Ultrafast Processes in Molecules Visualized with Femtosecond Pump-Probe Photoelectron Spectroscopy

SCHRIFTENREIHE DES HZB · EXAMENSARBEITEN

Ultrafast processes in molecules visualized with femtosecond pump-probe photoelectron spectroscopy

Torsten Leitner Dissertation

Institut für Methoden und Instrumentierung der Forschung mit Synchrotronstrahlung November 2012 HZB–B 37

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ISSN 1868-5781 doi: http://dx.doi.org/10.5442/d0031

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Ultrafast processes in molecules visualized with femtosecond pump–probe photoelectron spectroscopy

vorgelegt von

Dipl.-Phys. Torsten Leitner aus Kirchham

von der Fakult¨atII - Mathematik und Naturwissenschaften der Technischen Universit¨at Berlin zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften -Dr.rer.nat.-

genehmigte Dissertation

angefertigt am Helmholtz-Zentrum Berlin f¨urMaterialien und Energie Institut f¨urMethoden und Instrumentierung der Forschung mit Synchrotronstrahlung

Promotionsausschuss: Vorsitzender: Prof. Dr. Mario D¨ahne Gutachter: Prof. Dr. Dr. h.c. Wolfgang Eberhardt Gutachter: Prof. Dr. Alexander F¨ohlisch

Tag der wissenschaftlichen Aussprache: 01. November 2012

Berlin 2012

D83

Zusammenfassung

Eine der großen Herausforderungen der modernen Wissenschaft ist es, die Chemie auf ihrer fundamentalen inter- und intra-molekularen Ebene zu verstehen. Das Elek- tron ist der Hauptakteur in chemischen Reaktionen und erfordert Untersuchungen auf fundamentalen Längen-und Zeitskalen im Nanometer- bzw. Femto- bis Picosekun- denbereich. Photoanregung ist ein vielfach in der Natur vorkommender Auslöser für chemische Prozesse – ohne die Möglichkeit, das Sonnenlicht als Energiequelle zu nutzen, wäre Leben wie wir es kennen nicht möglich. Diese Arbeit untersucht Methoden zur Visualisierung der Interaktion von Licht mit der elektronischen Struktur von Molekülensowie der Dynamik in der elektronsichen Struktur nach Photoanregung. Die Methode, um die Funktion des Elektrons zu un- tersuchen, war zeitaufgelöstePhotoelektronenspektroskopie (TRPES – time-resolved photoelectron spectroscopy). Die Arbeit gliedert sich in zwei Hauptteile: Teil I “Methoden und Instrumente”, in dem experimentelle Aufbauten und Werkzeuge vorgestellt werden, die in der ultraschnellen Photoelektronenspektroskopie zum Einsatz kommen, und Teil II “Experimente”, in dem drei konkrete Experimente zur elektronischen Struktur von Molekülenvorgestellt und diskutiert werden. In Teil I wird die Implementierung und der Betrieb eines TRPES Aufbaus zur Unter- suchung ultraschneller Dynamik in elektronischen Strukturen detailliert dargestellt, der auf der Erzeugung Hoher Harmonischer eines Laser basiert. Desweiteren wird eine Hochtemperatur-Molekül-Verdampfungsquelle vorgestellt, die im Rahmen dieser Arbeit entwickelt wurde, und die TRPES Experimentieraufbauten werden erläutert, die für diese Arbeit am Max-Born-Institut in Berlin und am Freie Elektronen Laser FLASH in Hamburg, verwendet wurden. Die Herausforderungen und Lösungen zur Durchführung eines TRPES Experiments bei FLASH werden detailliert geschildert, insbesondere wird ein Schema zur präzisen Bestimmung der Pump–Probe Zeiten vorgestellt, die bei FLASH von einer großen Schuss-zu-Schuss Schwankung der Licht- pulsankuftszeiten beinflusst sind. Teil II demonstriert die Verwendbarkeit von Photoelektronenspektroskopie zur Visu- alisierung der Dynamik der elektronischen Struktur von Molekülen.Die Möglichkeit Schlussfolgerungen über die Symmetrieeigenschaften der Elektronendichteverteilung zu ziehen wird untersucht, indem die Polarisationsabhängigkeit eines zwei-Farben zwei-Photonen Ionisierungsprozesses mit einem theoretischen Modell verglichen wird. Die Visualisierung kohärenter Kern- und Elektronenwellenpaketoszillationen von NaI Molekülenim angeregten Zustand mittels TRPES mit sub 100 fs Zeitauflösungwird demonstriert und zeigt quantenmechanische E↵ekte, wie z.B. kohärente Uberlagerung¨ von Wellenpaketen, auf, die sich in der Koexistenz eines einzelnen Moleküls in verschiedenen intra-molekularen Abständen widerspiegelt. Weiterhin wird ein Trans- fer des Wellenpakets zwischen verschiedenen intra-molekularen Potenzialen, folglich molekularen Zustanden, visualisiert. Zuletzt wird ein Experiment zur O↵enlegung der transienten elektronischen Struktur während der schrittweisen Photo-Dissoziation von

iii Fe(CO)5 Molekülenin der Gas-Phase vorgestellt, Der Schwerpunkt liegt hierbei auf der Entflechtung des komplexen TRPES Datensatzes bzw. der Trennung der überlap- penden Photoelektronenspektren, die von den im Laufe des Photo-Dissoziations- Prozesses auftretenden verschiedenen molekularen Spezies stammen.

iv Abstract

One of the grand challenges in modern science is understanding chemistry on a fundamental inter- and intra-molecular scale. The principal player in chemical reactions is the electron and therefore, the fundamental scales to address are the sub to few nanometer length scale and the femto- to picosecond time scale. A widely occurring trigger for chemical reactions in nature is photo-excitation – without the ability of harvesting sunlight and using it for further chemical processes life as we know it would not be possible. Therefore, in order to contribute to understanding chemistry on a fundamental level, methods for visualizing the interaction of light with the electronic structure of molecules and the dynamics in the electronic structure after photo-excitation are investigated in this thesis. The method of choice to address the function of the electron was time-resolved photoelectron spectroscopy (TRPES). The thesis is divided into two major parts: Part I “Methods and Instruments” where experimental setups and tools used for ultrafast photoelectron spectroscopy are introduced and Part II “Experiments”, presenting and discussing three concrete experiments on electronic molecular structures. In Part I, the implementation and operation of a TRPES setup for investigating ultrafast electronic structure dynamics, based on laser high-harmonic generation, is discussed in detail. Furthermore, a high-temperature molecular evaporation source developed within the framework of this thesis is introduced and the TRPES setups used for this thesis at the Max-Born-Institute in Berlin and the free electron laser FLASH on the DESY site in Hamburg are detailed. The challenges and solutions for performing TRPES at FLASH are addressed in detail, especially a scheme for accurate pump–probe timing, which at FLASH underlies a large shot-to-shot arrival-time jitter. Part II demonstrates the usability of photo-electron spectroscopy for visualizing the dynamics of the electronic structure in molecules. The possibility of drawing conclusions on symmetry properties of the electron density distribution is explored by comparing the polarization dependence of a two-color two-photon ionization process to an approximative theoretical model. The visualization of coherent nuclear and electronic wave packet oscillations in excited state NaI molecules by means of TRPES with sub 100 fs time resolution is demonstrated, revealing quantum mechanical e↵ects like coherent superposition of wave packets reﬂected in the co-existence of a single molecule in several intra-molecular distances. Furthermore, a transfer of the molecular wave packet population between intra-molecular potentials, hence between molecular states, is visualized. Lastly, an experiment on revealing the transient electronic structure during the step-wise photo-dissociation of Fe(CO)5 molecules in gas-phase is presented, with a focus on how to disentangle the complex TRPES data set and separate the overlapping photoelectron spectra arising from the di↵erent molecular species occurring during the photo-dissociation process.

v vi Contents

1 Introduction 1

I Methods and Intruments 3

2 High-order Harmonic Generation at HZB 5 2.1 HHG as a three step process ...... 6 2.2 The HHG setup at HZB ...... 9

3 High-Temperature Sample Source 27

4 Pump-Probe Setup at the Max-Born-Institute Berlin 31

5 Pump-Probe Setup at the Free Electron Laser in Hamburg 33

II Experiments 41

6 Polarization Control in Two-Color Above Threshold Ionization 43 6.1 Polarization dependence ...... 44 6.2 Theoretical model ...... 46 6.3 Experiment ...... 49 6.4 Results ...... 51 6.5 Conclusion for this chapter ...... 54

7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI 57 7.1 How it works ...... 58 7.2 Experiment ...... 65 7.3 Ultrafast auto-ionizing dissociation ...... 67 7.4 Coherent electronic and nuclear wave packet oscillations ...... 69 7.5 Conclusion for this chapter ...... 83

vii 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5 87 8.1 Rate model ...... 88 8.2 Experiment ...... 91 8.3 Decay of transient Fe(CO)4 and creation of free CO ...... 95 8.4 Transient photoelectron spectra ...... 96 8.5 Conclusion for this chapter ...... 99

9 Conclusion 103

Bibliography 105

Acknowledgment 113

viii List of Figures

2.1 Exemplary HHG spectrum ...... 5 2.2 The three steps of HHG ...... 6 2.3 Pump-probe HHG setup at HZB ...... 9 2.4 Experimental chamber at HZB ...... 13 2.5 Time-of-flight electron spectrometer ...... 14 2.6 Exemplary auto-correlation measurement ...... 19 2.7 Exemplary cross-correlation measurement ...... 20 2.8 Divergence of the HHG source ...... 22 2.9 Modified HHG setup for absolute photon number measurements and GMD functional principle ...... 23 2.10 Shot-to-shot stability of the HHG source ...... 24 2.11 Purity of the GMD detection gas ...... 25 2.12 Reliability of a semiconductor diode vs. photon flux for several harmonic photon enegies ...... 26 2.13 Reliability of a semiconductor diode vs. radiant power ...... 26

3.1 High-temperature sample source ...... 28

4.1 Experimental setup at MBI ...... 31

5.1 Experimental setup at FLASH ...... 36

6.1 Two-color two-photon ATI principle ...... 43 6.2 Sideband polarization dependence in Helium ...... 44 6.3 Idealized one-photon ionization PADs for motivating the sideband polarization dependence ...... 45 6.4 Typical sideband polarization dependence measurement in Argon .. 50 6.5 Photoelectron spectra for parallel and perpendicular polarization ... 51 6.6 Polarization dependence: experiment vs. model ...... 52

ix 7.1 Calculated intra-molecular potentials for the NaI molecule ...... 59 7.2 Calculated electron binding energies versus intra-molecular distance for photo-excited NaI molecules ...... 60 7.3 Crossing, inner and outer turn visualized in the intra-molecular potentials picture ...... 61 7.4 Simpliﬁed modeled photoelectron spectral evolution from photo-excited NaI molecules ...... 62 7.5 Ground state spectrum of NaI ...... 65 7.6 TRPES map from photo-excited NaI molecules ...... 66 7.7 Photoelectron peak shift during dissociation to I ions for negative delays ...... 68 7.8 Distinguished features in the NaI TRPES maps ...... 69 7.9 TRPES maps depicting the NaI wave packet dynamics: Plain and normalized separately for each delay ...... 70 7.10 Delay scans for wave packet dynamics in the A–X potential trap ... 74 7.11 Delay scan map from photo-excited NaI molecules ...... 77 7.12 Delay scans for wave packet dynamics in the B–X potential trap ... 78 7.13 Simpliﬁed model versus experimental photoelectron spectra for selected delays ...... 82

8.1 Fe(CO)5 photo-dissociation sequence ...... 87 8.2 Rate model for Fe(CO)5 photo-dissociation ...... 90 8.3 Fastest feature – time resolution and t0 ...... 92 8.4 Comparison of valence photoelectron spectra for Fe(CO)5, pump– probe di↵erences and CO molecules ...... 93 8.5 Content of non-excited Fe(CO)5 in the TRPES data ...... 94 8.6 Creation of CO and decay of transient Fe(CO)4 ...... 95 8.7 Scaled di↵erences at selected delays ...... 96 8.8 Experimental valence spectra for Fe(CO)5, Fe(CO)4 and Fe(CO)3 .. 98 8.9 Calculated valence spectra for Fe(CO)5, Fe(CO)4 and Fe(CO)3 ... 98

x List of Tables

6.1 Electronic conﬁgurations for sideband formation from the HOMO for all investigated systems ...... 49 6.2 Sideband modulation and 2: experiment vs. literature ...... 53 6.3 Asymmetry parameter 2 for the HOMO of N2 ...... 54

7.1 NaI bound states and corresponding free fragments ...... 60 7.2 NaI ground state valence orbitals ...... 64

8.1 Rate model for Fe(CO)5 photo-dissociation sequence ...... 89

xi xii 1 Introduction

One of the grand challenges in modern science is understanding chemistry on an fundamental inter- and intra-molecular scale [1]. Understanding chemistry on this fundamental level means elucidating the complex dynamics of the correlated and coupled motion of nuclei and electrons, which build the basis for chemical processes. As the nuclei rearrange, intra-molecular bonds break and new bonds are formed within the natural molecular time scales of femto- to picoseconds and on length scales from sub- to few nanometers. Ultimately, understanding chemistry leads to the dream of gaining control over chemical reactions, enabling new ways of designing materials, driving them along the desired reaction path and corresponding transient states to the desired products. Gaining insight into photochemical reactions, as photosynthesis or photovoltaic processes or clarifying combustion processes in fuels, for example, can lead to new and optimized solutions for ecient light harvesting and fuel design, respectively. Therefore, understanding chemistry on the fundamental level can provide the knowledge to master one of the biggest challenges for humanity: “How to satisfy the world’s increasing demand of energy and at the same time account for the world- wide climate change and reduce the exhaustion of climate gases?”. The (valence) electrons are the ’glue inside molecules’, as transferring and sharing electrons between atoms means breaking and formation of molecular bonds. The electrons are hence the principal player in chemical reactions. Therefore, understanding chemistry requires us to address the function and dynamics of the evolution of the electronic structure during a reaction. Another important aspect of chemical reactions is that in general they start from molecules in an excited state, where the excitation provides the necessary energy to trigger the reaction. Photo-excitation, hence the absorption of one or more photons, is one of the most important ways for triggering chemical reactions in nature. Life as we know it would not be possible without the ability of using the earth’s primary energy source, sunlight. Time-resolved pump–probe photoelectron spectroscopy (TRPES) techniques can serve as a powerful tool to investigate the properties of the electronic structure of molecules and the dynamics therein. A pump laser pulse of desired photon energy excites the sample and triggers a photochemical reaction. A delayed probe pulse photo-ionizes the dynamically evolved sample, creating ions and photoelectrons. Measuring the properties of these photoelectrons, for example their kinetic energy or their ejection angular distribution, enables to directly map the properties of the electronic structure of the system under investigation. Varying the delay between pump and probe pulses thus enables recording a ’molecular movie’ of the dynamics in the molecular electronic

1 1 Introduction structure during photochemical reactions. Photo-ionization is capable of accessing all states within the energy of the ionizing probe photons, hence there are no invisible dark states [2]. Furthermore, TRPES enables us to visualize nature’s restlessness on the fundamental level of quantum mechanics, where the description of the physical reality falls apart to probability densities and interfering complex wave packets, in contrast to the intuitive description of the macroscopic world, based on the idea of assemblies of robust particles. Photoelectron spectra can be determined from atoms and molecules in the ground state as well as from highly complex, quantum mechan- ically entangled or superposed molecular states, arising from the interaction of two atoms to a few thousands or even millions of atoms, in macromolecules like DNA or biological viruses. The desired ultrafast femtosecond time resolution is provided by state-of-the-art laser and accelerator based light sources. This thesis deals with the implementation and operation of a laser high-harmonic generation based TRPES setup for experiments on matter in the gas-phase and furthermore with the interpretation of TRPES datasets, acquired in three di↵erent campaigns at three di↵erent light sources and experimental setups, moving us another small step towards understanding chemistry on its fundamental level. The thesis is divided into two major parts: Part I “Methods and Instruments” (chapters 2–5)andPart II “Experiments” (chapters 6–8). Chapter 2 describes a high-order harmonic generation based femtosecond pump– probe photoelectron spectroscopy setup for investigation of ultrafast processes in the electronic structure of molecules in the gas-phase, as implemented at HZB and the day-to-day operation of this setup. For enabling experiments with a larger number of samples, a high-temperature sample source for evaporating molecular or atomic samples, which are in solid or liquid phase under vacuum conditions and room temperature was developed within the framework of this thesis and is introduced in chapter 3. Chapters 4 and 5 describe the pump–probe photoelectron spectroscopy setups used in measurement campaigns at the Max-Born-Institute Berlin and at the free-electron laser FLASH in Hamburg, respectively. An experiment on polarization control of two- color two-photon ionization of small molecules and atoms, where the inﬂuence of the symmetry of the electronic structure on a two-photon ionization process is investigated is detailed in chapter 6. Based on the ground-breaking femtosecond spectroscopy experiments by A.Zewail and coworkers [3, 4], the coherent electronic and nuclear dynamics in photo-excited NaI molecules are revisited in chapter 7, by means of time-resolved pump–probe photoelectron spectroscopy, disclosing deeper insights into the coherent molecular wave packet dynamics. In chapter 8 an experiment on revealing the transient electronic structure during the step-wise photo-dissociation of Fe(CO)5 molecules in gas-phase is presented. The thesis is concluded in chapter 9.

2 Part I

Methods and Intruments

2 High-order Harmonic Generation at HZB

High-order harmonic generation (HHG) has emerged as a widely used tool to produce bright femto- and attosecond vacuum-ultraviolet (VUV) and soft x-ray pulses [5– 9]. These pulses can be used to study ultrafast atomic, molecular and magnetism dynamics [10–14] and are bright enough to perform coherent x-ray di↵ractive imaging for investigations on the nanoscale [15]. Furthermore, the HHG process itself can provide insight into the electronic structure of the generating molecule [16–21]. HHG occurs when an intense laser ﬁeld interacts with an atomic gas target. When rare gas atoms are irradiated by short laser pulses with peak powers of the order of 1014 to 1016 W /cm2, the gas medium responds in a highly non-linear way, generating radiation with higher frequencies co-propagating with the fundamental laser beam. In general, the obtained spectra consist of the fundamental frequency !0 plus its odd multiples !q = q!0, q (2N +1)uptothecut-o↵ frequency, where the spectrum ends abruptly. A typical2 HHG spectrum is depicted in ﬁgure 2.1.

Figure 2.1: Typical HHG spectrum measured at a previous version of the HZB HHG setup (reprinted with permission from [22]).

In the ﬁrst section of this chapter the high-order harmonic generation process and a simpliﬁed semi-classical three-step model to allow for understanding the major aspects of HHG is presented. The second section introduces the existing HHG source based pump–probe setup at HZB: the experimental arrangement, instruments and methods for operation and optimization, typical characteristics and a publication on the shot-

5 2 High-order Harmonic Generation at HZB to-shot variation of the absolute ﬂux of the HZB HHG source and the validity of a standard average photon ﬂux detector - a photodiode - are presented.

