and inner spiders and low-energy structures [5]. The CQSFA is a very general approach and the electron orbits cover a range of different types, including hard scattering, soft scattering and direct trajectories. Direct and hard scattered orbits have analogues in the SFA model of direct and re-scattered ATI [6]. We also address the question of how to treat singularities and branch cuts that arise when complex orbits are taken in the continuum propagation [7]. Overall, the CQSFA has proved to be very useful into providing additional physical insight and is capable of qualitatively describing nearly all the observed features present in the TSDE distributions. Furthermore, this method is easily generalized to multi-electron systems, where the TDSE currently is numerically inaccessible. [1] Y. Huismans et al., Science 331, 61 (2011); M. Haertelt et al., Phys. Rev. Lett. 116, (2016). [2] A. Rudenko et al., Phys. Rev. Lett., 253001 (2004); C. M. Maharjan et al., J. Phys. B 39, 1955 (2006). [3] X. Y. Lai, et al., Phys. Rev. A 9, 1 (2015); Phys. Rev. A 96, 013414 (2017). [4] A. S. Maxwell, A. Al-Jawahiry, T. Das, and C. F. d. M. Faria, Phys. Rev. A 96, 023420 (2017). [5] A. S. Maxwell, A. Al-Jawahiry, X. Y. Lai, and C. Figueira de Morisson Faria, J. Phys. B 51, 044004 (2018). [6] A. S. Maxwell and C. F. d. M. Faria, J. Phys. B Phys., 124001 (2018). [7] A. S. Maxwell, S. V. Popruzhenko and C. Figueira de Morisson Faria, arXiv:1808.00817

A general introduction to quantum trajectory Monte Carlo wave-function methods (QMCWF) in laser cooling and related problems will be given. In an application discussed in detail, the specific interest is to model the interplay between optical pumping effects and coherent optical drive in Rydberg electromagnetically induced transparency (EIT) in magnetic fields. These systems can have up to 128 relevant magnetic sublevels, which are all coupled via the coherent couplings and / or spontaneous decay. The large number of states makes direct integration of the Lindblad equation impractical. We use the QMCWF method to solve this problem. The interplay between Rydberg EIT, which reduces photon scattering, and optical pumping, which relies on photon scattering, is investigated. In the cesium system used, the magnetic interactions of the $\vert 6 S_{1/2} F_g = 4 \rangle$ ground, $\vert 6 P_{3/2} F_g = 5 \rangle$ intermediate, and $\vert nS_{1/2}, m_I, m_J \rangle$ or $\vert nD_{5/2}, m_I, m_J \rangle$ Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the deep hyperfine Paschen-Back regimes, respectively. The QMCWF simulation results are compared with experimental Rydberg-EIT spectra obtained in a room-temperature Cs vapor cell, for magnetic fields up to about 50 Gauss. We explain the dependence of the Rydberg EIT spectra and their unexpectedly pronounced asymmetry behavior on the magnetic field and the laser polarizations. The work is a collaboration with L. Zhang, S. Boa, H. Zhang, J. Zhao, L. Xiao, and S. Jia at Shanxi University, Taiyuan, PRC, and is funded by National Natural Science Foundation, China. GR also acknowledges funding National Natural Science Foundation, USA.

Hybrid quantum-classical theory of RIXS of liquids Faris Gel’mukhanov KTH Royal Institute of Technology, S-106 91 Stockholm, Sweden Understanding and modelling quantum nuclear effects in disordered systems in general and in liquids, in particular, is one of the major challenges of modern condensed matter physics. Hydrogen bonding in the electronic ground state of liquids and solutions influences numerous important processes in chemistry, biology and material sciences. Here, we face the fundamental problem of how to describe the vibrational quantum effects in a fluctuating hydrogen-bond network. Due to the high complexity of disordered systems, resonant inelastic X-ray scattering (RIXS) of liquid water has so far only been simulated with classical molecular dynamics approaches, which totally neglects the vibrational quantum effects observed experimentally. Our approach is the first successful attempt to describe coherent quantum molecular dy- namics in a fluctuating media of strongly interacting molecules. RIXS has recently been established from experiment and first principles theory as the perfect tool to probe the elec- tronic ground state (quasi-elastic RIXS). The absence of electronic inhomogeneous broaden- ing allows for vibrational resolution of RIXS in liquids. Together with its chemical sensitiv- ity, it becomes a natural tool to study local properties of disordered systems with controlled magnitude of disorder (spatial sensitivity). In our paper, we investigate the role of disorder in the fluctuating local surrounding by controlling the spatial extent of the quantum nuclear wave packet, as monitored in the vibrational progression. When tuned to a dissociative core-excited state, RIXS exhibits ultrafast nuclear dy- namics. This gives access to high vibrational levels in a swift transition, contrary to IR spectroscopy of liquids. Related coherent evolution of the OH bonds into the long range part of the potential energy curve (PEC) makes quasi-elastic RIXS very sensitive to the local environment. We exploit this property to probe hydrogen bond strength of liquid water via the structure sensitive distribution of intramolecular OH PECs extracted from ultra high resolution RIXS measurements. In addition, we shed light on the formation of the widely debated lone-pair peak splitting in RIXS of liquid water.

