09:00  09:30

Frank Grossmann
(Technische Universität Dresden)
Semiclassical electron dynamics
The semiclassical initial value formalism to solve the timedependent
Schroedinger equation using classical trajectories will be reviewed.
Special focus will be laid on the multitrajectory HermanKluk 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 electronelectron scattering is captured by the semiclassical HermanKluk 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 halfcycle pulse driving [5] and the dominant interaction Hamiltonian approach to highorder 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)

09:45  10:15

David Tannor
(Weizmann Institute of Science, Rehovot)
A new formulation of quantum mechanics using complex valued classical trajectories
Several years ago, we developed a formulation of the timedependent Schrodinger equation (TDSE) using complexvalued 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 timedependent 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, 22A5178 (2012).
[4] W. Koch and D. J. Tannor, Chem. Phys. Lett. 683, 306 (2017).
[5] W. Koch and D. J. Tannor, manuscript in preparation.

10:30  11:00

coffee break

11:00  11:30

Ulli Eichmann
(MBI Berlin)
Channel closings in strongfield excitation of atoms and molecules
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 strongfield excited homonuclear 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

11:45  12:15

Alejandro Saenz
(Humboldt Universität zu Berlin)
A more detailed look into enhanced ionization in intense laser fields
Enhanced ionization, i.e. a strongly increased ionization probability found for specific internuclear separations, is one of the most paradigmatic molecular strongfield 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 carbonhydrogen 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 timedependent Schrödinger equation in full dimensionality for fixed, but varying internuclear separation. A pronounced influence of the carrierenvelope 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.

12:30  13:30

lunch

13:30  14:00

Agapi Emmanouilidou
(University College London)
Slingshot nonsequential double ionization as a gate to anticorrelated two electron escape

14:15  14:45

Karen Hatsagortsyan
(MPI for Nuclear Physics, Heidelberg)
High energy direct photoelectron spectroscopy in strong field ionization
Recently, in the tunneling regime of strong field ionization an unexpected Coulomb field eect has been identified by numerical solution of timedependent 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.

15:00  15:30

Dejan B. Milosevic
(University of Sarajevo)
Quantum orbits in stronglaserfield physics
Using the phase space pathintegral formalism we derive an expression for the momentum space matrix element of the exact timeevolution 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. Zerothorder term of this expansion corresponds to the wellknown strongfield approximation (SFA). In this talk we concentrate on the firstorder correction to the SFA in the case of the abovethreshold ionization process [2]. The corresponding Tmatrix 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 fivedimensional integral over the ionization time, intermediate (3D) electron momentum, and the rescattering time. This integral is solved using the saddlepoint method [3]. Solutions of the saddlepoint equations are classified by the multiindex $(\nu,\mu)$ for forwardscattering quantum orbits and by the multiindex $(\alpha,\beta,m)$ for backwardscattering quantum orbits. Backwardscattering solutions are responsible for the highenergy electrons (having the cutoff energy $\approx 10U_p$ for a linearly polarized laser field; $U_p$ is the electron ponderomotive energy), while the forwardscattering solutions are responsible for the lowenergy electrons (wellknown lowenergy structures with energies $\le 0.1U_p$). We will present the corresponding quantumorbits 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 backwardscattering solutions, characterized by large imaginary parts of the corresponding times, contribute. We will introduce the concept of complextime quantum orbits in order to better explain physical meaning of these solutions [3]. The abovedescribed method can be applied to different highorder strongfield induced processes, including highorder harmonic generation, nonsequential double ionization, and highorder abovethreshold detachment, as well as to laserassisted strongfield processes such as xrayatom scattering, electronatom scattering, electronion radiative recombination etc. (see [4,5] and references therein). Finally, we will derive the semiclassical approximation for strongfield processes by expanding the momentumspace matrix element of the exact timeevolution 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 laserassisted potential scattering process [1].
[1] D. B. Milošević, "Semiclassical approximation for stronglaserfield processes", Phys. Rev. A 96, 023413 (2017).
[2] D. B. Milošević, "Phase space pathintegral formulation of the abovethreshold ionization", J. Math Phys. 54, 042101 (2013).
[3] D. B. Milošević, "Forward and backwardscattering quantum orbits in abovethreshold ionization", Phys. Rev. A 90, 063414 (2014).
[4] D. B. Milošević, D. Bauer, and W. Becker, "Quantumorbit theory of highorder atomic processes in intense laser fields", J. Mod. Opt. 53, 125 (2006).
[5] D. B. Milošević, "Strongfield approximation and quantum orbits", Ch. VII, pp. 199221, in D. Bauer (ed.), Computational strongfield quantum dynamics: Intense LightMatter Interactions (De Gruyter Textbook), (Walter de Gruyter GmbH, Berlin, 2016).

15:45  16:15

coffee break

16:15  16:45

Axel Schild
(ETH Zürich)
Time in quantum mechanics: A fresh look at the continuity equation
The timedependent Schrödinger equation for a quantummechanical system can be obtained from the timeindependent 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 quantummechanical clock. In this talk, the continuity equation corresponding to this clockdependent Schrödinger equation is discussed. As an illustration of the clockdependent 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 BornOppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons.
Additionally, implications of the clockdependent Schrödinger equation for the simulation of a quantum dynamics are mentioned and the possibility of obtaining Bohmian trajectories for the clockdependent Schrödinger equation, as well as their meaning, are discussed.

17:00  17:30

Jens Biegert
(ICFO, Castelldefels)
Energydispersive xray finestructure spectroscopy in graphite with attosecond pulses
The outcome of photoinduced 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 realtime. Here we present a decisive step forward by employing attosecond pulses covering the water window (284543 eV) for xray absorption finestructure spectroscopy in graphite. This powerful approach allows simultaneous access to both electronic and structural information with subfs resolution, and is equally applicable to gas, liquid or condensedphase matter.

17:45  18:30

poster preview

18:30  19:30

dinner & discussions

19:30  21:30

poster session