2.1 HHG as a three step process

HHG can be understood in an intuitive semi-classical view as a three step process [23–26]. This often is called Simple Man Model and is valid in the tunnel regime, where the frequency !0 of the fundamental generating laser is characterized by:

~!0 Ip Up ,(2.1) ⌧ ⌧ with the ionization potential of the atom Ip and the ponderomotive potential 2 2 2 Up = e E /(4m!0)ofafreeelectron,oscillatingintheelectricﬁeldofthelaser. Typically, IR laser sources with photon energies of ~!0 1.6 eV (800 nm) and rare gases are used for generating high harmonics. The ponderomotive potential can be 2 approximated from the laser peak intensity as Up(eV) 6 Ipeak(W /cm )for800 nm lasers [25]. Hence, peak intensities around 3 1014⇡W⇥/cm2 for Xe, Kr and Ar 14 2 ⇥ 14 (Ip=12.1, 14.1 and 15.8 eV), 4 10 W /cm for Ne (Ip=21.6 eV) and 5 10 2 ⇥ ⇥ W /cm for He (Ip=24.6 eV) or even higher peak intensities are necessary in order to well fulﬁll the tunnel regime constraints for typical femtosecond high power 800 nm Ti:Sapphire lasers. → energy

(1) tunnel ionization (2) acceleration (3) radiative recombination

Figure 2.2: The three steps of HHG: (1) The outer electron wave packet (Gaussian shape) of an atom is trapped in the coulomb potential of the ionic core (gray line). A strong laser electric field (thin straight line) superposes with the core potential, creating a finite potential barrier (black line), which enables tunnel ionization of the system. (2) The free electron is accelerated in the strong electric field, gaining kinetic energy, and driven back to the parent ion, when the laser field changes its sign. (3) The electron recombines with the parent nucleus and its excess energy, the gained kinetic energy Ekin of the electron plus the ionization potential Ip is emitted via a high harmonic photon (purple) of the frequency !q =(Ekin + Ip)/~.

6 2.1 HHG as a three step process

The three steps of HHG are depicted and described in figure 2.2. In the first step, where the atom ionizes, the electron has to tunnel through a coulombic barrier. The height of this barrier is characterized by the ionization potential Ip, therefore the condition ~!0 Ip implies that the absorption of many photons is necessary to ionize the atom,⌧ making HHG a highly non-linear multiphoton process. The tunneling process is not described quantitatively in this picture as this model serves only for a qualitative understanding of HHG. However, the highest frequency occurring in the HHG spectra can be determined quantitatively by considering the classical motion of an electron in the laser field. After ionization, when the electron appears in the continuum, it will immediately be accelerated in the strong laser field. Neglecting the core attraction, thus considering a free electron and assuming a linear polarized laser field in x-direction, the classical electron motion is described by:

@2x m = eE(t). (2.2) @t2 Solving this di↵erential equation within the slowly varying envelope approximation (i.e. E(t) E cos(!0t)) and assuming zero initial velocity leads to a time dependent electron velocity⇡ of

eE v(t)= (sin(!0t) sin(!0ti )) , (2.3) me !0 and the ponderomotive potential of the electron in the fundamental laser ﬁeld of wavelength as its classical mean kinetic energy,

2 2 2 1 2 e E e 2 2 Up = 2 me v = 2 = 2 2 E .(2.4) 4me !0 16⇡ me c ⌦ ↵ A numerical investigation of the maximum velocity of the electrons at their ﬁrst return to the parent ion results in an estimate for the maximum photon energy present in the HHG spectrum, the cut-o↵ law:

2 2 ~!c = Ip +3.17Up E .(2.5) / The cut-o↵ law clarifies, that the maximum harmonic frequency achievable from the HHG process is strongly linked to the ponderomotive potential Up and thus to the field amplitude and the wavelength of the fundamental laser light. The maximum applicable field amplitude is limited, because for very high intensities of the driving laser well above 1016 W/cm2, the magnetic component of the laser field becomes strong enough to⇠ induce a lateral acceleration, hence deflecting the electron, reducing the overlap between the electronic and the nuclear wave packet and thus preventing ecient harmonic generation. However, the cut-o↵ law states, that the maximum harmonic frequency in the HHG spectra will increase for longer wavelengths of the driving laser field. A shift of the cut-o↵ frequency towards the water window, or even

7 2 High-order Harmonic Generation at HZB the keV range of photon energy, by using driving lasers in the few µmrangewas demonstrated very recently at experimentally relevant harmonic flux in [9, 27]. Note that not only the cut-o↵ law, but also some other interesting limits on the HHG process are explained by the Simple Man Model. For instance, HHG will only occur if the driving laser field is linearly polarized. Electrons in an elliptically polarized laser field fly in spirals and therefore miss the parent nucleus. In terms of quantum mechanics, the overlap of the nuclear and the electron wave packet is reduced upon return. This has been observed in experiments, where the intensity of harmonics has decreased rapidly with increasing ellipticity [28]. However, it is possible to generate elliptically polarized harmonics with linearly polarized driving laser fields by using aligned molecules as non-linear medium for harmonic generation, for example laser aligned N2 molecules as demonstrated in [29].

Coherence and Phase Matching Within the Simple Man Model conclusions on the coherence properties of the HHG radiation can be drawn. The electron has to be considered as a quantum mechanical wave packet, which undergoes a transition from a bound state to a continuum state at a certain time ti , evolves in the laser field and finally descends to the bound state again under radiation of the kinetic energy gained while propagating through the continuum. This quantum wave packet oscillates with its own frequency, however the total phase of the electron at recombination and therefore the phase of the occurring XUV radiation is strongly linked to the time of ionization and to the strength of the fundamental laser. Thus the phase of the electronic wave packet at recombination and therefore the phase of the XUV light are locked to the phase and amplitude of the fundamental laser beam. This influences the collective behavior in the spatially domain, since spatial coherence properties of the irradiating laser are transfered to the harmonic emission, hence forth HHG is a spatially coherent process. The total emitted field in a macroscopic medium is given by a sum over the emissions from many atoms. Thus not only the single atom response, but also collective e↵ects as phase matching or re-absorption of the XUV light determine the intensity of the generated harmonics. Phase matching is given, if the radiation generated by di↵erent atoms at di↵erent positions in the medium interferes constructively at the exit of the medium. For a perfect match of phases, this condition reads as

K = k q k =0, (2.6) q 0 where K denotes the mismatch between the wave vectors kq of harmonic q and k0 of the fundamental. Approximate phase matching is achieved for

KLmed < ⇡ ,(2.7) where the vector Lmed describes length and direction of the medium. The dependence of the harmonic phase 'q on the laser intensity at the position of emission can be

8 2.2 The HHG setup at HZB

written as 'q = ↵qI , where ↵q is linked to the q-th Fourier component of the atomic polarization and proportional to the atomic dipole moment and density. An additional wave vector kI = 'q enters the phase mismatch, leading to a generalized phase matching conditionr for HHG [25, 30]:

K = k + k qk . (2.8) q I 0 This emphasizes, that transversal intensity proﬁle and wavefront shape do play an important role for optimizing the HHG yield.

2.2 The HHG setup at HZB

In this section, the high-order harmonic experiment at HZB is presented in detail. It is based on an existing setup [22], which was further developed within the framework of this thesis. The experiment on two-color two-photon ionization of small molecules described in chapter 6 and measurements on the reliability of semiconductor photodiodes [31] introduced at the end of this section were carried out at this setup.

power & polarization control delay ~ 10 m waveplates dichroic polarizer BBO mirror 0.3 mJ IR Ti:Sapphire

80 ap3 ap4 J BS / 785 nm 20 m SHG

1.5 mJ 2 HHG toroidal grating . dichroic mirror 50 fs 1 ap1 ap2 gas cell slit IR filter 3 kHz slit ap5 f=500 mm f=400 mm waveplate Al foils electron gas inlet spectrometer with hand valve removeable diode mirror camera available for experiments CCD vacuum chamber IR 785 nm, < 230 µJ SHG 393 nm, < 50 µJ toroidal HHG 30-70 nm, < 40 pJ mirror magnet & ion TOF

Figure 2.3: The pump-probe setup at HZB (see text for details).

Figure 2.3 shows a schematic sketch of the femtosecond pump-probe HHG setup at the HZB lab. The whole setup is driven by a Ti:Sapphire laser at a central wavelength of 785 nm, which delivers 50 fs pulses with a pulse energy of 1.5 mJ at a repetition rate of 3 kHz. A beam splitter (T=0.2, R=0.8) in the very beginning of the setup splits the incoming pulses into a 0.3 mJ pump pulse and an intense 1.2 mJ pulse for harmonic generation. The laser is situated in di↵erent hutch than the the HHG setup and the beam is transported via several mirrors to the beam splitter. The distance between laser and beam splitter is roughly 10 m, leading to an ampliﬁcation of possible

9 2 High-order Harmonic Generation at HZB pointing instabilities of the laser, which is transfered to the pointing stability of pump and probe and to the shot-to-shot intensity stability of the harmonic yield. In order to minimize these e↵ects, the laser hutch is equipped with a climate control system, ensuring well deﬁned and stable humidity and temperature. After individual manipulation, the pump and probe pulses are overlapped again. A rectangular in-vacuum mirror reﬂects the pump pulses into the interaction region, whereas the HHG probe pulses travel curtly above this mirror. This way, the pump and the probe beam are almost collinear in the experimental chamber at the end of the setup with a spreading angle well below 1, thus preventing broadening of the time- resolution due to non-collinear in-coupling. The experimental chamber is equipped with a photoelectron spectrometer, a molecular source and tools for aligning the setup. On the next pages, the two optical pathways and the experimental chamber are described in detail, as well as typical characteristics of the setup and tuning and optimization procedures.

2.2.1 High-Harmonic Generation Path The part of the laser reflected by the beam splitter consists of typically 1.2 mJ pulses and is used for harmonic generation (see figure 2.3, lower optical path). The pulses first pass a /2-wave-plate to control the polarization direction of the fundamental laser pulse which is directly transfered to the later generated harmonics. The wave- plate is tuned such, that the polarization is aligned along the groves of the grating further down the optical path to achieve optimum transmission of the grating. Two apertures (ap1 & ap2) are used for aligning the laser and tweaking the HHG output. The laser is focused by a f=500 mm lens into a 5.5 mm long stainless steel gas cell inside the vacuum chamber for high-harmonic generation, resulting in a focal spot size of 60 µmandanapproximatedpeakintensityintheorderof3–4 1014 W/cm2. The⇠ entrance and the exit of the gas cell along the laser path are⇥ sealed with a 0.1 mm thin copper foil in which the laser itself drills optimum sized holes of a few tens of µmforpropagatingthrough.Thecellisconnectedtoagasreservoirviaa hand valve which allows to control the flow into the cell and therefore control the quasi-static pressure which builds up inside the cell. The cell is operated with either Xe or Ar as non-linear medium for harmonic generation at pressures in the gas inlet tube of 0.46mbar for Xe or 3.2 mbar for Ar and a background pressure outside the 3 2 cell of 8 10 mbar or 1.1 10 mbar, respectively. This configuration enables cut-o↵ frequencies⇥ around the⇥ 21st harmonic, corresponding to 33.2 eV photon energy for Xe (Ip=12.2eV) as non-linear medium and around the 23rd harmonic (36.3 eV) for Ar (Ip=15.8eV). However, mostly Xe was used in every day operation as the harmonic yield is one order of magnitude higher than for Ar. In order to tune the phase matching condition, the cell is mounted on a manipulator which allows for optimizing its position along the laser path and therefore change its relative position with respect to the laser focus. Additionally, the apertures ap1 & ap2 before the

10 2.2 The HHG setup at HZB vacuum chamber can be tuned to achieve maximum HHG output. When tuning the apertures, the maximum intensity in the focal spot is optimized by cutting o↵ part of the laser beam, as well as the wavefront is manipulated due to di↵raction at the aperture (for details see below). After generation, the light passes through a monochromator equipped with an entrance and an exit slit of 0.5 mm width. Dispersion is achieved by a 550 lines/mm gold coated toroidal grating operated at a constant deviation angle of 142. The calculated eciency of the grating is 4-5% at 20 eV and 6-8% at 30 eV. Two aluminum foils (150 nm thick) one before the grating and one after the exit slit can be moved into the beam to block the IR light and ensure that no fundamental IR photons pass through to the experimental chamber and influence ongoing experiments when the monochromator is used in zero order and e↵ectively acts as mirror. The transmission of each of these foils amounts to 70% [32]. The monochromatized VUV pulses ⇠ have a duration of 110 10 fs at full width half maximum (FWHM)determinedby VUV-IR cross correlation± with photo-ionization sidebands of Ar, explained in detail on page 19 later in this chapter. The bandwidth of the pulses is 140 meV as shown in earlier work [22]. For experiments usually the 15th or 17th harmonic⇠ of the laser are selected, corresponding to a photon energy of 23.7 eV or 26.9 eV. In the next chamber along the beam, a removable piezoelectric driven 2 inch mirror mount is installed giving the possibility to reflect the VUV pulses on a CCD camera to inspect their spatial profile. Within the framework of a diploma thesis this mirror mount was equipped with a reflective zone plate to explore new monochromatization schemes [33]. Such a zone plate monochromatizes and focuses the beam at once making a more compact setup feasible. Additionally, a lower temporal stretch of the pulses than for standard grating monochromatization can be expected. Next along the beam path, a GaAsP semiconductor photodiode (Hamamatsu model g112704) is mounted on a translational stage which allows for measuring absolute average photon numbers of our HHG setup [31]. Finally, the VUV pulses are focused into the interaction region of the experimental chamber by a gold coated toroidal mirror at a grazing angle of 6 and a calculated reflectivity of 0.83 in the range of 20 - 30 eV of photon energy. The focal spot size is of approximately 100 µmhorizontallyandslightlylessvertically[22].

2.2.2 Pump Path The part of the laser transmitted through the beam splitter consists of 0.3 mJ pulses which serve as pump in time-resolved experiments. In the following, the preparation of the pump pulses is described element by element along the optical setup (see ﬁgure 2.3, upper optical path). First the light travels through a high-precision delay stage for varying the di↵erence in length of the two optical paths and therefore varying the di↵erence in the time of arrival of pump and probe at the experiment. The delay stage’s reproducible positioning accuracy is 1 µm. Thus, as the laser travels the delayed path back and forth,

11 2 High-order Harmonic Generation at HZB the minimum variation of the optical path is 2 µmandhencetheminimumrepro- ducible step size in time delay in this setup amounts to 7 fs. Note however, that while scanning the delay range, it is possible to use smaller steps, but reproducibility is not guaranteed. After passing an aperture (ap3) which is used for aligning and reduction of the beam diameter, if necessary, the laser enters a stage for power and polarization control. This stage consists of a /2-wave-plate — polarizer — /2-wave-plate sequential arrangement. The polarizer is set to a fixed position, therefore by controlling the polarization of the incoming laser beam with the first /2-wave plate, one e↵ectively controls the transmission through the polarizer and thus the power of the of the outgoing beam. The additional /2-wave-plate after the polarizer enables to adjust the direction of the polarization of the pump beam to any desired angle. The overall throughput of this stage is variable in the range from 20% to 85% of initial laser power. Next along the beam path, a BBO crystal is installed for frequency doubling, often called second harmonic generation (SHG). The BBO is fixed in a rotatable kinetic mirror mount which enables tweaking the BBO to highest available eciency. Note that the polarization of the SHG pulses is perpendicular to that of the fundamental IR pulses. After another aligning aperture (ap4), the two color beam (fundamental & SHG) is split by a dichroic mirror reflecting the blue and transmitting the IR light. After short individual pathways, both beams are recombined by another dichroic mirror. The path for the blue light is equipped with an additional IR filter, to ensure monochromaticity. This assembly enables easy pump color selection by simply placing a beam stop in the optical path of the undesired color, without touching any optical elements, and hence, without influencing the optical alignment. However, the optical path lengths are di↵erent, mainly due to the additional IR filter in the blue path. Measurements have shown, that pulses from the blue path arrive 19.7 0.1 ps later than the red pulses. ± After recombination, both colors pass through a last aperture (ap5) which enables blocking of possibly occurring stray light. The last optical element outside vacuum is a f=400 mm focusing lens. The lens is mounted on a 3-way translation stage for exact positioning in both transverse directions and along the beam path. Hence, the position of the focus in the experimental chamber can be controlled in all three directions, enabling optimization of the focal position with respect to the detector and tweaking the spatial overlap between pump and probe pulses. Lastly, the beam enters the experimental chamber through a fused silica view port and is reflected by an in-vacuum mirror towards the interaction region of the experimental chamber. The size of the focus of the pump pulse amounts to approximately 200 - 400 µm[22].

12 2.2 The HHG setup at HZB

2.2.3 The Experimental Chamber

side view top view

electron gas inlet spectrometer YAG:Ce screen camera auto-correlator

diode BBO IR filter

evaporation magnet & source ion TOF

Figure 2.4: The experimental chamber. Either the camera depicted in the left sketch or the auto-correlator setup shown in the right sketch can be mounted behind the chamber.

The last assembly of the HZB HHG setup shown in figure 2.3 is our experimental chamber, in which both light beams are collinearly coupled in and focused. A more detailed side and top view of the assembly is given in figure 2.4. The chamber is equipped with a variety of tools for aligning and setting up a pump-probe experiment and of course the main detector, a magnetic bottle photoelectron time-of-flight spectrometer (MBPES), which is described in detail in the next section. The interaction zone for experiments is in the very center of the chamber, indicated in the picture by the foci of the pump and probe beams. Besides the detector, a main part of the chamber is the evaporation source for bringing the sample into the interaction zone. In the left part of figure 2.4 the high-temperature sample source developed within this thesis is depicted, see chapter 3 for a detailed description. Instead of the high-temperature source, it is possible to mount a simple metal tube with a hand-operated fine valve, which allows for connecting various samples which are gaseous at least under the vacuum conditions in the chamber 5 (well below 10 mbar). For example, the experiments on above-threshold ionization described in chapter 6 were carried out with this metal tube. For using samples, which are liquid under normal conditions, they were filled into a glass dome which was connected to the tube, enabling measurements, for example, on H2O. Either evaporation source is mounted on a 3-way manipulator for optimal positioning of the source underneath the interaction volume. From top, a combination of a YAG:Ce scintillation crystal screen holder and another gas inlet are mounted to the chamber on a translational stage. The YAG:Ce screen is used for visualizing the light pulses at the interaction point and thus the transverse spatial overlap. Setting up the spatial overlap is described in detail on page 21 in this chapter. The gas inlet, equipped with a hand-operated fine valve, is used for inserting

13 2 High-order Harmonic Generation at HZB test gas (in our case mostly Ar) to the interaction point for cross-correlating the pump and probe pulses and therefore determining their temporal overlap (in detail on page 17). Our setup provides the possibility to mount a magnifying video camera system behind the view port at end of the experimental chamber for imaging the YAG:Ce screen and thus observing the transverse positions of the pump and probe beam. If required, the camera system can be replaced by an intensity auto-correlator setup, as shown in the top view on the right in ﬁgure 2.4. The functionality and operation of the auto-correlator is described in detail on page 17. Inside the experimental chamber, there are high vacuum conditions with pressures well 7 below 10 mbar, when HHG is in operation, but all other inlets are closed. During 5 operation of the gas inlet or the evaporation source, pressures of up to 10 mbar are acceptable in the chamber.

2.2.4 The Time-of-Flight Photoelectron Spectrometer

magnet meshes drift tube with solenoid mesh phosphor MCP screen

PMT

interaction volume Uret +kV

Figure 2.5: Schematic diagram of the time-of-ﬂight electron spectrometer installed at the HHG setup at HZB.

The core of the experimental chamber is a magnetic bottle photoelectron time-of- flight spectrometer (MBPES) for measuring kinetic energies of photoelectrons. The design is based on work by Eland et al. [34] and is nearly identical to a device developed by Michael Meyer (XFEL) operated at FLASH in Hamburg [35]. An overview of the assembly is given in figure 2.5. All Electrons ejected from photo- ionization in the interaction volume are directed by a strong permanent magnet (0.5 T) towards a drift tube. The tube is approximately 80 cm long and equipped with metal meshes for electron retardation at the entrance and another mesh at the exit on the same potential as the entrance mesh, to ensure electric field free space inside. A solenoid produces a weak magnetic field inside the drift tube, guiding almost all the electrons to a stacked micro channel plate detector (MCP). The electron shower created in the MCP stack is accelerated by a high voltage in the kilovolt range towards a phosphor screen and converted into visible light. A photomultiplier tube (PMT), which is mounted outside vacuum behind a view port detects the light from the screen. The phosphor screen – PMT combination is used for electron detection

14 2.2 The HHG setup at HZB instead of a metal anode to allow for visual inspection of the electron distribution on the MCP stack and thus for detection of misalignment. The collection eciency is 50–100% and the energy resolution without retardation amounts to 2% of the kinetic photoelectron energy, determined in commissioning measurements [22]. The signals from the PMT are recorded by a computer equipped with a triggered 4096 bit analog-digital converter card with 1 ns wide time slots, yielding a total detection window of 4096 ns. The trigger signal is obtained from a diode measuring the leakage of the laser through a mirror. The photoelectron spectra are typically recorded for ﬂight times of 300 ns–1500 ns. The resolution for the photoelectron spectrum under investigation can be further increased by tuning the retardation voltage. Already small retardation voltages are a powerful tool to reﬂect slow photoelectrons arising from multiphoton ionization by the pump laser only.