In view of the increasingly stronger available laser fields it is becoming feasible to employ them to test the predictions of QED when processes occur in the presence of a background electromagnetic field effectively comparable to the so-called critical field of QED. Pioneering experiments in this regime, known as the strong-field QED regime, have been carried out at SLAC in the late nineties and the experimental results could have been reproduced theoretically by approximating the laser field as a plane wave. Present and upcoming high-power laser facilities, however, aim at reaching ultra-high intensities by tightly focusing the laser energy both in space and in time. In this talk I will discuss the main theoretical challenges brought about when processes occur in the presence of electromagnetic fields of complex spacetime structure. Moreover, I will report on an analytical technique, which has been developed to take into account the influence of tightly focused laser beams onto strong-field QED processes. The approach is based on the possibility of describing the propagation of ultrarelativistic charged particles in (almost) arbitrary electromagnetic field by means of their classical trajectory and on the corresponding use of the Wentzel-Kramers-Brillouin (WKB) approximation for solving the relativistic quantum equations of motion in the external field.

As the laser technology continues its spectacular development, ever higher field intensities and power levels become accessible in laboratories. The ELI project opens new horizons for laser applications in ultra-bright sources of short wavelength radiation. At the same time, the laser pulse quality – like the contrast ratio – is greatly improved so that fine structured targets maintain their structure till the main pulse arrival. This opens new and unexpected possibilities for laser-plasma engineering towards new physics. In the talk, we consider laser pulse interaction with nano- and micro-structured targets like nano-grass [1-4] in the intensity range 1018-1020 W/cm2. At intensities higher than 1022 W/cm2, the radiation damping force becomes important and can exceed the Lorentz force acting on an electron [2]. The gamma-ray emission and pair creation are then the major channels of laser energy absorption [5-7]. References: 1. MA Purvis, VN Shlyaptsev, R Hollinger, C Bargsten, A Pukhov, et al. Nature Photonics 7, 796 (2013) 2. Vural Kaymak, Alexander Pukhov, Vyacheslav N. Shlyaptsev, Jorge J. Rocca, “Nano-scale ultra-dense Z-pinches formation from laser-irradiated nanowire arrays”, Physical Review Letters 117 (3), 035004 (2016) 3. R Hollinger, C Bargsten, VN Shlyaptsev, V Kaymak, A Pukhov et al., “Efficient picosecond x-ray pulse generation from plasmas in the radiation dominated regime”, Optica 4 (11), 1344-1349 (2017) 4. JJ Rocca, V Shlyaptsev, R Hollinger, C Bargsten, A Pukhov, V Kaymak, et al. “Compact ultra-intense lasers and nanostructures open a path to extreme pressures” LASER FOCUS WORLD 53 (5), 21-26 (2017) 5. LL Ji, A Pukhov, IY Kostyukov, BF Shen, K Akli Physical review letters 112, 145003 (2014) 6. Longqing Yi, Alexander Pukhov, Phuc Luu-Thanh, and Baifei Shen, Phys. Rev. Lett. 116, 115001 (2016) 7. XL Zhu, TP Yu, ZM Sheng, Y Yin, ICE Turcu, A Pukhov "Dense GeV electron–positron pairs generated by lasers in near-critical-density plasmas" Nature communications 7, 13686 (2016)

Electronic structure computations of atoms and ions have a long tradition in physics with applications in basic research, spectroscopy, life sciences and technology. Various theoretical methods (and codes) have therefore been developed to account for the many-particle structure of atoms, from simple semi-empirical estimates to accurate predictions of selected data, and up to highly advanced time-independent and time-dependent numerical techniques. — Here, I present a fresh concept and implementation of (relativistic) atomic structure theory that supports the computation of interaction amplitudes, properties as well as a large number of excitation and decay processes for open-shell atoms and ions across the whole periodic table. The implementation is based on Julia, a new programming language for scientific computing, and provides an easy-to-use but powerful platform to extent atomic theory towards new applications.

We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential and nonsequential photoionization. This clear separation demonstrates the potential of elliptically polarized XUV fields for improved control of electronic emission processes.