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High-harmonic spectroscopy for core-hole dynamics

Periodic Reporting for period 1 - HHGhole2 (High-harmonic spectroscopy for core-hole dynamics)

Reporting period: 2016-12-05 to 2018-12-04

X-ray photons strongly interact with core electrons, exciting them into unoccupied valence or continuum states. The core-hole state left behind decays very fast (few femtoseconds) via the rearrangement of electrons in the system to fill the core hole. This ultrafast core rearrangement can induce the emission of a photon (fluorescence) or an electron (Auger process). These mechanisms are universal and play also a fundamental role in radiation damage of physical systems of interest, as biomolecules.

Hence, it is timely to study molecular core-hole dynamics. To achieve the complete understanding of the core-hole dynamics one needs to follow the time-evolution of the intermediate states. Here we use high-order harmonic spectroscopy (HHS) to study core-hole dynamics. In HHS, an intense infrared source is used to probe the system after the pump pulse (here an x-ray pulse). The non-linear interaction with the IR field results in a complex harmonic spectrum that encodes the transient dynamics. This technique has been proven to resolve molecular dynamics with attosecond resolution.

Conclusions of the action: The MC researcher obtained a tenure-track position and we needed to terminate the contract 10 months before expected. However, we have made enormous progress towards the final goal of developing a numerical code to calculate the HHG spectroscopy for core-hole molecular dynamics.
1) The first step was to develop a time-dependent code to simulate the core-hole dynamics in molecular systems. Based on this theory, we started to implement the numerical code. These calculations allow the possibility to obtain the x-ray absorption spectrum of a static state. We collaborated with experimentalists that performed x-ray absorption spectroscopy measurements in synchrotron facilities [JACS 139, 12907 (2017) and Chem. Eur. J. 24, 6464 (2018)]. Then we implemented the time-propagation program to describe the response of the molecule interacting with x rays. We obtain interesting results for charge migration induced by the x rays.
2) We started to work on the implementation of calculating the HHG spectrum of the evolving system, within the Strong-Field Approximation (SFA). We started with the simple molecule, hydrogen molecular ion (a complete solution of the Time-Dependent Schrödinger Equation (TDSE) is possible). First calculations look promising, when we compared the time-dependent SFA (td-SFA) with the TDSE. Also, we adopted the code to also consider two-dimensional materials to broaden the applications.
"We describe the work performed during the active period:

- During the 0-3 months, the MC researcher settled in Universidad de Salamanca and performed the introductory tasks mentioned in Work Plan 1 (WP1). The theory for later implementing the time-dependent core-hole dynamics was published in [1].
- In the five following months, 3-8 months, we started to implement the code that calculates the electronic structure of any molecule, needed for WP2 and WP3. We choose to build the time-dependent code on the top of a Gaussian basis library that allowed calculating all electronic structure of any molecule. Then we develop a scattering code to calculate the continuum orbitals for photoelectrons and Auger electrons (WP3).
- During the 8-11 months period, we started to implement the time-dependent program to calculate the molecular core-hole dynamics (WP3). We choose to implement the equations published in [1] with a four-order Runge-Kutta to evolve the quantum system, parallelized with Open MP libraries. The program has been initially designed to simulate both excitation and ionization of the x-ray pulse, and the following Auger decay via electron correlations. Also, we could simulate the nuclear propagation, but this has not been tested. This new code allowed us investigating the charge migration in the dication molecular ion. In Figure 1 we show the coherent electron transfer calculated for FC2H. An x-ray pulse ionizes the 1s electron from the F atom, and after Auger decay, a two-hole distribution is created in the valence shell. When we solve the dynamics, accounting for all possible interferences between different Auger channels, we observe a coherent oscillation (blue line), in contrast to a standard exponential incoherent decay (red line). We noticed that the coherent oscillation produce a clear electron transfer across the molecule, Fig 1b. Our results are submitted for publication [3].
Also, we adopt our code to simulate the dynamics in two-dimensional materials. In Figure 2 we show the calculate HHG spectrum from graphene interacting with a 3-cycle 3mm-wavelength pulse, with two different intensities. We submitted our results to New J. Phys. [2].
- During the last two months, 11-14 months, we have been working in connecting the SFA code of the host group with the code that simulates the core-hole molecular dynamics. First we tested with hydrogen molecular ion, in which we can obtain an exact solution and make a quantitative comparison with the SFA model. First results are promising and we will continue working in this line.

[1] A. Picón, ""Time-dependent Schrödinger equation for molecular core-hole dynamics"", Phys. Rev. A 95, 023401 (2017).
[2] O. Zurrón, A. Picón, and L. Plaja, ""Theory of high-order harmonic generation for gapless graphene"", accepted in New J. Phys.
[3] A. Picón, C. Bostedt, C. Hernández-García, and L. Plaja, ""Auger-induced charge migration"", submitted to PRX.

- RSEF +Física, Universidad de Salamanca, Spain 27 November 2017. Outreach talk.
- USTS 2017 - Ultrafast Science & Technology Spain, Salamanca, Spain 22-24 November 2017. Oral conference.
- XXXVI Reunión Bienal de la Real Sociedad Española de Física, Santiago de Compostela, Spain 17-21 July 2017. Oral conference.
- CLEO - ECEQ European Quantum Electronics Conference, Munich, Germany 25-29 June 2017. Oral conference.
- SPIE Optics + Optoelectronics, Prague, Czech Republic 24-27 April 2017. Oral conference.
- IWP-RIXS-2017 ""International workshop of photoionization and resonant inelastic x-ray scattering"", Aussois, France 26-31 March 2017. Oral conference."
We have made an important scientific contribution by creating a numerical code that allows simulating in a full-quantum-mechanical framework the dynamics triggered by ultrashort x-ray pulses in molecules. This allows studying the coherence left in the molecular ion and calculating the charge migration (electron transfer that does not involve nuclear motion). We believe it is an important result and we recently submitted it to PRX. Also, our results open a completely new scenario to be investigated in modern x-ray free electron facilities that deliver attosecond pulses and HHG laser laboratories [Science 355, 264 (2017) and PRL 119, 154801 (2017)].

We also adapt the program to investigate two-dimensional materials. In particular, we investigated the nonlinear response of graphene under an ultrashort intense mid-IR pulse. This broadens the impact of the developed code.

Although we needed to finish the project before than expected, we did very good progress towards the final goal of calculating the induced HHG spectrum of a molecule that interacts with an attosecond/few-femtosecond x-ray pulse. Our implemented code is suitable to be connected with the SFA code of the host group and further collaborations with the MC researcher and host group will finish the implementation of the program.
Figure 1
Figure 2