2.2.5 Tuning HHG High-harmonic generation is a sensitive process depending on carefully handling a whole set of parameters, to achieve good phase-matching and therefore high radiation yield. As described in section 2.1, the cut-o↵ frequency in the harmonic spectrum depends on the wavelength and the peak intensity of the fundamental laser, thus on the focusing strength and the pulse duration. However, the harmonic yield or conversion eciency strongly depends on phase matching inside the generation medium, strongly influenced by the generation gas density, the transverse intensity profile, the shape of the wavefront of the laser and the length of the generating medium. The medium length is given by the length of our gas cell and fixed in our setup. We experimented with several cell lengths and found the 55 mm cell is optimal for our source. The other parameters transfers to the following knobs, used for tweaking the HHG yield from our source. position of gas cell with respect to laser focus • flow/pressure of generation gas • beam diameter / aperture width • chirp & pulse duration of the laser • For tuning, these parameters are optimized until the HHG yield converges to a stable optimum. Usually it is enough to optimize the laser chirp and the gas cell position only once, while the aperture width and the flow through the gas cell have to be optimized in an iterative cycle. The optimum chirp of the laser corresponds to the shortest available pulses (45 - 65 fs), which was checked with an auto-correlator installed directly at the laser. The pressure inside the gas inlet tube is set with a hand valve to 0.46 mbar for Xenon or 3.2 mbar for Argon as generation gas, then the generation is optimized by slightly

15 2 High-order Harmonic Generation at HZB tweaking the hand valve. Unfortunately, it is not possible to measure the optimum pressure with higher accuracy. Tuning the width of the aperture in front of the vacuum chamber cuts the laser beam and adjusts the beam diameter and hence, the peak intensity in the focus. Too high peak intensities would lead to a breakdown of the harmonic generation, as the magnetic component of the laser field becomes high enough to induce a non-negligible lateral shift to the electron trajectory in the laser field (see figure 2.2). Hence, the electron will miss the parent nucleus, thus radiative recombination is prevented and the gas medium is ionized instead. Cutting the laser beam also influences its wave front and thus the phase matching in the HHG process. As our setup is not equipped with a wave front sensor, measuring and quantifying the exact influence of the wave front distortion is not possible. Hence, when tuning the opening of the aperture, it cannot be distinguished, in which proportion the optimization of the HHG yield arises from wavefront distortion or from peak intensity optimization. The width of the aperture is a very sensitive number as changing it by less than 0.5 mm can already change the harmonic output by more than a factor of 2. However, the width set after completing the tweaking procedure varies a lot from day to day due to varying performance of the fundamental laser between two start-ups, which a↵ects for example its transverse intensity profile. Typically, the pulse energy e↵ectively used for HHG after cutting the beam amounts to 0.7–1.2 mJ. Assuming a pulse duration of 60 fs of the laser inside the gas cell and a focal spot size of 60 µm, the laser⇠ peak intensity available for high- harmonic generation is in the order⇠ of 3–4 1014 W/cm2. The cut-o↵ in the harmonic spectrum for Xe as generation medium should⇥ therefore be around the 21st harmonic (corresponding to 33.2 eV photon energy), well above the 15th (23.7 eV) or 17th (26.9 eV) harmonic, which are usually used for experiments.

16 2.2 The HHG setup at HZB

2.2.6 Temporal Overlap – Cross- & Auto-Correlation One of the most important parameters in time-resolved pump-probe measurements is T0 and the time resolution. T0, i.e. full temporal overlap, is given at the delay stage position where both pulses arrive simultaneously at the experiment. Assuming a delay step size well below the pulse durations, the time-resolution is dominated by the cross- correlation function of pump and probe. In this setup, T0 and the time resolution are determined in a two stage approach. First, an approximate value of T0 is estimated with an optical intensity auto-correlator setup, mounted behind the experimental chamber, then T0 and the time resolution are determined most accurately at the interaction point with an intensity cross-correlation experiment using two-color photo- ionization. Intensity auto- & cross-correlation is a widely used technique to determine temporal characteristics of signals. In optics this technique serves as a tool for measuring the duration of light pulses and their temporal overlap. From the mathematical point of view, the intensity cross-correlation function X (⌧)oftwolightpulsesE1 and E2 for delay ⌧ is deﬁned as the convolution of the two pulses:

+ 2 1 2 X (⌧)= E E = E ⇤(t)E (t ⌧) dt | 1 ⇤ 2| | 1 2 | 1 Z + 1 = I (t) I (t ⌧) dt 1 2 Z1 = I I .(2.9) 1 ⇤ 2 Let’s assume Gaussian shaped intensity distributions of height A and width :

2 I (t)=A exp t .(2.10) 22 ⇣ ⌘ Then the cross-correlation becomes:

+ 1 t2 (t ⌧)2 Xg (⌧)=I1 I2 = A1A2 exp 22 22 dt ⇤ 1 2 Z1 2 ⇣ ⌘ t p 12 =exp 2(2+2) 2⇡ 2+2 A1A2 1 2 ⇥ 1 2 ⇣ t2 ⌘ =exp 22 AX .(2.11) X ⇥ ⇣ ⌘ Xg (⌧)isofGaussianshapeandtherelationbetweenthewidthofthecross-correlation measurement and the initial pulse durations is given by:

2 2 2 X = 1 + 2 .(2.12)

Hence, if one knows the duration of one of the pulses, the duration of the second pulse can be determined from the cross-correlation width X . Furthermore, X gives

17 2 High-order Harmonic Generation at HZB an estimate of the time resolution available for experiments. Equation (2.12)also states, that the cross-correlation width is an upper limit for the pulse durations. For an auto-correlation, where 2 = 1, the pulse duration reads as:

1 = X /p2. (2.13)

In these considerations a zero centered relative delay axis ⌧ is assumed. In praxis, adelaystagepositionz in length units is often recorded. The maximum of X (z) determines z0 the point of maximal temporal overlap, thus T0. The transformation between delay stage position z and relative time-delay ⌧ is:

⌧ =(z z )/c , (2.14) 0 where c denotes the speed of light. Next, the implementation of auto- & cross-correlation at the HZB HHG setup is presented. A sketch of the auto-correlator setup is shown on the right side in figure 2.4. It consists of a sequential arrangement of a BBO SHG crystal, an IR filter and a photodiode, forming an intensity auto-correlator. Such auto-correlation schemes are awidelyusedtechniqueinlaserlabsandwelldescribedintextbooks,forexample[36]. To run the auto-correlation, the monochromator in the HHG path is set to zero order and all Aluminum filters are moved out letting the IR pulses pass through the vacuum system to the auto-correlator. In the pump path, IR is selected and the focusing lens is tuned to overlap both light beams in the BBO crystal for second harmonic generation (SHG). After filtering out the IR, the on-axis SHG signal, which is proportional to E(t)E(t ⌧)isdetectedbyaphotodiode.Thediodeisanintensitydetectorandits time constant is large compared to the pulse durations, hence it integrates over time t. The recorded signal is

+ + 1 1 I (⌧) E(t)E(t ⌧) 2 dt = I (t)I (t ⌧) dt (2.15) D / | | Z1 Z1 and corresponds to an intensity auto-correlation as described above. Figure 2.6 shows an exemplary auto-correlation taken with our setup. The FWHM of the correlation is 121 2fs,thereforethedurationofthelaserpulsehereis 86 2fs.However,thegroupvelocitydispersionintheexitwindowofthevacuum± chamber± prolongs the highly chirped pulses, therefore the pulse duration deduced from auto-correlation behind the chamber does not correspond to the duration inside at the interaction point. In order to estimate the pulse length inside, we simulated this situation by placing a fused silica view port of same type as the laser in-coupling view ports in front of a SPIDER commercial auto-correlator and measured the duration of the laser pulses before entering the vacuum. The simulation suggests a pulse duration in the vacuum chamber of 45 - 65 fs.

18 2.2 The HHG setup at HZB

0.9 fit FWHM = 121 ± 2 fs data 0.8

0.7

0.6 rel. intensity (a.u.) 0.5

−500 0 500 delay (fs)

Figure 2.6: Auto-correlation function measured with the arrangement of BBO crystal and photodiode behind the experimental chamber.

Note that overlapping the pulses in the BBO crystal slightly changes the di↵erence of pump and probe path, therefore T0 gained in this auto-correlation is only accurate within 300 fs with respect to the interaction zone. ±

For precise determination of T0 at the interaction volume in front of the photoelectron spectrometer and for cross-correlating pump and HHG probe pulses, sidebands are measured. The occurrence of sidebands in the photoelectron spectra from ionization with a VUV/XUV pulse in presence of a long wavelength electromagnetic dressing field was first discovered and described by Glover et al. in 1996 [37]. Sidebands arise from two-color multiphoton absorption, when the electron in a single ionization process interacts simultaneously with the ionizing VUV/XUV photon and one or more photons from the dressing field. Their formation is described in detail in chapter 6, where an experiment on polarization dependence of sidebands is introduced. The height of the sidebands depends on the intensity of the dressing field at ionization and thus on the relative time delay ⌧. Assuming Gaussian shaped pulses, a delay scan of the sideband height corresponds to a cross-correlation as introduced in equation (2.11). For carrying out a sideband intensity delay scan with our setup, a gas jet is brought into the interaction volume by the gas inlet tube mounted to the chamber together with the YAG:Ce screen holder, see figure 2.4. After ensuring spatial overlap in the interaction region, the delay dependence of the intensity of one of the sidebands in the photoelectron spectrum of the detection gas is measured. We used mostly Ar as gas for sideband generation, because it shows an intense peak at 15.8 eV binding energy with a high sideband generation cross-section for our VUV radiation, hence enabling high contrast cross-correlation measurements, but, in principle, any other gaseous sample with electronic states accesible by the VUV radiation is suitable.

19 2 High-order Harmonic Generation at HZB

1000 fit FWHM = 72 ± 2 fs fit FWHM = 123 ± 2 fs 200 data data 800

150 600

400 100 rel. intensity (a.u.) rel. intensity (a.u.) 200

50 0

−500 0 500 −500 0 500 delay (fs) delay (fs) (a) unmonochromatized VUV beam (b) 17th harmonic, 26.9 eV

Figure 2.7: Cross-correlation functions deduced from two-color two photon ionization sidebands in the interaction volume of the experimental chamber.

In ﬁgure 2.7 exemplary cross-correlation measurements with ﬁtted Gaussian curves obtained from our setup are shown for (a) the unmonochromatized VUV beam and (b) the 17th harmonic at a photon energy of 26.9 eV. T , determined from these measurements is accurate within 5fs,asestimatedfrom 0 ± repeating the measurements several times. Note that T0 for the unmonochromatized beam di↵ers by approximately 10–20 fs from T0 for the harmonics, due to a slight change of the optical path length, when tuning the monochromator. An estimate for the time resolution given by the FWHMsofthecross-correlationfunctionsis72 2 fs for the unmonochromatized beam and 123 2fsforthemonochromatized17th± harmonic. These numbers are typical for our setup,± however on a day to day basis, they vary by 10 fs. In a pump-probe experiment, actual time resolutions better than stated above± may be achieved by increased data statistics. With the FWHMsfromcross-correlationsandassuming45-65fspumppulses,the pulse duration of the HHG signal can be determined by applying equation (2.12). Taking into account the day to day variation of the pulse widths and the uncertainty in pump pulse duration, the average HHG pulse duration is 47 19 fs for the unmonochromatized light and 110 12 fs for the 17th harmonic,± which should well apply for the other high-harmonics± in the spectrum. Thus, the temporal stretching of the probe pulses induced by the grating in our monochromator amounts to 63 22 fs. Note that the line density of our grating, 550 lines/mm is not optimal, the stretching± could well be reduced by installing a grating with fewer lines/mm and still keeping the dispersion high enough to ensure separation of the individual harmonics.

20 2.2 The HHG setup at HZB

2.2.7 Spatial Overlap Another crucial parameter in pump-probe experiments is good spatial overlap of both light beams. In order to image the transversal sections of the light beams, hence their spatial overlap, a 24-fold magnifying video camera system is mounted to the experimental chamber and focused on the YAG:Ce scintillation crystal, positioned at the point of interaction (see ﬁgure 2.4). The crystal converts VUV radiation into visible light by photoluminescence and di↵usively di↵racts the optical pump pulses, ensuring that both beams are imaged at same depth. The HHG focal spot of 60 µm diameter is magniﬁed 24-fold to a spot of 1.4 mm diameter on the 12.7 12.7⇠ mm2 CCD chip in the camera, hence to roughly⇠ 10% of the image size. The camera⇥ image is displayed on a monitor and by tuning the position of the lens in the pump path both light spots are centrally overlapped. The pump beam is usually 2 - 4 times bigger in size than the VUV. This procedure is accurate enough to measure a two-color photo- ionization signal, thus enabling cross-correlation and temporal overlap measurements. After assuring temporal overlap, the lens position, hence the spatial overlap can be further optimized by maximizing the two-color sideband photo-ionization yield.

2.2.8 Divergence of the VUV Beam In order to estimate the divergence of our VUV source, an X-ray CCD camera (Andor iKon-L 936)wasmounteddirectlytotheexitofthemonochromatorinadedicated experiment for measuring the spot sizes on the CCD and thus the divergence of the beam. The additional chamber after the monochromator in figure 2.3, equipped with aremovablemirrorandaCCDcamerawasinstalledlater,inconsequenceofthis experiment. The harmonic yield was varied by tuning the gas pressure inside the gas cell, the cell’s position along the laser beam and the width of the apertures in front of the vacuum chamber (ap1 & ap2 in figure 2.3). Figure 2.8 shows exemplary measurements of the divergence of the 17th harmonic (26.9 eV) generated in Xe for four di↵erent flux levels with intensity profiles and Gaussian fits for vertical (Y) and horizontal (X) direction. The measurements yielded an average divergence of the VUV pulses from our source of div(Y) = 3.7 0.6 mrad vertically and div(X) = 2.6 0.4 mrad horizontally, which should well translate± to other harmonics from our source.±

21 2 High-order Harmonic Generation at HZB

4 4 2 2 0 0 −2 −2 div Y (mrad) div Y (mrad) −4 −4 6.8×108 ph/s 5.2×108 ph/s −4 −2 0 2 4 −4 −2 0 2 4 div X (mrad) div X (mrad) (a) 2.6 4.4 mrad2 (b) 2.4 3.6 mrad2 ⇥ ⇥

4 4 2 2 0 0 −2 −2 div Y (mrad) div Y (mrad) −4 −4 4.6×108 ph/s 2.8×108 ph/s −4 −2 0 2 4 −4 −2 0 2 4 div X (mrad) div X (mrad) (c) 3.1 3.7 mrad2 (d) 2.2 3.2 mrad2 ⇥ ⇥ Figure 2.8: Divergences for the 17th harmonic of our HHG source generated in Xe for several values of the photon flux (indicated in white). Normalized intensity profiles (green) with Gaussian fits (red) are plotted on top for the divergence in horizontal direction (X) and aside for vertical divergence (Y). The subtitles (a-d) give the corresponding widths (FWHM) of the fits as div(X) div(Y). ⇥

22 2.2 The HHG setup at HZB

2.2.9 Absolute Photon Flux & Shot-to-Shot Stability A separate experiment on the reliability of semiconductor photodiodes under radiation with ultrashort pulses was carried out and published in [31], where the photon numbers measured with a diode are compared against calibrated absolute photon numbers obtained from a Gas Monitor Detector (GMD). In the following, the main parts of this publication are reproduced and summarized. Semiconductor photodiodes are calibrated a synchrotron light sources, at high repetition rates under quasi-cw irradition, whereas a femtosecond photon source like our HHG setup produces short intense pulses with peak intensities exceeding those during calibration by several orders of magnitude. This brings up the question, if the calibration is still reliable under these extreme conditions.

Figure 2.9: The HHG setup as modiﬁed for the measurements on the shot-to-shot stability and absolute photon ﬂux from our source and on the reliability of semiconductor photodiodes. Inset: (principal) sketch of the assembly inside the GMD illustrating its basic functional principle. (reprinted from [31])

For cross-calibration measurements, we mounted a GMD to our setup directly behind the monochromator and the semiconductor photodiode behind the GMD, see figure 2.9. The GMD is based on the photo-ionization of a (rare) gas and was developed for on-line measurement of the radiant power of VUV and soft X-ray FELs [38–41]. Measurements of absolute average photon fluxes as well as shot-to-shot photon numbers with an accuracy below 5% are feasible with this device. The inset of figure 2.9 illustrates the functional principle of this detector. The VUV radiation ionizes the target gas (either Xe or Ar in our experiment) and the generated ions and electrons are extracted and accelerated in opposite directions by a homogeneous static electric field. The extraction field of 333 V/cm (corresponding to an extraction voltage of 1000 V) is chosen to be high enough to ensure complete collection of the charged particles created in the interaction volume accepted by the

23 2 High-order Harmonic Generation at HZB respective particle detector. In our experiment the ion signal was measured only. A ﬁrst simple metal plate detection electrode allows for measuring a slow averaging current IAV by a calibrated Keithley 617 electrometer with a time constant of a few seconds, which is not a↵ected by any individual intra-pulse time structure or shot-to- shot variations of the radiation. Moreover, a fraction of the ions enters a drift section through a small aperture in the detection electrode and is detected by an open electron multiplier (ETP 14880) operated in a linear regime. The multiplier delivers a single shot current ISS , which can be utilized for pulse resolved (shot-to-shot) relative ﬂux measurements. Knowing the averaged absolute photon number NAV , single shot absolute photon numbers, determined from the peak value of the multiplier signal ISS read as:

ISS NSS = NAV (2.16) ⇥ IAV

Figure 2.10: Shot-to-shot stability of the fundamental IR laser (top) and the generated harmonic VUV output (bottom). (adapted from [31])

Figure 2.10 depicts the shot-to-shot stability of the fundamental laser, deduced from leakage through a mirror and stability of the HHG source measured with the GMD at 3kHzrepetitionrate.Theintensityofthefundamentallaserisstablewithin 2.3% ± FWHM, in contrast, the flux of the HHG source varies by 26.6%. This points out the highly non-linear nature of the HHG process. Note that the± source was not optimized for minimal shot-to-shot fluctuations. Additionally, the multiplier can be used for ion time-of-flight spectrum measurements (see figure 2.11)whichenablescheckingthepurityofthetargetgasandruling out multiple ionization. Both e↵ects would perturb the ion-current signal by adding

24 2.2 The HHG setup at HZB currents from other ions than singly ionized target gas particles and therefore the absolute calibration of the GMD would no longer be valid [31].

Figure 2.11: Two exemplary GMD ion time-of-ﬂight spectra (averaged over 5000 shots) ⇠ illustrating the purity of the target gas. The spectrum of Xe target gas and residual air is shown in (a),while(b) shows the spectrum of pure singly ionized Xe target gas as used for the ﬂux measurements. (adapted from [31])

In figure 2.12 the relative deviation (in percent) between the average photon flux derived from the diode signal and that from the GMD is plotted against the absolute average flux measured with the GMD. Four data sets (connected with lines) are shown for four di↵erent photon energies corresponding to di↵erent harmonics of our source. To vary the harmonic yield and therefore the fluxes, the width of an aperture in the generating laser beam was tuned. In a next step we calculated the resulting power (product of photon energy and flux) of the VUV radiation. Figure 2.13 depicts the deviation (in percent) between the average photon flux calculated from the response of the diode and that of the GMD versus the absolute average power given by the GMD signal. The error bars in both graphs are deduced by taking into account the 5% accuracy of the GMD and the accuracy of the measurement of the photo current from the diode. The photo current was measured with a Keithley 6485 electrometer in slow averaging mode. The accuracy of the photo current values were approximated for every measurement by carefully observing the variation of the photo current signal and amounted to be in the range of 3% to 10%. The graphs show, that the diode systematically underrated the photon flux by up to 15%. This points to saturation e↵ects in the diode due to the high peak power emitted from our HHG source. However, our results proof, that a calibrated photodiode is still a good and easy-to-use tool for measuring the flux of femtosecond VUV HHG photon sources within, as in our case, an accuracy of around 15%. Depending on the

25 2 High-order Harmonic Generation at HZB day-to-day laser performance, 106–107 photons/pulse/harmonic, corresponding to a ﬂux of 109–1010 photons/s/harmonic could be measured at our HHG source with the diode.

Figure 2.12: Relative deviation of the photon numbers estimated from our semiconductor photodiode and the GMD versus the photon ﬂux for several VUV harmonics: ⌥ H11 (17.4 eV), H13 (20.5 eV), ⌅ H15 (23.7 eV), H H17 (26.9 eV). (adapted from [31])•

Figure 2.13: Relative deviation of the photon numbers estimated from our semiconductor photodiode and the GMD versus the average power of the VUV radiation. (adapted from [31])

26 3 High-Temperature Sample Source

In order to enable gas-phase measurements on samples which are solid or liquid in vacuum at room temperature, a high-temperature sample source with an oven was developed within the framework of this thesis. The oven was planned and used for measurements on NaI (chapter 7), but will in future serve as source for various substances, where temperatures of up to 1000 Careneededforevaporation. High-temperature in-vacuum ovens have long since been used as molecular sources for many experiments on atoms, clusters and molecules or as sources for sputtering and layer deposition of materials. Various concepts of molecular ovens have been realized so far, meeting the demands of the individual applications. A summary on ovens for metal atom beam sources by Ross and Sonntag [42] has inspired the development of our molecular source. Our oven had to meet several constraints: it had to be dimensioned to fit our existing experimental chamber (p.13↵), the maximum reachable temperature had to be well above 600 CtoevaporateNaIatasucient rate and the exit nozzle of the oven had to be positionable very close underneath the interaction point without touching the magnet of our magnetic bottle, thus the nozzle has to be of small outer diameter. Following these constraints, we developed, designed and built the molecular oven in aclosein-housecollaborationwithK.KalusandT.NollfromtheHZBengineering department and A. Drescher and his co-workers from the scientific workshop at HZB. A sketch of the resulting molecular oven is depicted in figure 3.1. The smaller picture on the left shows a complete view of the oven mounted on top of the main rod, which is fixed to a CF63 flange. Water tubes and an electric feedthrough are built into the flange to feed electric power and cooling water to the oven assembly. The large drawing on the right shows the oven assembly in more detail. A water cooled cup, housing the oven is mounted to the main rod. Cooling is achieved by ameanderingwatercircuitjustunderneaththesurfaceofthecupande↵ectively shelters the surrounding, i.e. the experimental chamber, from heat. The oven itself is mounted in this cup. It consists of a heated main body, where a separate stainless steel crucible, later containing the sample, is put in, and a copper nozzle with a 2 mm inner diameter tip is plugged into the crucible. For filling in sample material, only the copper nozzle has to be removed. A resistively heated wire is wrapped in spiral carvings around the main body and clamped by a thin metal cylinder. The inconel alloy sheathed, 987 mm long, 28 ⌦ resistance heating wire is well-suited for

27 3 High-Temperature Sample Source

molecular evaporation source mounted in water cooled cup copper nozzle

heat shelter

water cylindric intake tubes wire clamp

main rod inductive heating wire melting pot CF 63 flange

main oven body cooling cup with integrated water circuit electric feedthrough main rod and water intake mounting assembly tubes

Figure 3.1: The high-temperature sample source designed and constructed at HZB, suitable for temperatures of up to 1000 C.

temperatures of up to 1000 C. Such heating elements are commercially available from the companies Thermsys or Thermocoax. We tried wires from both suppliers and could see no di↵erence in operation. According to the technical speciﬁcations of the wires, voltages of up to 110 V can be applied, corresponding to a current of 3.9 A and an electric heating power of 430 W. However, we never ran the oven above 250 W (3 A). When starting up the oven, the current must be ramped up not faster than 1.5 A per 30 min, to ensure a slow thermal stretching of the wire and that all humidity possibly in the wire has evaporated before applying high currents thus preventing electrical or mechanical destruction of the heating element. During an experiment, the current for operation is set and optimized using the molecular signal from the experiment itself, as no thermocouples or other devices allowing for measuring the temperature are installed to the oven assembly. In the case of NaI, for example, ﬁrst signals from NaI molecules are usually visible around a current of 1.7 A. However, to achieve a good signal-to-noise ratio, currents between 2.0 A and 2.7 A are necessary. Private communications with the engineers from the manufacturing companies suggest, that such currents correspond to temperatures of 500 - 700 C.

28 Under these conditions, the oven has to be refilled with fresh NaI sample every 10- 14 hours. By now, the oven was used only with NaI as sample, but there is no principal con- straint in using any other liquid or solid sample, which is non-corrosive to copper and stainless steel. After operation with NaI, left overs in the oven show glass-like structure, supporting the conclusion that during operation, the whole sample is at least liquefied or even completely gasified. For a constant heating current, this leads to a constant gas pressure inside the pot–nozzle assembly and therefore to a constant flow through the tip of the nozzle. The copper nozzle is in tight contact with the crucible and hence indirect heating prevents plugging of the 2 mm diameter channel in the tip of the nozzle. The oven was used in three di↵erent setups so far: for test measurements at the HZB HHG setup, at the MBI laser pump–probe setup (see chapter 4) and at FLASH in Hamburg, by a group from Lund University to whom we lent the oven. The experimental results obtained at MBI are presented in chapter 7.

4 Pump-Probe Setup at the Max-Born-Institute Berlin

For the measurements on NaI in chapter 7, a collaboration between the Max-Born- Institute Berlin (MBI) and HZB was formed and the experiment was carried out at the laser laboratory at MBI in April 2011. The general setup is described in detail in [43], except that for our purpose the original liquid jet was replaced by our high-temperature molecular oven (see chapter 3)andthemagneticbottleelectronspectrometerwas replaced by a velocity map imaging spectrometer (VMI). The pump-probe setup as used for the NaI experiments is brieﬂy described here. A principal sketch is given in ﬁgure 4.1.

TOPAS Ti:Sapphire VMI spectrometer light conversion BBO 310-410 nm 800 nm <100 fs focusing 3 mJ 3-7 µJ mirror 40 fs delay 1 kHz

BBO BBO 200 nm <100 fs 2-3 µJ 2 hv 3 hv BBO

4 hv molecular oven

Figure 4.1: Schematic diagram of the experimental setup at the Max-Born-Institute.

A titanium sapphire laser delivering short and intense 40 fs, 2 mJ pulses at a central wavelength of 800 nm and a repetition rate of 1 kHz serves as primary light source. The pulses are split in order to generate two beams of di↵erent photon energy which later serve as pump and probe. One part of the laser drives a commercial TOPAS light conversion stage, equipped with a frequency doubling BBO crystal at its exit. In combination with the bandwidth of the mirrors, this assembly delivers pulses with wavelengths between 310 nm and 410 nm (corresponding to 4.0 - 3.0 eV photon energy) with a bandwidth of 0.06 eV (FWHM), pulse durations well below 100 fs and pulse energies of 3-7 µJtothe experiment. The second part of the primary laser travels through a delay stage, before entering a fourth harmonic generation setup. In a sequence of three BBOs, the fourth harmonic of the laser wave is generated stepwise by ﬁrst frequency doubling in the ﬁrst BBO

31 4 Pump-Probe Setup at the Max-Born-Institute Berlin and then wave mixing of the fundamental and the harmonic output from the previous BBO in two more stages. Thereafter, two narrow band wavelength ﬁltering dielectric mirrors ensure clean 200 nm (6.2 eV) pulses shorter than 100 fs and with an energy of 2-3 µJ and a bandwidth in the order of 0.06 eV. After recombination, both colors are focused into the interaction volume in the vacuum chamber by a spherical focusing mirror. The vacuum chamber is equipped with an VMI spectrometer for measuring the kinetic energy and the angular velocity distribution of photoelectrons. The detection scheme is described, for example in [44]. The molecular oven used for evaporating NaI in this experiment is mounted on a 3D manipulator for exact alignment of the molecular jet. The oven was developed and constructed at HZB and is introduced in detail in chapter 3.

32 5 Pump-Probe Setup at the Free Electron Laser in Hamburg

The measurements on photo-induced dissociation of Fe(CO)5 described in chapter 8 were carried out in a collaboration between DESY Hamburg, XFEL Hamburg and HZB within the framework of two measurement campaigns at the Free electron LASer in Hamburg (FLASH) [45–47] (4 shifts, 21-25 April and 8 shifts, 27 Mai - 6 June 2011). This section describes the experimental setup used at FLASH and the technical challenges to be dealt with when performing a time-resolved pump-probe experiment at a free electron laser (FEL).

5.1 FEL principle

A free electron laser is an accelerator based, highly brillant and coherent light source. Electron bunches are accelerated to energies in the GeV range and sent through an undulator, a periodic alternating assembly of magnets, in which the electrons are forced on a sinusoidal trajectory and emit spontaneous synchrotron radiation. The radiation moves faster than the electrons and slips over the electrons further up in the bunch, imprinting an energy modulation at the period of the fundamental resonant wavelength of the undulator. Coherent oscillation of the electrons in this well-defined periodicity leads to an exponentially enhanced emission of coherent, high power radiation at the resonant wavelength. This process is called self-amplified spontaneous emission (SASE) and takes place during one single pass of the electrons through the undulator without the use of any optical resonator. SASE starts from spontaneous, stochastically distributed emission, therefore the spectral distribution and the intensity of the yielded radiation vary from shot to shot in a SASE FEL. At Flash, the electron bunches are accelerated in a super conducting linear accelerator to an energy of about 1GeVandsentthrougha30mlongundulator.Thefundamentalwavelengthavail- able at FLASH is in the range from 47 nm to 6.9 nm, corresponding to 26 - 180 eV photon energy and the inherent spectral bandwidth of FLASH amounts to 1% [47]. Other FELs are designed for even higher photon energies in the hard x-ray⇠ range, for example the Linac Coherent Light Source (LCLS) in Stanford (USA) can go up to 10 keV [48], the SPring-8 Angström˚ Compact Free Electron Laser (SACLA) at the RIKEN Harima Insitute (Japan) recently lased at 12 keV [49] and the European X-ray Free Electron Laser (XFEL), currently built in Hamburg (Germany) is designed to reach photon energies of more than 12 keV [50].

33 5 Pump-Probe Setup at the Free Electron Laser in Hamburg

5.2 Monochromator beamline

In many spectroscopic experiments, it is crucial to exactly know and control the incoming photon energy with an accuracy better than the inherent 1% bandwidth of FLASH, therefore the FLASH facility o↵ers monochromatic beamlines behind a plane grating monochromator unit, PG1 and PG2 [47]. The design of the monochromator unit is described in [51, 52]. A variable slit at its entrance allows for controlling the number of grooves illuminated on the Carbon coated grating and thus for controlling the temporal stretch induced upon monochromatization. Illuminating fewer grooves decreases the prolongation of the light pulses, on the cost of transmission eciency and energy resolution. A second variable slit after the grating is used for limiting and adjusting the spectral bandwidth of the di↵racted, spatially energy dispersed photon beam. The transmission through the monochromator for open slits and in zero order is 64% for a 200 lines/mm grating [47] and about 12% for the monochromatized first order beam for 2 mm exit slit width, 88.3 eV photon energy and a constant fixed focus (c↵)valueof1.5[51]. In [35], first order transmission of 4% for the complete PG2 beamline is reported at 114.9 eV photon energy, a c↵ value of 1.5 and 300 µmexit slit width. The smallest focal spot available for experiments at the PG2 beamline is in the order of 50 µmdependingonphotonenergyandmonochromatorsettings[47]. However, in⇠ our experiment at the PG2 beamline, the focal spot size was about 280 µmin horizontal and 400 µminverticaldirection,for123eVphotonenergy,c↵=1.5 and the exit slit width set to 2 µm, corresponding to 0.1 eV bandpass.

5.3 Timing in pump–probe experiments

The FLASH facility provides a high power femtosecond optical laser system for pump- probe experiments, transported to the experimental stations by a separate laser beamline system and synchronized to the electron accelerator via an RF source. However, due to a number of reasons mainly arising from electron acceleration, the pulses from the FEL itself show shot-to-shot jitter, short term and long term drifts with respect to the RF source, and hence with respect to the optical laser. Electron bunch arrival monitors (BAMs) are installed at FLASH and used as feedback for jitter reduction and drift compensation. It has been demonstrated that this feedback can reduce the stochastic shot-to-shot jitter to 40 fs RMS However, due to a vast number of reasons originating from size and complexity of the machine, in praxis, pump–probe experiments su↵er signiﬁcantly larger shot-to-shot jitter between FEL and optical laser pulses in the order of 250 fs RMS, corresponding to 600 fs FWHM [53]. Furthermore, the BAM system is not directly correlated to the optical laser and drifts of the FEL pulses with respect to the laser in the order of picoseconds per hour are still remaining [47]. Hence, for performing precise pump–

34 probe experiments, it is crucial to monitor the actual timing between FEL and optical laser. In an FEL, the arrival time of the electrons at the undulator is directly linked to the arrival time of the photons at the experiment by a constant o↵set. Thus, if the electron arrival time can be correlated with the optical laser, accurate pump–probe timing is feasible by sorting the data in time domain during post processing. At FLASH two di↵erent timing tools are installed, directly linking the optical laser and electron arrival: a streak camera system, cross-correlating optical laser and dipole radiation from the electron dump, and timing by electro-optical sampling (TEO). TEO is based on the Pockels e↵ect in an electro-optical crystal [54–56]. The electric field of an electron bunch flying near by ( 1mm)inducesabirefringencewhich rotates the polarization of a laser pulse traveling⇠ through the crystal. At FLASH, the crystal is mounted perpendicular to the propagation direction of the electrons. A pulse split from the optical pump laser and widened to large diameters, is shined on the crystal at an incident angle of 45. This geometry correlates the transverse coordinate of the laser profile and the time coordinate along the electron path. Only the polarization of that part of the laser interacting with the crystal at the same time as the electrons pass by is rotated, thus the arrival time of the electron bunch is encoded in the transverse polarization profile. The polarization profile is measured with a CCD camera behind an optical analyzer for shot-to-shot determination of the relative arrival time of electron bunch and optical laser. Time sorting of the data with respect to the arrival times during post processing enables a reduction of the jitter and thus an increase of the time resolution to 90 fs RMS (210 fs FWHM)andbetter [56]. The streak camera (Hamamatsu C5680) correlates the optical laser pulses and dipole radiation produced by a bending magnet after a undulator for directing the electrons to a beam dump. The nominal streak camera resolution is only about 2psFWHM, hence precise shot-to-shot jitter measurements are not feasible. But for⇠ determination of the relative arrival time only the position of the correlation maximum on the streak camera has to be analyzed, which is feasible with an accuracy of 400 fs [35]. Further averaging can provide for estimation of short and long term drifts within about 100 fs accuracy [47], but admittedly this gives only an estimate for the central time value around which the FEL jitters. Another promising method for direct x-ray/optical shot-to-shot correlation has recently been reported [53, 57], where the x-ray pulses induce transient reflectivity changes in a GaAs substrate and intensity changes in reflected optical pulses are used for deducing relative arrival times. In contrast to measurements of the electron timing, this technique monitors the pump–probe delay directly at the experiment, taking into account all possible jitter sources in the electron and in the photon beamlines of FLASH and providing for an accuracy in the order of about 100 fs FWHM [53]. However, this method is rather photon hungry and can not be utilized for the monochromatized first order beam of FLASH so far and hence was not an option for our experiments at PG2.

35 5 Pump-Probe Setup at the Free Electron Laser in Hamburg

5.4 Experimental setup at FLASH

Figure 5.1 shows a principal sketch of the setup, which previously has been described in [35].

streak camera 3 hv dielectric mirrors BBO 2 hv Ti:Sapphire BBO electron 800 nm spectrometer < 1 mJ telescope 50 fs 10 Hz delay 267 nm < 80 fs, < 50 µJ

FLASH PG2 10 nm focusing mirror nJ - µJ vacuum with pinhole 200-300 fs chamber magnet 10 Hz

Figure 5.1: Schematic diagram of the pump-probe setup at FLASH.

From the Ti:Sapphire laser system, 50 fs, 1 mJ, 800 nm pulses are delivered to the experiment at the 10 Hz repetition rate of FLASH, after a minor portion of the laser power was directed to the streak camera system. The laser first passes a delay stage, allowing for a variable delay over a total range of 3 ns, before driving athirdharmonicgeneration(THG)setup.THGisachivedinatwoBBOfrequency conversion crystal sequential arrangement and yields 267 nm pump pulses, shorter than 80 fs FWHM and of up to 50 µJpulseenergy.Asetofthreedielectricnarrow band mirrors directly behind the THG stage is used for filtering out the fundamental and the second harmonic beams. A Galilean telescope in front of the experimental chamber allows for adjusting the focal position of the laser along the beam path by 1mm.Changingthedistanceof the telescope lenses to a value o↵ the nominal telescope± distance alters the divergence of the beam and controls the focusing of the spherical mirror inside the chamber and thus the longitudinal position of the pump laser focus. The monochromatized pulses from the PG2 beamline pass through a pinhole in the spherical mirror, hence both, the pump and the probe beam can be overlapped in a collinear geometry in the interaction region. For our experiment, FLASH was tuned to 123 eV photon energy (10.1 nm) and a pulse energy of approximately 30 µJ, resulting in monochromatized pulses fluctuating in the range from approximately a few tens of nJ to µJpulses.Theintrinsicshot-to-shotfluctuationsinpulseenergy arising from the SASE process are even increased by monochromatization, because shot-to-shot instabilities in the spectral distribution of the FEL light translate to intensity fluctuations, when only a limited bandwidth of the spectrum is selected by amonochromator.Thepulsedurationavailableafterthemonochromatorwasinthe range of 200 - 400 fs FWHM, depending on the appointed monochromator slit widths.

36 In the experimental chamber, a simple thin metal tube just underneath the interaction volume (not shown figure 5.1)servesassamplegasinlet.Thetubeismountedon a3-waytranslationstageforexactpositioningandconnectedtoanelectronicleak valve for regulating the sample gas flow. For detecting photoelectrons, a magnetic bottle time-of-flight electron spectrometer is installed, o↵ering an energy resolution of 1–2% of the kinetic energy of the photoelectrons. The photoelectron time-of-flight distributions are determined from a micro channel plate (MCP) in current mode. The signals are either analyzed and stored via a digital oscilloscope or directly stored to the FLASH data storage system via a network connected 10 bit digitizer system provided by FLASH (see next section). This spectrometer is described in detail in [35] and served as model for ours at the HZB HHG setup (see p.13↵).

5.5 Post processing and time sorting

FLASH is equipped with a facility-wide data acquisition (DAQ) system, which stores all properties and monitored parameters from FLASH — from the accelerator to the experimental endstations — to a central server at the DESY site and labels the datasets for every single shot with a unique electron bunch ID number [58]. The experimental data can either be stored locally at the experiment by the users themselves or, as in our case, fed into the DAQ system via an Acqiris 10 bit digitizer system provided at FLASH. The amount of data produced in time-resolved experiments at FLASH is enormous, because for enabling sorting of the data in time domain during post processing, each measured photoelectron distribution has to be stored separately for each shot. In our campaign, for example, data in the order of 1600 GB were produced in 80 hours of total acquisition time, corresponding to a rate of 20 GB/h or 5.7 MB/s. In order to handle this huge flux of data, a fast network reserved for DAQ trac only and a state of the art file server and storage system including a dedicated binary data container file format designed and implemented by DESY are part of the DAQ system. DESY provides a software library for Linux/Unix systems for later access to the datasets in the binary containers. Based on this library, we developed a set of applications for extracting the relevant data from the DAQ system and for sorting the datasets with respect to pump-probe delay times, taking into account the position of the delay stage and jitter measurements available from the streak camera system. We tried to include the timing signal from the BAM system into our post processing procedure for an estimate and reduction of the shot-to-shot jitter, but could not achieve an improvement of time resolution, as the BAM is not directly linked to the optical laser, and as it is not clear how the di↵erent timing signals depend on each other. Hence, it was not clear how to account for and disentangle contributions to the arrival jitters measured by di↵erent timing tools. Unfortunately, the TEO system, which could have served as stand-alone timing tool for shot-to-shot jitter and drift

37 5 Pump-Probe Setup at the Free Electron Laser in Hamburg deduction with 200 fs accuracy and better was not functional during our campaign. As mentioned before, for sorting the datasets in the time domain, the arrival times deduced from the streak camera system have to be averaged over several shots for a reliable compensation of short and long term drifts in post processing. Accord- ing to FLASH sta↵,themostreliabledriftcorrectionfordatasetn is obtained by exponentially weighted averaging:

cam cam cam < t >n = wtn +(1 w) < t >n 1 ,(5.1) cam cam with the actual value from the streak camera tn , the averaged value < t > and q the exponential weight w =1 e ; q =0.05wasfoundtobeagoodexponentin tests by H. Redlin from FLASH. The time allocated to dataset n reads as:

stage cam tn = tn + < t >n ,(5.2)

stage where t is derived from the delay stage position. The time tn di↵ers from the real di↵erence between pump and probe pulse by a constant o↵set t0, which has to be assigned by the pump-probe experiment itself. Knowing this o↵set, the pump-probe delay for the nth recorded spectrum is given by:

t = t t .(5.3) n n 0

Post processing is performed in a two stage approach: first the relevant datasets are extracted from the raw data stored in the DAQ system and second a time sorting and error detection script is applied to the raw data, creating final datasets for further scientific analysis. For extraction, a C ++ application was developed, which catches the experimental data, the photoelectron spectrum, streak camera time, delay stage position, monochromator settings, relative pump intensity, GMD and BAM signals from the DAQ raw data containers for each shot. The photoelectron spectrum is stored in a temporary binary container file and all the other meta data is stored to a separate mat file. The mat file format is the native binary format from Matlab, a widely used high-level programming language and scientific software package developed by Math- works. This format is supported by most scientific data analysis programs, hence still leaving the freedom of choosing one’s favorite software package for further analysis of the data. In a second step, sorting in time-domain and basic error analysis is performed by a Matlab script. The meta data mat file is read and for error analysis, the GMD signal, monitoring the intensity of the FEL shots, is analyzed and shots, where the intensity is below a given threshold are marked as false shots, where FLASH was delivering only very few or no photons, thus not running optimal. In order to prevent unknown perturbations to our measurements, these shots are omitted upon time-sorting. Fur- thermore, the live signals from streak camera, delay stage, BAM, monochromator

38 energy setting and relative pump intensity are checked for steadiness and an error message is printed, when huge jumps are found. In this case, detailed, manually performed consistency checks of the data are required. Fortunately, this was not necessary for the datasets from our campaign at FLASH. For time-sorting, the arrival time is computed for each shot according to equation (5.2), and the photoelectron spectrum is read from the temporary container file and added up to the corresponding time slot. The number of datasets sorted into each slot is counted in a separate variable. The width of the time slots (in our case 50 fs) is chosen well below the jitter of the FEL and further binning in time is left to later analysis. This ensures that the maximum available time resolution is transfered to the post processed data. In case, the monochromator energy setting was varied during the experiment, the data is additionally sorted with respect to the incident photon energy from FLASH. Finally, the resulting sorted dataset with all meta data is saved to one single mat file, containing all information relevant for the detailed scientific analysis. The amount of hard disk space occupied by the post processed dataset is reduced by a factor of 50 - 1000 with respect to the initial raw DAQ data, depending on several factors as for example scanned delay range, acquisition time and photon energy range.

Part II

Experiments

6 Polarization Control in Two-Color Above Threshold Ionization

The occurrence of satellite peaks in the photoelectron spectra from ionization with a VUV/XUV pulse in presence of an IR dressing field was first discovered and described by Glover et al. in 1996 [37]. These satellite peaks, also called sidebands, arise from multiphoton two-color above-threshold ionization (ATI), occurring when the dressing field photon density is high enough to enable simultaneous absorption or emission of one ore more additional IR photons by the photoelectron created by the XUV/VUV pulse. The sidebands show up in the photoelectron kinetic energy distribution left and right of the main peaks from single photon ionization at integer multiples of the IR photon energy.

1 IR off IR on 0.8

0.6

0.4

normalized intensity 0.2

0 12 14 16 18 20 electron energy (eV)

Figure 6.1: The process of two-color two-photon sideband formation shown here for photoionization of the 3p shell in Ar (left) and corresponding idealized photoelectron spectra (right) for single photon ionization (blue line) and for two-color two-photon ionization in presence of a dressing IR ﬁeld (red line). The binding energy of Ar 3p6 is 15.8 eV (see table 6.1).

Figure 6.1 illustrates the process of sideband formation for two-color two-photon ATI of the outer shell of Ar 3p6, creating Ar+ 3p5 (left) and shows idealized calculated photoelectron spectra with the IR ﬁeld present or absent (right). Note that spin-orbit 2 2 2 splitting of the Argon P peak at 15.8 eV into P3/2 (15.76 eV) and P1/2 (15.94 eV) [59] is not plotted.

43 6 Polarization Control in Two-Color Above Threshold Ionization

A VUV photon lifts an electron from the outer shell into the continuum above the ionization threshold. The electron can simultaneously interact with the dressing IR field by either absorbing or emitting an IR photon, hence gaining or loosing kinetic energy of the equivalent of the energy of one IR photon. In the photoelectron spectra, the main peak is depleted with respect to single photon ionization without the IR field present by the amount of electrons undergoing interaction with the IR field and these electrons form satellite peaks to the main peak, the sidebands. For higher IR photon densities, the electron can interact with several IR photons and thus a whole series of higher-order sidebands can occur in the photoelectron spectrum (not visualized in figure 6.1). The probability for sideband formation depends on the intensity of the dressing field, therefore following the sideband intensity versus the time delay between the two light pulses enabled the first direct measurement of the pulse duration of femtosecond high-order harmonic radiation by intensity cross-correlation [37]. Nowadays, this technique has evolved as standard tool for characterizing ultra-short XUV/VUV pulses, for example at the HZB HHG source (see subsection 2.2.6).

6.1 Polarization dependence

Recent experiments on sideband formation in atoms confirmed that the intensity of sidebands depends on the relative angle between the polarization vectors of the ionizing and the dressing light fields. This was demonstrated with HHG VUV light for Argon [60] and with XUV light from FLASH for Helium [61, 62]. An exemplary measurement from [62] is reprinted in figure 6.2, where the relative sideband intensity is plotted versus the relative angle ✓ between the polarization vectors of IR and XUV pulses.

Figure 6.2: Polarization dependence of two-color two-photon sideband formation in He- lium. (reprinted with permission from [62])

44 6.1 Polarization dependence

This polarization dependence is linked to the geometry and especially to the symmetry of the electronic structure of the system under investigation. Interaction with an electromagnetic field prepares a principal direction in the electronic distribution of the system along the polarization of the field, and if the electromagnetic field ionizes the system, a characteristic photoelectron angular distribution (PAD) will be measured by an angular resolved photoelectron detector. In the case of one-photon ionization of isotropically oriented gas-phase atoms or molecules, the PAD is cylindrically symmetric around the polarization vector of the ionizing light field and characterized by a dimensionless asymmetry parameter 2 [ 1, 2], which is a measure for the asymmetry in perpendicular and parallel dimensions2 of the PAD with respect to the polarization vector. Two exemplary PADs are plotted in figure 6.3 for di↵erent degrees of asymmetry, hence di↵erent 2 (see equation 6.2, introduced in the next section for an analytical expression). Let’s assume in a gedankenexperiment that a dressing IR field, with a polarization angle ✓, relative to the ionizing VUV pulses, interacts with the angularly directed PADs and that the length of the overlap of PAD and IR polarization vector is a measure for the sideband formation cross-section (yellow line in figure 6.3). Within these assumptions, it follows from figure 6.3, that the higher the asymmetry of the one-photon PAD, the smaller the sideband intensity modulation for varying relative polarizations of VUV and IR light. This links the amplitude of the sideband intensity modulation to the geometry of the electronic state.

θ θ

IR IR (a) VUV (b) VUV

Figure 6.3: Idealized one-photon ionization PADs for a high (a) and a medium (b) degree of asymmetry, 2=1.5 and 2=0.5, respectively. The polarization vectors of the ionizing VUV and the dressing IR light ﬁelds and the overlap of PAD and IR polarization vector (yellow) are indicated for an exemplary relative polarization angle ✓.

However, in the gedankenexperiment, interaction with isotropically oriented atoms or molecules by the VUV pulse is assumed and the IR light is thought to interact with the resulting 2-dimensional PAD, which represents the averaged outcome of many repeti- tions of the interaction. In reality the two light ﬁelds interact with the 3-dimensional electron density distribution of the system. A 2-dimensional PAD depends on the symmetry properties of this electron distribution, but does not completely reﬂect its

45 6 Polarization Control in Two-Color Above Threshold Ionization geometry or shape. In terms of sequential one-photon ionization, the outgoing electron wave has to perform an angular momentum transition (l = l 1), thus a geometry and symmetry transition, for each photon taking part in the ionization± process. Note that in quantum mechanics the succession of the interaction with the two photons is not decidable. But, as in the gedankenexperiment, a principal direction in the electron distribution is prepared by each pulse and therefore the relative polarization of the pulses should inﬂuence the eciency of the two-color two-photon ionization process of sideband formation and link the initial electronic distribution geometry with the sideband polarization dependence. This link can enable an alternative way of testing the symmetry of the angular distributions of photoelectrons from atoms and molecules by determination of the sideband polarization dependence, without the need of an angularly resolved photoelectron detector. In order to see the inﬂuence of the molecular electronic structure on the polarization dependence and in order to test, if symmetry properties of the electronic geometry of the system under investigation can be estimated from the process of sideband formation, we performed measurements on the polarization dependence of two-color two-photon ionization intensity of several atoms and small molecules, in our case Ar, H2O, O2 and N2, and compared the experimental results to a theoretical approximative model.

6.2 Theoretical model

Two-color sideband formation is related to photoelectron angular distributions (PADs) formed by multiphoton ionization. The general theoretical form of a PAD for absorption of m photons from an excitation pulse and n photons from an ionization pulse of arbitrary polarization can be expressed as [63]:

2n+2m +L I (✓, ') B Y (✓, '), (6.1) / LM LM L=0 M= L X X where YLM (✓, ')denotessphericalharmonicsandL must be even for parity reasons. The BLM coecients depend on the molecular alignment prepared by the exciting pulse and thus on the geometry of the molecular electronic structure, on the photoionization dynamics and on the relative polarization of the exciting and the ionizing pulse. In order to obtain the sideband intensities, as measured by the angularly integrating magnetic bottle electron spectrometer of our HHG setup (p.14), the PAD has to be integrated over both angles. Note that for the case of one-photon ionization with linear polarized light, the above equation simpliﬁes to:

I (✓) 1 (1 + P (cos ✓)) , (6.2) / 2 2 2

46 6.2 Theoretical model

with the second order Legendre polynomial P2 and the asymmetry parameter 2, well known in photoelectron spectroscopy. The PAD for single photon ionization has cylindrical symmetry, hence equation (6.2)isindependentof'. In a two-color two-photon process, like the formation of ﬁrst-order sidebands, as considered in this chapter, it is n = m =1,hencetheﬁrstsumoverL in equation (6.1) runs only to 4, but still leaves 9 complex terms to compute. However, the relative decrease in sideband intensity for the extremal cases of perpendicular and parallel relative polarization can serve as a characteristic property of their polarization dependence. Reference [63] provides the form of the PADs for these two special cases of relative polarization: parallel (cylindrical symmetric ' independent) ) I (✓, ' =0) B Y (✓,0)+B Y (✓,0)+B Y (✓,0) , (6.3) / 00 00 20 20 40 40 and perpendicular

I (✓, ') B Y (✓, ') / 00 00 (6.4) + BL 2YL 2(✓, ')+BL0YL0(✓, ')+BL+2YL+2(✓, '), LX=2,4 where the Z axis is deﬁned by the polarization of the ionizing pulse. If the detector is mounted in the plane spanned by the two polarization vectors, the PAD for perpendicular relative polarization becomes cylindrical symmetric as well and thus independent of '. Equation (6.4)thansimpliﬁesto:

I (✓, ' =0) B 0 Y (✓,0)+B 0 Y (✓,0)+B 0 Y (✓,0) . (6.5) / 00 00 20 20 40 40 0 Equation (6.5)hasnowaformsimilartoequation(6.3), but the factors BLM depend on the factors BLM from equation (6.3)forparallelpolarizationplusB22 and B42 (see ref. [63] for detailed formulas), thus the problem is reduced to calculating a total of 5factorsBLM . As mentioned above, the coecients BLM depend on the molecular electronic structure of the molecule and the molecular orbital under investigation and are of high complexity, hence hard to compute already for well deﬁned polarization geometries, therefore a simplifying easy-to-compute approximative model is desired. Such an approximation, tracing back the polarization dependence in two-color two- photon ionization to the asymmetry parameter 2, known from one-photon ionization, is given in [60]. The model was developed to be valid for two-color two photon ionization starting from atomic p-states and describes the modulation of the relative sideband intensity as:

3 2 2 ISB(✓) 1 sin ✓ ,(6.6) / 5+22

47 6 Polarization Control in Two-Color Above Threshold Ionization with the angle ✓ between the two polarization vectors and assuming the soft-photon limit, where the IR photon energy is assumed considerably less than the kinetic energy of the observed photoelectrons and small compared to the ionizing VUV/XUV photon energy. For deriving equation (6.6), the authors of [60] express sideband formation in terms of transition amplitudes for ground state to continuum transitions via an intermediate continuum state. The polarization dependence arises from polarization dependent coupling of this intermediate state to the final state. In each transition, the selection rules for the angular momentum have to be fulfilled: l = 1, hence starting from a p-state, the intermediate continuum state is either ✏s or ✏±d, leading to two possible final continuum states, ✏p or ✏f . Although, the above statement suggests that by varying the relative polarization, one probes the coupling between intermediate and final states, the polarization of the photon preparing the intermediate state still introduces a principal direction, thus the second photon probes the symmetry of the initial state as well. Note that this model is derived under the assumption of an initial p-state and is explicitly not valid for other initial angular electron momenta. The model equation (6.6)clearlylinksthesymmetryoftheinitialstatewiththe strength of the sideband polarization dependence via the one-photon ionization asymmetry parameter 2. For the normalized sideband intensity polarization modulation, the characteristic di↵erence between maximum and minimum, corresponding to parallel and perpendicular relative polarization, reads as:

max min ISB ISB 3 2 = max = .(6.7) ISB 5+22

Hence, from this experimentally easily accessible value, the asymmetry parameter can be deduced within this model as: 5 = .(6.8) 2 3 2

In private communications, R. Ta¨ıeb,one of the authors of [60], has pointed out that this model should be applicable as ﬁrst-order approximation for ionization from p-like states even in small molecules. This could lead to a new simple experimental method for identifying the 2 asymmetry parameters of materials in gas-phase.

48 6.3 Experiment

6.3 Experiment

The experiment was carried out at our pump–probe HHG setup, described in chapter 2. The 15th harmonic from our source, corresponding to a photon energy of 23.7 eV is overlapped with the fundamental IR laser (785 nm, 1.6 eV) in the interaction zone of our experimental chamber, which is equipped with a magnetic-bottle photoelectron spectrometer. Ensuring full spatial and temporal overlap of both beams, we varied the relative polarization of the two pulses and followed the intensity modulation of the sidebands corresponding to ionization of the highest occupied molecular orbital (HOMO)ofthesystemunderinvestigationandsimultaneousabsorptionof one IR photon. We chose the IR laser intensity such that only ﬁrst-order sidebands occurred. Contributions to these sideband peaks from multiphoton processes, where for example two IR photons are absorbed and one is emitted by the electron can be neglected due to their low probability. The measurements were repeated several times for each species to check the reproducibility and to estimate the accuracy of the data.

ground state ionized state

2 6 1 + 2 5 2 Ar 3s 3p ( S0)+~!vuv Ar 3s 3p ( P)+(✏s, ✏d)+~!ir (✏p, ✏f ) ! ! 2 1 + 1 2 H2O (1b1 2p) ( A1)+~!vuv H2O (1b1 2p) ( B1)+(✏s, ✏d)+~!ir (✏p, ✏f ) ! ! 2 3 + 1 2 O2 (⇡g⇤ 2p) ( ⌃g)+~!vuv O2 (⇡g⇤ 2p) ( ⇧g )+(✏s, ✏d)+~!ir (✏p, ✏f ) ! ! 2 1 + + 1 2 + N2 (g 2p) ( ⌃g )+~!vuv N2 (g 2p) ( ⌃g )+(✏s, ✏d)+~!ir (✏p, ✏f ) ! !

Ar H2OO2 N2 binding energy (eV) 15.8 12.6 12.3 15.6

Table 6.1: Electronic conﬁgurations for sideband formation from the HOMO and the corresponding single-photon ionization electron binding energies for all species investigated in this work. The binding energies, taken from [59], refer to the dominating 2 ionization chanel. Substructures, for example the splitting for Argon in P3/2 and 2 P1/2, are not taken into account, as they are not properly resolved in this work. The term (✏s, ✏d)+~!ir (✏p, ✏f ) visualizes the interaction of the electrons ! with the IR ﬁeld. ✏x denotes an electron continuum state of angular momentum character x.

All systems investigated in this experiment (Ar, H2O, O2,N2)haveap-likeHOMO, therefore meeting the requirements for equation (6.6)tobeapplicable.Theground and ionized state electronic configurations for sideband formation from the HOMO are listed in table 6.1 for each species. An overview of a typical measurement is given in figure 6.4. Sidebands are clearly visible at 14.2 eV and 17.4 eV on both sides of the single photon ionization peak at 15.8 eV in figure 6.4.(a). Minor contributions from second order sidebands show up in the spectrum around 12.6 eV and 19 eV as well, because the laser intensity was slightly

49 6 Polarization Control in Two-Color Above Threshold Ionization

1 1 Ar+2P 0.9 0.9 ∆ 0.8 0.8 0.7 0.7 (b) 0.6 0.6 90° relative sideband intensity 42° 0 45 90 135 180 0.5 −6° 0.4 (c) 1

normalized intensity 0.99 0.3 0.98 0.2 SB SB 0.97 0.1 (a) 0.96 relative peak intensity 0 12 14 16 18 20 0 45 90 135 180 binding energy (eV) relative polarization (°)

Figure 6.4: Overview of a typical polarization dependence measurement of two-color two- photon ATI in Argon. Photoelectron spectra for three di↵erent relative polarizations are shown (a), with the x axis given in binding energies with respect to ionization of the Ar 3p level (15.8 eV, see table 6.1). The dependence of the intensity on the relative polarization of the light pulses is plotted for the left sideband (b) and the main photoelectron peak (c). too high. By the time the experiment was carried out no IR power control, except tuning the width of apertures in the beam path was available, therefore we could not achieve better adjustment of the laser intensity. However, the second order sideband intensities are very small and their contributions are neglected with respect to our model. Figure 6.4.(b) shows the polarization dependence of the intensity of the first- order sideband of interest from absorption of a VUV and an IR photon around 14 eV, left of the main peak. The intensity was determined by integrating the photoelectron signal for the whole sideband peak. The intensity of the main photoelectron peak is shown in figure 6.4.(c) and is maximum for minimum sideband intensity at ✓=90,as expected. The error bars were calculated before normalization as the square root of the total electron counts (Poisson statistics) and scaled with the same normalization factor as the data points. Both polarization dependent curves are fit by a cosine-like function and the di↵erence between maximum and minimum sideband intensity is visualized in figure 6.4.(b). The model equation (6.6)canbeexpressedintermsofacosinefitfunctionfor providing easier numerical handling during analysis. Assuming normalization to the maximum signal for parallel polarizations, this fit function directly contains the characteristic amplitude of the modulation of the normalized sideband intensity as the

50 6.4 Results doubled amplitude of the cosine:

I (✓) 1 cos(2✓ + )+c ,(6.9) SB / 2 0 where 0=0 for sidebands, 0=90 for depletion of the single photon ionization peak and c =1 1 is the zero-o↵set of the cosine function. 2 6.4 Results

The photoelectron spectra for Ar, H2O, O2 and N2 are presented in figure 6.5 for parallel (red) and perpendicular polarization (blue). The spectra were calibrated to the binding energies for the individual systems, see table 6.1 and [59]. The sidebands under investigation from absorption of one photon from each light field, left of the main peaks and their polarization dependence are clearly visible. Those sidebands showing up right of the main peak, thus corresponding to emission of aphotontotheIRfieldarenotconsideredhere,becauseforsystemswithmorethan one electronic state close to the ionization threshold it is impossible to disentangle signals from these lower states, the sidebands from these states and the sidebands from the HOMO. Very small contributions from second-order sidebands are visible in

0.9 Ar 2P H O 2B 2 1 0.7

0.5

0.3 SB SB 0.1

0.9 O 2Π N 2Σ+ 2 g 2 g 0.7

normalized spectral intensity 0.5

0.3 SB SB 0.1

9 11 13 15 17 19 9 11 13 15 17 19 binding energy (eV)

Figure 6.5: Photoelectron spectra for the four systems under investigation for parallel (red line) and perpendicular relative polarization (blue line) of VUV and IR light.

51 6 Polarization Control in Two-Color Above Threshold Ionization all spectra left of the first sidebands, pointing to a slightly too much dressing IR field intensity. Figure 6.6 depicts the polarization dependences of the sidebands for all four systems and compares them with the model presented in section 6.2. The plots are ordered by the characteristic modulation amplitude , starting with the highest value for Ar in the upper left panel. Blue markers represent the measured data, red lines are corresponding cosine fits, and black lines show theoretical sideband intensity modulations, calculated from the model, equation (6.6), with values for 2 taken from the literature [64–68]. Colored shades indicate the uncertainties in the model plots originating from the uncertainties of the literature values of 2. The measured characteristic modulation amplitudes ,derivedexperimentalasymmetryparameters2 and previously published values for 2 are listed in table 6.2 and table 6.3.

0.9

0.8

0.7

0.6 Ar H O 0.5 2

0.9

0.8 normalized sideband intensity 0.7 ν 1 ν 0.6 0 O ν ,ν not resolved N 0.5 2 1 0 2

0 90 180 0 90 180 relative polarization (°)

Figure 6.6: Modulation of the sideband intensity as a function of the relative angle between the polarization vectors of VUV and IR pulses. Experimental data with error bars (blue markers) and cosine ﬁts (red lines) are shown for our four investigated systems. Black lines represent the theoretically expected intensity modulations according to our model with values for 2 taken from the literature and colored shades indicating the uncertainty. Three model curves are plotted for N2, corresponding to 2 literature values from vibrational decay channel resolved measurements (⌫1, ⌫0) and from an earlier vibrationally unresolved experiment.

52 6.4 Results

We observed that the normalized amplitude of the sideband modulation varies for di↵erent atomic or molecular species, as expected from the model for varying 2. The sideband modulation should be highest for the most oriented electronic state, hence high 2. This is reflected in the data, as Ar shows the highest modulation amplitude. The data for Ar, H2OandO2 are in reasonably good agreement with the model. For Ar and H2O, the plotted shades indicating the uncertainty from the literature values of 2 almost meet the experimental data points, but the model predicts sideband intensity modulations slightly higher than measured. For O2, the sideband modulation is underestimated, but still in good agreement, especially if one keeps in mind that the model was derived for p-states of atoms. The situation is more complex for N2. The molecule shows a resonance for excitation with the 23.7 eV photons used in our experiment. At this photon energy two decay channels compete with each other, corresponding to di↵erent vibrational final states + of the created N2 ion. Auto-ionization processes take place and perturb the two- color two-photon ATI process forming the sidebands. Hence, here the approximative model apparently fails. In the bottom right panel of figure 6.6, the experimental data and the predictions from the model are plotted for N2 with 2 values taken from the literature for a vibrationally resolved measurement [67] and for an experiment where 2 was determined without distinction between vibrational final states [68]. The di↵erent values of 2 are listed in table 6.3. None of the predicted curves or tabulated values is close to the data, which clearly indicates the failure of the model, as it was not designed to be valid within aresonance.Thebreakdownofthemodelinturndemonstratesthesensitivityof two-color two-photon ATI to vibrational resonances in the ionized system. Moreover, this sensitivity could be utilized in future pump–probe photoelectron spectroscopy experiments for quickly testing, if a resonance is hit, without the necessity of a tunable photon source.

Ar H2O O2 N2 experimental 0.42 0.02 0.35 0.05 0.24 0.03 0.14 0.04 ± ± ± ± (this work) 0.97 0.07 0.76 0.14 0.48 0.07 0.26 0.08 ) 2 ± ± ± ± literature 1.18 0.12 1.08 0.17 0.31 0.08 see 2 ± ± ± ref. [64] [65] [66] table 6.3

Table 6.2: Magnitudes of the sideband intensity modulation and the 2 values deduced with our model compared to 2 values from the literature.

53 6 Polarization Control in Two-Color Above Threshold Ionization

N2 2 value [67] vibrational channel ⌫ 0.78 0.05 0 ± ⌫ 0.50 0.07 1 ± [68] no distinction of ⌫ , ⌫ 0.67 0.07 0 1 ± this work 0.26 0.08 ±

Table 6.3: Asymmetry parameter 2 of the HOMO of N2 from a vibrational channel resolved experiment and from an experiment not distinguishing between the two decay channels compared to 2 determined from this experiment.

6.5 Conclusion for this chapter

A theoretical approximation was introduced, describing the polarization dependence of sidebands in photoelectron spectra, formed by two-color two-photon above threshold ionization, valid for p-character initial electronic molecular states. The model links the sideband polarization sensitivity with the one-photon ionization asymmetry parameter 2, which describes the asymmetry in photoelectron angular distributions. Experimental tests of this approximation were performed at our HHG based pump- probe setup on four small atomic and molecular systems, namely Ar, H2O, O2 and N2. The model is in reasonably good agreement for three of the investigated systems, Ar, H2OandO2. The disagreement of model and experimental results for N2 shows that we stroke a resonance in N2 with our HHG photons and thus the model is not valid for this system. A more precise approach, taking into account more information about the electronic system is desirable, for example higher order asymmetry parameters and resonances. The group around R. Ta¨ıeb, one of the authors of [60], where this model was introduced, is currently working on extending and more precisely rendering the theoretical model and on extending it to other initial angular momenta than p-like states. From an experimentalist’s point of view, repeating the experiment with an angular resolved detection scheme, for example with an angular resolved time-of-ﬂight spectrometer (ARTOF) [69] or a velocity map imaging spectrometer (VMI) [44], enabling the determination of photoelectron angular distributions for each relative polarization angle or at least for the two extremal relative polarizations, parallel and perpendicular, should be the next step. The experiment should be equipped with accurate control of the IR intensity in order to prevent the formation of higher order sidebands and thus to better meet the assumptions for the theoretical approach. Additionally, more molecular systems could be investigated with various angular momenta of the HOMO and the on– and o↵–resonance situation could be speciﬁcally compared.

54 6.5 Conclusion for this chapter

This could provide deeper insight into, and understanding of fundamental processes and symmetries in light matter interaction for small molecules and atoms and possibly clarify the deviations between experiment and theory, observed in this work.

Acknowledgement for this chapter

The presented experiment on polarization control in two-color above threshold ionization was carried out at the high-harmonic generation setup at Helmholtz-Zentrum Berlin, Germany, described in chapter 2. Experiment and data evaluation were performed by the author of this thesis, Torsten Leitner. Phillipe Wernet (Helmholtz-Zentrum Berlin, Germany) and Michael Meyer (European XFEL, Hamburg, Germany) greatly contributed with their very help- and fruitful ideas and in numerous discussions. In private email communications, Richard Ta¨ıeb(UPMC, Universit´eParis 06, France) provided help and insights regarding the theoretical model adapted from previous work of him and his group.

7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

In the past decades, femtochemistry has made remarkable progress and intensive research is going into the investigation of dynamic processes in molecules on the femtosecond time-scale. In 1988 the group of A. Zewail pioneered this progress by performing extensive studies on the temporal evolution of molecular wave packets in photo-excited NaI using femtosecond transition state spectroscopy (FTS) by laser- induced fluorescence (LIF) [3, 4]. In the following years they continued with intense research on this subject, yielding a number of publications on the dynamics of photo- excited NaI molecules and on techniques to visualize chemical processes on fundamental pico- to femtosecond time scales [70–77]. In one of their original experiments, the wave packet is prepared from the ground state of NaI into the first excited state by a pump laser pulse and the evolution of the system is followed by a delayed probe laser pulse, which induces a transition 2 to an upper dissociative potential, where the Na atom is an excited PJ state. The 2 2 yield of the laser-induced fluorescence of the atomic Na D–line ( PJ S1/2)at 589 nm is followed versus the pump–probe delay time. The wavelength! of the probe laser defines a optically coupled region (OCR), where both potentials are resonantly coupled and the wave packet can undergo a transition to the upper potential. Thus, fluorescence will only be observed for those delays, where the wave packet is at equal intra-molecular distance as the OCR. Varying the probe wavelength enables shifting of the OCR along the potentials. These studies have enabled the characterization of the potential energy surfaces of the excited state and the (lower) unbound states, as well as the characterization of wave packet oscillations happening in excited NaI molecule, due to an intersection of the first excited state A and the ground state X forming an e↵ective trapping potential (see figure 7.1). Since then, a vast number of theoretical and computational papers dealing with potential energy surfaces and wave packet dynamics in NaI molecules have been published [78–89]. For monitoring dynamics in the electronic structure, time-resolved photoelectron spectroscopy (TRPES) techniques have shown to be a powerful tool [2, 90, 91]. In TRPES, the system is excited by a pump laser pulse pmp and photo-ionized by a time delayed probe pulse prb. The kinetic energies of all created photoelectrons are then measured simultaneously, and therefore all electronic states with binding energies below the probe photon energy are accessible. Hence, in contrast to FTS by LIF as performed by Zewail and co-workers, energy resolved photoelectron distributions and

57 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI therefore the temporal evolution of the full electronic structure of the system under investigation can be recorded, enabling conclusions on the dynamics of the electronic and the nuclear wave packets of the corresponding molecular wave packet. Already in 1989, shortly after the first publications on femtosecond NaI dynamics, it was pointed out, that TRPES should yield improved, deeper results on the dynamics than fluorescence spectroscopy, used in the first experiments [79]. However, to our knowledge, it took another eight years for the first TRPES study with femtosecond pulses on NaI molecules to be published, in 1997 by C. Jouvet and his group [92, 93]. In their experiment, they could only distinguish between slow and fast electrons, hence not using the advantage of resolving all electronic states simultaneously. Their results were well reproduced by numeric simulations of the experiment, published in 2007 [87]. In this chapter, our results from a photoelectron energy resolved TRPES experiment in April 2011 at the Max-Born Institute Berlin (MBI) on the electronic and nuclear wave packet dynamics in photo-excited NaI molecules with 320 nm (3.87 eV) pump and 200 nm (6.2 eV) probe pulses are presented. First a description of the experiment, calculated potentials and expected photoelectron spectra, modeled in a simplified approach are introduced. Thereafter the results from our measurements are presented and discussed in detail.

7.1 How it works

7.1.1 Calculated intra-molecular potentials In figure 7.1 intra-molecular potentials for the NaI molecule, calculated by Michael Odelius (Stockholm University, Sweden) [94] based on previous theoretical work [83, 85], and an illustration of the principle of our experiment are shown. The intra-molecular potentials for the molecular ionic ground state X, the spin-orbit split excited molecular covalent states A and B and the first three states of NaI+ ions, named ↵, and are plotted. The labels at the potential curves, on the right side for long distances give the corresponding free fragments for the asymptotic limit of infinite distances. The energy axis is chosen relative to the lowest energetic free neutral fragments, for the asymptotic limit of the A potential. An overview of the molecular states of NaI, the corresponding fragments and their ionization energies is given in table 7.1. Potential curves for higher lying excited states of the NaI molecule, between the B and ↵ potentials, which are not relevant for our experiment, are not depicted in order to maintain a clearly laid out picture. Note that in the experiment by Zewail and co-workers, their probe pulses induced a resonant transition to one of these higher excited NaI states.

58 7.1 How it works

7 E photoelectron γ kin 6 + β Na + I 5 α 4 λ 3 prb

2 + − B Na + I

potential (eV) 1 Na + I 0 A Na + I −1 λ pmp −2 X −3

2 4 6 8 10 12 14 16 intra−molecular distance (Å)

Figure 7.1: Illustration of the pump–probe experiment on NaI with calculated intra- molecular potentials [94] for the NaI molecule (ionic ground state X and the ﬁrst two excited covalent states A and B) and for the NaI+ ion (↵, and ) versus the intra-molecular distance. A detailed description is given in the text.

The ionic ground state potential X and the covalent excited states A and B intersect at an intra-molecular distance of 7.6 A˚ and 13.5 A,˚ respectively, and form e↵ective trapping potentials. Note that the intra-molecular distance for the A–X intersection was previously estimated as 6.93 A[˚ 77], however, the exact distance of the intersection is not scope of this work. In our experiment, a molecular wave packet (yellow Gaussian shape) is created on the A state by a pump pulse pmp and oscillates in the A– X trap. In each oscillation, a fraction of the wave packet (gray Gaussian shape) can tunnel through the intersection, breaking the molecular bond and forming free, neutral fragments. A delayed pulse prb is used to probe the system by photo-ionization. The system is lifted to one of the NaI+ ion states ↵, , by the probe pulse and the excess energy is liberated as kinetic energy Ekin of the photoelectrons. Hence, the di↵erence E is the binding energy E of the corresponding ionized molecular prb kin b orbital. Note that pump, probe and Ekin arrows are not plotted to scale. In this intra-molecular potential picture, the binding energy of the valence electrons for a given intra-molecular distance is the di↵erence between the potential energies of the initial molecular and the final ion state. In the following, a notation with the final state as superscript to the initial state will be used to denote the transitions, for example, pumping would read as X A and the probing example as depicted in figure 7.1 corresponds to A↵, A and A transitions.

59 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

NaI state fragments (NaI) state fragments

1 + 1 1 X(⌃0+ )Na( S0)+I( S0) ↵ 3 2 + 1 2 2 2 Na ( S0)+I (P 3 ) A(0,1,2) Na ( S 1 )+I (P 3 ) 1 2 ± 2 2 2 ) 2 2 + 1 2 B(0,1) Na ( S 1 )+I (P 1 ) 1 Na ( S0)+I (P 1 ) ± 2 2 2 2

+ fragment Na Na II ionization energy (eV) 5.14a 47.3a 10.45a 3.06b

Table 7.1: (top) The molecular states of neutral and ionized NaI and corresponding fragments for inﬁnite intra-molecular distances. Subscripts denote the molecular or atomic total angular momenta ⌦ or J, respectively. (bottom) Ionization energies for the fragments (a ref.[95], b ref.[96]).

7.1.2 Binding energies and simpliﬁed modeled photoelectron spectral evolution

The potential di↵erences, hence the electron binding energies depend on the intra- molecular distance upon ionization, thus oscillations of the wave packet translate to oscillations of the energy of the observed photoelectrons. Figure 7.2 depicts binding energies versus the intra-molecular distance calculated for NaI molecules photo- excited to the A state [94] with respect to the intra-molecular potentials introduced in ﬁgure 7.1 and provides for an impression of the positions and the dynamic oscilla-

10 Xα,β Xγ

6 molecular distance (Å) − 4 Aα Aβ Aγ

4 4.5 5 5.5 6 intra binding energy (eV)

Figure 7.2: Calculated binding energies for the valence orbitals versus intra-molecular distance for NaI molecules initially exited to the A potential [94]. The lines are plotted in red for ionization from the covalent A state (NaI) and in blue for the + ionic X (Na I), respectively, and labeled with the corresponding electronic transition.

60 7.1 How it works tion range in binding energy of the photoelectron peaks expected in an experiment. Only the highest of the three A state potentials is included in this calculation, hence the spin–orbit splitting is not shown in this plot. Red lines mark ionizations from the covalent A state and blue lines ionization from the ionic X state, on which the wave packet evolves for distances longer than the position of the A–X crossing. Figure 7.3 magniﬁes the potential region, where the wave packet dynamics in photo- excited NaI molecules occur. The crossing of the potentials is indicated and inner and outer turn of the oscillating wave packet are deﬁned as the intersection of the potential curves and the available excitation energy provided by one pump photon (vertical line).

2 inner turn outer turn 1

0 A

−1 λ crossing potential (eV) pmp −2 X −3

2 4 6 8 10 12 intra−molecular distance (Å)

Figure 7.3: Crossing, inner and outer turn deﬁned and visualized in the calculated intra- molecular potentials picture.

Figure 7.4 schematically shows the expected evolution of photoelectron distributions for the first three oscillations of the wave packet, modeled in a simplified approach. It is assumed in the model that upon pumping an excited wave packet is created on only one of the A potential curves. The photoelectron peaks, originating from 2 2 ↵ 2 3 1 the initial ground state molecular orbitals ⇧ /2 , ⇧ /2 (X , X transition) and ⌃ (X transition), now correspond to A↵, A and A transitions and shift to higher binding energies as the wave packet approaches the crossing (red lines). Additionally, the splitting of A↵, A vanishes. Thereafter the wave packet travels on the ionic X potential and is reflected at the outer turning point, yielding an oscillation of the photoelectron peaks to lower binding energies and back (blue lines). After passing the crossing a second time and entering the covalent region again, the wave packet evolves on all spin-orbit A potential curves in a superposition of several internuclear distances. A splitting to many peaks is expected in the photoelectron spectrum (red lines). This assumption follows [83], where it is pointed out that due to symmetry reasons the + energetically discernible ⌦=0,1,1 multiplet-levels of the A state, corresponding to the curve triplet in figure 7.1, are accessible via dipole allowed transitions from the

61 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI ground state X. The oscillation sequence restarts after the wave packet has been reﬂected at the inner potential barrier. Contributions from that part of the wave packet, which tunnels through the crossing and evolves further on the A state outside the trapping potential and dissociates to free neutral fragments are indicated with green lines.

crossing outer turn crossing

inner turn

crossing → outer turn time crossing

inner turn

crossing outer turn crossing

onset

4 4.5 5 5.5 6 binding energy (eV)

Figure 7.4: Modeled evolution of the photoelectron spectra from the valence orbitals of excited NaI molecules, as expected to be observed in a pump–probe photoelectron spectroscopy experiment with distinguished distances as defined in figure 7.3 indicated on the right. The spectra were modeled in a simplified approach and the oscillation period is in the order of 1ps, but the time axis is plotted non-linear, see text for a detailed description.

Note that, in principle, a similar situation, as assumed in our model can occur, if a wave packet trapped on a single potential curve or on several closely lying potential curves interacts with itself, leading to constructive and destructive quantum interferences along the intra-molecular distance coordinate, after the wave packet has evolved and started to dephase. Such wave packet quantum interferences have been reported in [97], for example, where they could visualize quantum beating in dissociating O2 wave packets, due to slightly di↵erent wave packet speeds on closely lying dissociative potential curves.

62 7.1 How it works

In reality, both e↵ects, splitting onto several potential curves and quantum interference, should occur together and alternately influence each other. However, the resolution in time and energy available in the photoelectron spectroscopy experiment described in this chapter was not suitable for deciding between both e↵ects. In order to proof wave packet quantum interferences with photoelectron spectroscopy, one would need resolutions high enough, in order follow the evolution and shifting of each photoelectron peak separately at an accuracy level, which allows for detection of discontinuities in the photoelectron peak’s path. Such discontinuities can serve as a proof that destructive quantum interference took place. Accurate determination of these e↵ects becomes even harder, as the ionization cross-section for creating a photoelectron varies for the di↵erent potential curves and depends on the intra-molecular distance, therefore a strong drop in ionization eciency due to cross-section jumps might be miss-interpreted as quantum beating. In figure 7.4 the photoelectron spectra for each distance are modeled as a sum of Gaussian distributions with their centers located at the binding energy of the corresponding transition. Three peaks in the photoelectron spectrum for transitions to the NaI+ ion states ↵, , are visible and when the wave packet evolves, they shift to higher binding energies. The double peak structure for the transitions to ↵ and morphs to a single peak, as the splitting of the corresponding NaI+ ion states vanishes for longer distances. After passing the crossing for the first time, the wave packet travels on the ionic X potential curve (blue lines) and is reflected at the outer turning point (assumed to be around 9 A˚ in this model, without loss of generality). Additionally, contributions from parts of the wave packet on the A potential, which already tunneled through the crossing, become visible at around 5.1 eV and 5.95 eV (green lines). The still trapped part of the wave packet passes the crossing a second time, coming from long distances on the X potential and can now spread onto all spin orbit split A potential curves (red lines), leading to a multiplet of three photoelectron peaks for each transition (A↵,,). Due to energy conservation, the part of the wave packet on the upper A potential curve will not reach the initial intra-molecular distance again, as the potential height reaches the excitation energy already for larger distances – the wave packet is in a superposition of several intra-molecular distances. Further more, it is assumed that the wave packet on the upper A state potential has not enough energy to reach intermolecular distances short enough in order to distinguish between transitions to ↵ and ion states, therefore a splitting to only five instead of six photoelectron peaks is modeled for the oscillations on the left at binding energies in the range of 4.5 eV to 5.1 eV. For simplicity, the shift in binding energy with respect to the lowest potential of these additional peaks is modeled increasing linearly with the distance between the crossing and the position of the wave packet on the lowest potential curve, resulting in the broadest splitting for the inner turn. The variation of the photo-ionization cross-section for di↵erent transitions and varying intra-molecular distance is not taken into account in this approach, therefore relative intensities are not modeled correctly for the photoelectron distributions. Also damping of the wave packet population and therefore of the photoelectron yield due to leakage

63 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI through the crossing in each oscillation, leading to free fragments, is not included in our simple model. The spectral evolution along the y-axis is generated by equal steps in intra-molecular distance for each spectrum without accounting for the actual speed of the wave packet. Thus, the visible separations of, for example, crossing and inner turn, relative to crossing and outer turn along the evolution axis (y-axis) in the model plot do not correlate to visible separations in a plot of a real pump–probe experiment, where the delay time is plotted against the photoelectron energy. Also a relative dephasing of the wave packet fractions on the individual A potential curves or a dispersion of the oscillating wave packet in the potential trap is not accounted for in this simpliﬁed approach.

7.1.3 The ground state spectrum of NaI

The ground state spectrum of the NaI molecule was measured in an earlier test campaing on NaI with two-color two-photon ionization by 370 nm and 200 nm pulses at the laser laboratory at MBI with a magnetic bottle electron spectrometer (described in [43]) and is presented in ﬁgure 7.5. Peaks originating from ionization out of the 2 2 ↵ 3 1 spin-orbit split ⇧ /2 , ⇧ /2 molecular orbitals, corresponding to X , X transitions are clearly discernible at 7.8 eV and 8.1 eV. The most intense peak at 9.1 eV corresponds to a X transition, hence ionization of the 2⌃ orbital of the ground state NaI molecule. Table 7.2 gives an overview of the binding energies of these valence orbitals and compares values calculated by Michael Odelius [94] to those measured in this experiment and to previously published ones. The discrepancy of calculated and measured binding energies is in the order of the accuracy of the absolute binding energies of the calculation. The di↵erence of our experiment and the literature can be explained, if one takes into account, that the literature values were obtained by single photon ionization, but in contrast, our experiment relies on two-color two-photon ionization and therefore the ground state spectrum is perturbed by ultrafast dynamics occurring within the cross-correlation width the pump and probe pulses.

binding energy (eV) transition molecular orbital calculation this experiment literature X↵ 2⇧ 7.89 7.8 ( .05) 8.03a 3/2 ± X 2⇧ 8.14 8.1 ( .05) 8.25a 1/2 ± X 2⌃ 9.01 9.1 ( .05) 9.21a /9.0b ± Table 7.2: Overview of the ground state valence orbitals of NaI and their binding energies from a numeric calculation [94] compared to values from this experiment and previous publications (a ref.[98], b ref.[99]).

64 7.2 Experiment

120 2Σ 100 2Π 1/2 80 2Π 60 3/2

40 intensity (a.u.) 20

0 7.5 8 8.5 9 9.5 binding energy (eV)

Figure 7.5: Ground state photoelectron spectrum of the NaI molecule measured at zero time delay, hence with two-color two-photon ionization. The data points (black dots) are connected with a cubic spline ﬁt (black line) as guide to the eye. The uncertainty is plotted as gray shade and the corresponding molecular orbitals are indicated above the peaks.

7.2 Experiment

The experiment was performed in a collaboration with and at the Max-Born-Institute Berlin (MBI), see chapter 4 for a detailed description of the experimental setup. The molecular oven, described in chapter 3 and developed at HZB served as NaI evaporation source. For the measurements, presented in this chapter, a pump wavelength of 320 nm (3.87 eV) was chosen. Both, the 200 nm (6.2 eV) probe pulses and the pump pulses were about 70 fs in duration (FWHM)andthereforetheFWHM of the cross-correlation function is in the order of 100 fs. The bandwidth of the pulses was in the order of 0.06 eV (FWHM)forpumpandforprobe,yieldingacombined cross-correlation bandwidth of 0.085 eV (FWHM). Delay time resolved photoelectron velocity maps were recorded with a velocity map imaging spectrometer (VMI). The VMI was set to record photoelectrons up to a maximum kinetic energy of 2.35eV for a time window from -1.3 ps to +7.7 ps with 53 fs delay step size and for a time window from -1.3 ps to +3.1 ps in 27 fs steps (the 320 nm pump pulses arrive ﬁrst for positive delay times). Our collaborators, Per Johnsson and Linnea Rading (Lund University, Sweden), post-processed the recorded VMI datasets and extracted photoelectron kinetic energy distributions with 10 meV bin width for each delay step in order to obtain TRPES maps for the further analysis presented here.

Figure 7.6 depicts the ﬁnal photoelectron energy distributions, with the photoelectron kinetic energy Ekin given in the top axis, whereas the bottom axis shows the total absorbed photon energy: E = E + E E ,(7.1) abs pmp prb kin with the photon energies of pump and probe pulses, Epmp and Eprb. This axis gives

65 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI the total energy, absorbed by the NaI molecule from both pulses for creating the detected photoelectron, regardless of the time delay between the pulses. In the present experiment, pump and probe pulses exchange their role for negative delays and the 3.35 eV pump pulses ionize the system, instead of the 6.2 eV probe pulses, hence same kinetic photoelectron energies do not correspond to same binding energies of the electrons in the excited NaI molecules for positive or negative delay times, as the energy of the ionizing pulse is di↵erent. In contrary, Eabs can serve as uniﬁed axis for all delays, even if the pump and/or probe photon energy is tuned. The binding energy of an electron is estimated as the di↵erence between Eabs and the photon energy of the non-ionizing, ﬁrst arriving pulse:

E = E E , t > 0, (7.2) b abs pmp E = E E , t < 0. (7.3) b abs prb

For t =0,thecaseofsimultaneoustwo-colortwo-photonionization,Eabs represents the electron binding energy for the ground state of NaI. In ﬁgure 7.6 the expected oscillations in the photoelectron spectra are clearly visible for positive delays. The oscillating signal in the range of Eabs =[8–9] eV corresponds

kinetic energy (eV) kinetic energy (eV) 2 1.5 1 0.5 0 2 1.5 1 0.5 0 1 3 7

2.5 0.8 6

5 2 0.6 4 1.5 3

delay (ps) 1 0.4 2 relative intensity 1 0.5 0.2 0 0 −1 0 −0.5 8 8.5 9 9.5 10 8 8.5 9 9.5 10 total absorbed photon energy (eV) total absorbed photon energy (eV) (a) (b)

Figure 7.6: TRPES maps (delay vs. energy) from NaI molecules photo-excited by 320 nm (3.87 eV) photons (a) for pump–probe delay times up to 7.7 ps with 53 fs delay steps and (b) for the ﬁrst three oscillations up to 3.1 ps, recorded with 27 fs delay steps. The excited state binding energy is given in the top axis, whereas the bottom axis shows the total absorbed photon energy (see equation (7.1)for a deﬁnition).

66 7.3 Ultrafast auto-ionizing dissociation to ionization to ﬁnal ↵-and-NaI+ ion states and the signal from ionization to the + ﬁnal -NaI ion state is visible for Eabs =[9–10] eV. On the negative delay side, no oscillations, are visible, but an ultrafast dissociation process, leading to a very intense peak at Eabs 9.25 eV. The observed processes for both, negative and positive delay times, are discussed⇠ in detail in the next sections.

7.3 Ultrafast auto-ionizing dissociation

The main process observed for negative delays is auto-ionization to free Na+ and I ion fragments. The 200 nm (6.2 eV) pulses arrive first and highly excite the NaI molecules. It is not clear to which of the potential curves the system is excited to, either to A, B, a higher excited NaI potential curve not depicted in figure 7.1 or to a wave packet superposition involving several of these excited state potentials. In any case, the amount of energy brought into the system is enough to overcome the X potential, therefore the excited molecular wave packet evolves on the ionic X potential to the asymptotic limit of infinite intra-molecular distances and the system auto- + ionizes to free Na and I ion fragments. The photoelectron peaks shift in energy to the corresponding energies of the fragments during this ultrafast dissociation process, as for example reported in [10] for ultrafast Br2 dissociation. The shift of the intense peak for in figure 7.6 to Eabs =9.25 eV, corresponding to the ground state 2⌃ orbital of the NaI molecule , is magnified in figure 7.7 for a series of negative delays up to -1300 fs. The plots in figure 7.6.(a) were extracted from the data discussed in this chapter, measured with 320 nm (3.87 eV) ionizing pulses and a VMI spectrometer, whereas (b) shows results acquired in a test campaign in April 2011 at the same laser setup with a magnetic bottle electron spectrometer, 370 nm (3.35 eV) ionizing pulses and delay steps of 100 fs. The binding energy for the bottom axis is given with respect to ionization of the excited system or dissociation products by the ionizing pulses, see equation (7.3). The fitted peak maximum shifts by 100 15 meV within a dissociation time ⌧diss 400 fs to 3.06 eV excited state binding± energy in figure 7.7.(a) and to 3.02 eV in⇠ (b), which is in good agreement with the I electron anity of 3.05 eV (see table 7.1). The di↵erence between the fragment photoelectron energies in (a) and (b) can be explained by uncertainties for the values of the di↵erent ionizing photon energies, which directly influence the transformation from kinetic photoelectron energies to Eabs and Eb. The ionization potential of the created Na+ fragments is 47.3 eV (see table 7.1)and therefore photoelectrons from free Na+ ions are not observable in this experiment, as the ionizing pulses do not provide enough photon energy for ionization.

67 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

total absorbed photon energy (eV) total absorbed photon energy (eV) 8.9 9 9.1 9.2 9.3 9.4 8.9 9 9.1 9.2 9.3 9.4

0 0

−100 −100 −200 −200 −300 −300 −400 delay (fs)

−400 −500

−500 −700

−750 −1000 −1000

−1300 −1300

2.7 2.8 2.9 3 3.1 3.2 2.7 2.8 2.9 3 3.1 3.2 excited state binding energy (eV) excited state binding energy (eV)

(a) pmp=200 nm, prb =320 nm (b) pmp=200 nm, prb =370 nm

Figure 7.7: Dissociation to free I ions for negative delays, extraceted from data measured with (a) 320 nm ionizing pulses and a VMI spectrometer (see also ﬁgure 7.6), and (b) for data acquired in a previous campaign with 370 nm ionizing pulses and a magnetic bottle electron spectrometer. The orange spectra at t=0 show the 2⌃ peak from ground state NaI molecules and the black spectra illustrate the shifting of this peak during the dissociation process. All data sets (black dots) are interpolated with cubic splines (lines) and the maxima of the splines are marked by red dots. The excited state binding energy for negative delays is given in the bottom axis, whereas the top axis shows the total absorbed photon energy. The ﬁnal peak energy, arising from ionization of free I fragments is reached within ⌧ 400 fs after a relative energy shift of the peak by 100 15 meV diss ⇠ ⇠ ± (marked by blue lines).

68 7.4 Coherent electronic and nuclear wave packet oscillations

7.4 Coherent electronic and nuclear wave packet oscillations

The molecular wave packet dynamics, proposed in the model introduced in subsection 7.1.2 and figure 7.4 are observed for positive delay times. The 320nm (3.87eV) pulses arrive first and excite the NaI molecules onto the A potential, creating a wave packet in the A–X potential trap (see figure 7.1). For easier discussion of the TRPES data, first a detail view of the photoelectron data for the first one and a half oscillations of the molecular wave packet in the potential trap is shown in figure 7.8 with outer turn, inner turn and the crossings labeled. ’Crossing outwards’ denotes the wave packet evolving to long distances towards the outer turn and ’crossing inwards’ denotes the wave packet evolving back to short distances. No values for energy and delay time are given in the plot in order to draw the attention only to the visual appearance of the individual features in the TRPES map. A black vertical line in the map divides the TRPES map into energy regions for photoelectrons arising from (A,X)↵, transitions on the left and from (A,X) transitions on the right.

binding energy

outer turn

crossing outwards inner turn

y crossing inwards a l e d outer turn

crossing outwards

(A,X)α,β (A,X)γ

Figure 7.8: Distinguished features indicated in an exemplary detail of the TRPES maps.

Figure 7.9 shows the full TRPES maps recorded in our experiment for the plain data set in figure 7.9.(a) and with the photoelectron distributions normalized separately for each delay step in figure 7.9.(b). The data recorded for pump–probe delay times up to 7.7 ps with 53 fs delay steps is shown in the left column and the right column depicts the data recorded with smaller delay steps of 27 fs for delay times up to 3.1 ps. In the upper panel, figure 7.9.(a), showing the unnormalized plots, reoccurring peaks for the outer turn of the wave packet on the ionic X potential are visible around ↵, Eb=4.4 eV, corresponding to the X transitions, arising from the spin-orbit split 2 ground state ⇧ orbitals and peaks are visible around Eb=5.4 eV, corresponding to the X transitions and arising from the ground state 2⌃ orbital. Furthermore, the photoelectron intensity traces right of these peaks visualize, as the wave packet runs through the crossing, ’uphill’ to the outer turn and back again, after being reflected.

69 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

excited state binding energy (eV) binding energy (eV) 4 4.5 5 5.5 6 4 4.5 5 5.5 6 1 3 7

2.5 0.8 6

5 2 0.6 4 1.5 3

delay (ps) 1 0.4 2 relative intensity 1 0.5 0.2 0 0 −1 0 −0.5 8 8.5 9 9.5 8 8.5 9 9.5 total absorbed photon energy (eV) total absorbed photon energy (eV) (a) interpolated TRPES map of the NaI wave packet oscillations

excited state binding energy (eV) excited state binding energy (eV) 4 4.5 5 5.5 6 4 4.5 5 5.5 6 1 3 7

2.5 0.8 6

5 2 0.6 4 1.5 3

delay (ps) 1 0.4 2 intensity (a.u.)

1 0.5 0.2 0 0 −1 0 −0.5 8 8.5 9 9.5 8 8.5 9 9.5 total absorbed photon energy (eV) total absorbed photon energy (eV) (b) interpolated TRPES map, normalized separately for each delay

Figure 7.9: TRPES maps depicting the wave packet dynamics in NaI molecules photo- excited by 320 nm (3.87 eV) photons: Plain data (a) and the data, normalized separately for each delay step (b). The left column depicts a scan for pump– probe delay times up to 7.7 ps with 53 fs delay step size and the right column shows a scan recorded with 27 fs delay step size for the ﬁrst 3.1 ps.

70 7.4 Coherent electronic and nuclear wave packet oscillations

The individually normalized TRPES maps, figure 7.9.(b), provide for a visualization of the evolution of the maximum of the photoelectron distribution versus delay time and visualize the width or spread of the photoelectron energy distributions. The intensity traces right of the outer turns, pointing to higher binding energies are now visible at high contrast. The high energy ends of these features arise from the wave packet passing through the crossing, as the binding energies of the electrons of the oscillating wave packet are the highest at the crossing (see figure 7.2). The outer turn is observed for delays around 0.55 ps, 1.65 ps, etc, but at delay times around 1.1ps, 2.2ps, etc, a spreading of the electron distribution is observed, which is not visible in the unnormalized TRPES map. This spread arises from the inner turn and supports our initial assumption for the model (subsection 7.1.2), that the wave packet populates all A potential curves, when evolving back through the crossing. Note that this spreading out on several states leading to a whole family of photoelectron peaks is not observable with laser-induced fluorescence, used by the Zewail group. The broadening of the molecular wave packet along the evolution axis (intra-molecular distance) manifests, for example, in the increasing temporal width of the peaks corresponding to evolution on the X potential around the outer turn. From the asymmetry of these features, broadened to longer delays, one can conclude that the wave packet disperses on the low repulsive, rather flat ionic X potential, but is re-sharpened upon the inner turn, when being reflected by the highly repulsive inner potential barrier. This e↵ect was previously reported and postulated to arise from the Coulombic force field counteracting the dephasing of the wave packet due to the anharmonicity of the intra-molecular potential A–X trap, in which it evolves, leading to a sharp, highly localized wave packet only for short intra-molecular distances around the inner turn, where the potential gradient is comparably large and to a broad wave packet for small potential gradients around the crossing region and the outer turn, see [77] and refer- ences therein. However, both TRPES maps, plain and normalized, show that the total dispersive broadening of the wave packet is still high enough, so that for the third and later outer turns part of the wave packet is observed at photoelectron energies corresponding to the outer turn, whereas part of the wave packet is already at the inner turn or even back on the X potential on its way to the next outer turn. This is especially visible in the individually normalized TRPES map for long delay times [left panel in figure 7.9.(b)], where the end and start points of subsequent ’straight line’ features visible at each outer turn overlap in time. These features correspond to the evolution of the photoelectron distribution maximum on the outer turn. Furthermore, for the last two depicted outer turns, end and start point touch, hence for those delay times there is evidently always some amplitude of the wave packet on the ionic X potential. This is another example for the trapped molecular wave packet existing in aquantummechanicalsuperpositionofseveralintra-moleculardistancesandshows the ability of time-resolved photoelectron spectroscopy to reveal quantum mechanical phenomena on sub-molecular length scales. Apparently, the positions of the maxima of the outer turns (Eb 4.5 eV & Eb 5.3 eV) shift to higher binding energies by about 50 meV in the first⇡ 7 oscillations.⇡ This

71 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI reﬂects a damping of the oscillations not only in total wave packet intensity, as proposed by Zewail and coworkers, but also a damping of the total energy, available for the oscillations. Therefore the maximum and minimum intra-molecular distance for the wave packet’s outer and inner turn decrease.

7.4.1 Delay scans In order to quantify some of the visible dynamic and periodic e↵ects and features in the TRPES maps, delay scans have been extracted, where the integrated photoelectron intensities in a defined energy window are plotted versus the delay time. In a first approximation, selecting an energy corresponds to selecting a distinguished intra- molecular distance, where a bypassing wave packet is registered as change in the intensity. A single Gaussian wave packet on a single potential curve yields a Gaussian shaped trace in the delay scan, just as in the original experiments on photo-excited NaI molecules by the Zewail group, when a wave packet passes through the optical coupled region defined by the probe pulse energy (see the introduction of this chapter on p. 57 for a brief description of Zewail’s experiment). For the turns of the wave packet the re-occurrence time of the Gaussians directly corresponds to the oscillation period ⌧osc, if inner and outer turn occur at separable binding energies, hence, if the transformation between intra-molecular distance and binding energy is unique. This is not the case for NaI as the binding energies at inner and outer turn overlap. However, the photoelectron intensity for the outer turn exceeds that of the inner turn by orders of magnitude, therefore the transformation between intra-molecular distance and binding energy becomes quasi-unique and dis- tinguishable for the outer turn and is observed as peaks separated by ⌧osc in a delay scan, see figure 7.10.(a,b). For a region in between the turns, the wave packet passes by two times in each oscillation period, thus a doublet of peaks is observed separated by a time ⌧sep, which depends on the intra-molecular distance between the selected energy region and the turns, see figure 7.10.(c–f). Again, this e↵ect is only determinable, if the distance–energy relation is at least quasi-unique, hence, if the photoelectron intensity is dominant for one of the intra-molecular distances corresponding to the selected binding energy region, for example, for energy regions between crossing and outer turn in the TRPES map.

In those regions, where a quasi-unique relation between intra-molecular distance and binding energy exists, a model for a delay scan y(t)isdescribedinequation(7.4)asa sum of Gaussian peaks with an exponential damping of the peak maxima (decay time ⌧exp)toaccountforthedecreaseofphotoelectronintensityduetotheleakageofthe wave packet through the crossing in each oscillation, yielding free neutral fragments Na and I for the asymptotic limit of inﬁnite distances on the A potential.

72 7.4 Coherent electronic and nuclear wave packet oscillations

N 2 t ti ti y(t)=c + A exp 4ln2 ± ↵± ⇥ wi ⌧exp ⇥ i=1 ✓ ◆ ! X (7.4) ⌧ t =(i 1) ⌧ + t , = sep , w = w +(i 1) dw i osc 1 2 i 1

The positions ti are defined via the time t1 of the wave packets first outer turn and the number of bygone oscillations with period ⌧osc and correspond to the delay time for the ith outer turn, whereas the ith inner turn is located at tinner = i⌧osc. The first outer turn should occur after a half period ⌧osc/2, therefore when fitting the model to a given data set the di↵erence between the half period and parameter t1 can be utilized to fine adjust the point of zero pump–probe delay time. The peak doublets occurring for distances o↵ the turns are modeled at t = t ⌧sep / , left i ± 2 and right of the position of the outer turn. Therefore ⌧sep can be interpreted as the time, the wave packet needs to evolve from the selected energy/distance region to the outer turn and back. Furthermore, for an energy window corresponding to the crossing, ⌧sep represents an estimate for the time the wave packet spends on the X potential in each oscillation. The cofactor ↵± is introduced to model the asymmetry of the peak intensities left and right of the outer turn, arising from broadening and re-sharpening of the molecular wave packet due to the antithetical influences on the dispersion of the wave packet by the Coulombic force field and the anharmonicity of the intra-molecular potentials [77]. The right peak intensity is modeled as a fraction + ↵ =q of the left peak intensity (↵=1), which is defined by the exponential decay (⌧exp)oftheinitialamplitudeA. Broadening of the wave packet is included in the model by a linear increase of the peak width wi in each oscillation period by dw. The coecient of the quadratic term in the exponential, representing the Gaussian, is introduced, so that wi represents the FWHM of the peak. Possible background is accounted for by the parameter c and the sum is restricted to N oscillations for computational reasons in order to ensure the converging of a fit of the model to a dataset, which is intrinsically restricted to a finite number of recorded oscillations.

A set of delay scans for several excited state binding energies Eb is presented in ﬁgure 7.10. The delay scans in (a,b) correspond to the outer turn of the wave packet ↵, on the ionic X state at (a) Eb=4.4 0.05 eV (X )and(b)Eb=5.35 0.05 eV (X ). Delay scans (c,d) show spectral intensities± from X x transitions of the± wave packet between crossing and outer turn for (c) Eb=4.8 0.1 eV and (d) Eb=5.6 0.1 eV and (e,f) show spectral intensities for the A–X crossing± energy regions, (e) E =5.1± 0.1 eV b ± for transitions to ﬁnal ↵, ion states and (f) Eb=5.9 0.1 eV for transitions to the ion state. ± The main oscillation period is ⌧ =1104 14 fs, resulting in an oscillation frequency of osc ± ⌫osc=0.91 0.01 THz and is in good agreement with ⌧osc=1090 fs, reported for a pump wavelength± of 321 nm in [71]. The exponential decay time, describing the damping

73 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

10 E = 4.4 ± 0.05 eV 10 E = 5.35 ± 0.05 eV τ b τ b osc osc 8 8

6 6

4 4 intensity (a.u.) intensity (a.u.) 2 2

0 0 t t −1 0 1 1 2 3 4 5 6 7 −1 0 1 1 2 3 4 5 6 7 delay (ps) delay (ps) (a) outer turn, transition to ↵, (b) outer turn, transition to

τ τ E = 4.8 ± 0.1 eV osc E = 5.6 ± 0.1 eV 10 osc b 10 b τ τ 8 sep 8 sep

6 6

4 4 intensity (a.u.) intensity (a.u.) 2 2

0 0 t t −1 0 1 1 2 3 4 5 6 7 −1 0 1 1 2 3 4 5 6 7 delay (ps) delay (ps) (c) in between, transition to ↵, (d) in between, transition to

τ 10 osc E = 5.1 ± 0.05 eV 10 E = 5.9 ± 0.1 eV τ b b sep τ 8 8 osc τ 6 6 sep

4 4 intensity (a.u.) intensity (a.u.) 2 2

0 0 t t −1 0 1 1 2 3 4 5 6 7 −1 0 1 1 2 3 4 5 6 7 delay (ps) delay (ps) (e) crossing region, transition to ↵, (f) crossing region, transition to

Figure 7.10: Delay scans for wave packet dynamics in the A–X potential trap at selected excited state binding energies Eb as indicated in the plots: (a,b) Photoelectron spectral intensities vs. pump–probe delay at the outer turn on the ionic X state. (c,d) Spectral intensities from X x transitions of the wave packet between crossing and outer turn and (e,f) spectral intensities for the crossing energy regions. The separation of the peaks in the crossing region is ⌧ cross=710 9 sep ± fs for both plots. The oscillation width is ⌧ =1104 14 fs and therefore the osc ± time of the ﬁrst outer turn is t1=552 fs (red lines).

74 7.4 Coherent electronic and nuclear wave packet oscillations

of the peak intensities for the outer turn is ⌧exp=4.4 0.2 ps in this experiment. The separation of the double peaks in delay scans 7.10±.(e,f), taken for energy regions corresponding to the A–X crossing, where the wave packet undergoes a transition between the covalent A potential and the ionic X potential, is equal for both scans cross and amounts to ⌧sep =710 10 fs. This time can be interpreted as the time the wave packet spends beyond the crossing± on the X potential in each oscillation. Hence, the pump–probe delay times corresponding to the crossings before and after outer turn i can be approximated as: ⌧ cross tcross = t sep =(i 1 ) 1104 fs 355 fs ( 17 fs). (7.5) i i ± 2 2 ⇥ ± ± (c) (d) The separation times for delay scans (c,d), ⌧sep=588 8fs and ⌧sep =491 6fs, are cross ± ± smaller than ⌧sep , therefore one can conclude from the definition of ⌧sep that these scans depict signals from intra-molecular distances between crossing and outer turn. In principle, the energy windows for delay scans (c,d) also cover intra-molecular distances smaller than the crossing, but due to the reduced photo-ionization eciency on the A potential, the quasi-unique distance–energy relation at this energy refers to the much more intense signals observed for the wave packet on the X potential beyond the crossing. The main oscillation period ⌧osc=1104 fs, introduced above, was estimated as average from all presented delay scans. If the oscillation period is estimated separately for the transitions to final ↵, ion states, figure 7.10.(a,c,e) and for transitions to the ↵, final ion state (b,d,f), one obtains: ⌧osc =(1115 8) fs and ⌧osc =(1093 12) fs, respectively. The di↵erence ± ± ⌧ 320nm = ⌧ ↵, ⌧ =22 14 fs (7.6) osc osc osc ± points to di↵erent speeds with which the electronic cloud follows the nuclear motion as delay scans (a,c,e) and (b,d,f) are taken for transitions to di↵erent final ion states and, hence, the delay scans and the corresponding oscillation periods represent ionization of di↵erent molecular orbitals of the photo-excited NaI molecule and therefore di↵erent geometries of the underlying electron density distributions around the molecule. 370nm This finding is supported by a di↵erence in oscillation period of ⌧osc =17 10 fs, deduced from TRPES data taken at 370nm (3.35eV) pump wavelength in an± earlier test campaign on NaI, performed at the same laser setup, but with a magnetic bottle electron spectrometer. Furthermore, the di↵erence in speed seems to increase with increasing pump photon energy, hence, with increasing total available energy. How- ever, the relative uncertainties of the oscillation di↵erences are rather high and the values for both oscillation di↵erences overlap within their full uncertainty widths. Note that the visualization of such a di↵erence in the evolution speed of electronic wave packets corresponding to di↵erent molecular electronic orbitals is not observable in an experimental arrangement as used by Zewail and co-workers. A closer look to the delay scans additionally reveals that the oscillation period ⌧osc decreases with time, as the peaks from the data set arise slightly before the fitted

75 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI peaks for longer delay times. This is in agreement, with the observed damping of the total energy available for the oscillations, on which ⌧osc is dependent (see ﬁgure 7.9 and p.72 in section 7.4).

Delay scan map The plain TRPES data, figure 7.9.(a), was normalized separately for each energy channel along the (vertical) delay axis, yielding a map of normalized delay scans, presented in figure 7.11. In this norm, a shift of photoelectron intensity along the binding energy axis, corresponding to energy shifts of the molecular electronic states can be visualized as reoccurring patterns even in energy regions, where the photoelectron intensity is very small. In contrast, the common method of normalizing the photoelectron spectra separately for each delay along the (horizontal) energy axis, see figure 7.9.(b), enables comparing the evolution of the relative intensity distribution, hence the evolution of the shape of the photoelectron spectra for each delay time and maintains the relative photoelectron intensities for each spectrum, therefore patterns in the low intensity regions remain unrevealed. Figure 7.11.(a) shows a delay scan map from the data set recored for pump–probe delay times up to 7.7 ps with 53 fs delay steps and figure 7.11.(b) depicts the delay scan map of the data set for the first three oscillations up to 3.1 ps delay, recorded with 27 fs delay steps. The white line is drawn at the binding energy of free Na fragments, 5.14eV (see table 7.1), generated when the wave packet tunnels through the crossing. Furthermore, the line approximately separates the maps into regions for (A,X)↵, on the left and (A,X) on the right, or at least into regions, where photoelectrons from the respective transitions dominate the spectra. A footprint of the main sinusoidal oscillations of the electronic wave packet in the energy landscape is nicely visible and spreading out of the wave packet to all A potential curves is suggested for the inner turns (delay = 1.1 ps, 2.2 ps, etc). New light is shined on the broadening of the wave packet for the outer turn on the X potential. At their low binding energy sides, the sinusoidal traces for both excited state orbitals, (A,X)↵, and (A,X) transitions, are continued to the left by almost straight lines with steepnesses increasing in each oscillation. This reflects that the high energy part of the dispersed molecular wave packet evolves further to longer distances, ’uphill’ on the X potential (see figure 7.1), while the main part of the wave packet is already evolving inwards again, down the X potential. In figure 7.11.(b), where smaller delay steps and longer integration times than in (a) were applied, the straight lines even connect with a periodical feature around Eb 4.1eV. This binding energy is in the order of the energy needed for photo ionization⇠ of the molecular wave packet evolving around the crossing region of the higher excited covalent B potential and the ionic X potential, hence for a (B,X)↵, transition (see figure 7.1). This points to the high energy part of the dispersed wave packet on the outer turn tunneling through the B–X crossing and oscillating in the B–X potential trap. There are traces visible for the wave packet running up the X potential

76 7.4 Coherent electronic and nuclear wave packet oscillations

excited state binding energy (eV) excited state binding energy (eV) 4 4.5 5 5.5 6 4 4.5 5 5.5 6 1 3 7

2.5 0.8 6

5 2 0.6 4 1.5 3

delay (ps) 1 0.4 2 intensity (a.u.)

1 0.5 0.2 0 0 −1 0 −0.5 8 8.5 9 9.5 8 8.5 9 9.5 total absorbed photon energy (eV) total absorbed photon energy (eV) (a) (b)

Figure 7.11: Delay scan map from normalization of the TRPES map for photo-excited NaI molecules [ﬁgure 7.9.(a)] along the delay axis separately for each electron energy channel. (a) shows a scan for pump–probe delay times up to 7.7 ps with 53 fs delay steps and (b) for the ﬁrst three oscillations up to 3.1 ps, recorded with 27 fs delay steps. The excited state binding energy is given in the top axis, whereas the bottom axis shows the total absorbed photon energy. The white lines indicate the ionization potential of free, neutral Na fragments (Eb=5.14 eV), generated when the wave packet tunnels through the crossing and approximately separate the plots into energy regions for (A,X)↵, transitions (left) and (A,X) transitions (right). to lower binding energies only, but no traces are visible for the wave packet coming back to higher binding energies, therefore we conclude that the complete high energy part of the wave packet tunnels through the B–X crossing and dissociates on the B potential or further oscillates in the B–X potential trap. This represents a one-sided coupling of the wave packet dynamics for the two degrees of molecular excitation (excitation to the A–X or the B–X potential trap), where the higher excited state (B–X trap) seems to be fed by the high energy part of the wave packet in the A–X trap in each oscillation and gives rise to a second oscillation period for the part of the wave packet in the B–X trap. However, a second dissociation channel on the dissociative B potential, beyond the B–X crossing, is opened up and the photoelectron intensity for contributions from the B–X potential strongly decrease in time, pointing to a high probability for the wave packet to dissociate.

The trace at the very left in ﬁgure 7.11.(b) for Eb<4eV, visible in the measured energy window already around a delay of 0.3 ps, therefore before the 1st outer turn, seems to

77 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI come from lower binding energies. This points to a ﬁnite probability for an excitation directly to the B state upon pumping by two pump photons (7.74eV). Hence, the B- state potential is populated by parts of the wave packet already at t =0.Pumping with two photons yields a molecular wave packet with enough energy to overcome + the X potential and the system dissociates to free ion fragments Na and I. In our experiment these fragments are not observable for positive delays, as for both fragments, the lowest bound photoelectrons show up at binding energies outside the + recorded energy window (Eb=47.3 eV for Na and Eb=3.06 eV for I, see table 7.1).

E = 4.1 ± 0.1 eV E = 3.85 ± 0.05 eV 10 b 10 b

8 8

6 6

4 4 intensity (a.u.) intensity (a.u.) 2 2

0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 delay (ps) delay (ps) (a) transition to ↵, (b) transition to ↵,

Figure 7.12: Delay scans for transitions of the wave packet in the B–X potential trap to ↵, ion states. The re-occurrence periods of the peaks are (a) ⌧ (a) =1410 10 fs, B–X ± determined from the data set recorded up to 7.7ps delay time and (b) ⌧ (b) =1100 10fs, determined from the data set recorded up to 3.1ps delay B–X ± time.

The oscillation period in the B–X potential trap is longer than for the A–X trap, due to the relative flatness of the B–X trap and because the B–X crossing is at longer intra-molecular distances. In order to determine the B–X oscillation period, the delay scans, depicted in figure 7.12 were analyzed. However, the expected longer oscillation period in the B–X potential trap is disturbed by a transfer of wave packet intensity to the higher excited potential at a repetition rate determined by the oscillation period in the A–X potential plus the time the high energy part of the A–X wave packet needs to evolve from the outer A–X turn to the B–X crossing. Thus, the re-occurrence periods of the peaks in the delay scans in figure 7.12 do not represent time scales for pure B–X oscillations, but represent time scales for a beating between the molecular wave packet fractions transfered from A–X to B–X oscillations and the wave packet fractions already evolving in the B–X potential. The period for the (a) wave packet beating is ⌧B–X=1410 10 fs at Eb=4.1 0.1eV, determined from the ± (b) ± data set recorded up to 7.7 ps delay time and ⌧B–X=1100 10 fs at Eb=3.85 0.05 eV, ± (a) ± determined from the data set recorded up to 3.1 ps delay time. ⌧B–X is larger than the period ⌧osc for the main oscillations in the A–X trap and the respective delay

78 7.4 Coherent electronic and nuclear wave packet oscillations scan, and points to the high energy part of the wave packet evolves further on the (b) X potential beyond the main outer turn towards the B–X potential crossing. ⌧B–X meets the period ⌧osc for the main oscillations, however it is not clear, if this is for a deeper reason or if the period of the beating for the respective binding energy region coincides with ⌧osc just by chance. In order to completely understand this beating and the determined re-occurrence periods, accurate quantum mechanical wave packet dynamics simulations are desired, including population and coupling of both potential traps, A–X and B–X. The delay scan maps in figure 7.11 show a similar situation on the right side of the white separator lines for transitions to final ion states than discussed above for transitions to final ↵, ion states left of the separator lines. The coupling of the wave packet in the A–X trap to the higher lying B–X potential trap is visible as a shifting of parts of the X photoelectron peak to lower binding energies. However, the (B,X) transitions from the wave packet oscillating in the B–X trap occur around the same photoelectron energies than the highly intense (A,X)↵, transitions and are therefore not observable. To our knowledge, a transfer of photoelectron intensity and therefore wave packet amplitude between the first two excited states at the outer turn as observed here has never been reported to be visualized experimentally.

7.4.2 Photoelectron spectra – model vs. experiment In a next step, the photoelectron spectra for distinguished distances from the modeled evolution, introduced in subsection 7.1.2, are compared to the measured spectra for associated pump–probe delay times. Figure 7.13 depicts the modeled photoelectron spectra for the initial onset (brown), the 1st crossings (black) for outwards propagation of the wave packet to longer distances and for inwards propagation on the way back to the inner turn, the 1st and 2nd outer turn (green) and the ﬁrst four inner turns (blue) in subplot (a) and the corresponding measured photoelectron spectra in subplot (b). All measured spectra are depicted for those experimental delay times, which are closest to the predicted times for the respective situations. The left y-axis in subplot (b) states the relative maximum intensity of the experimental spectra, providing for acomparisonintensityandstatisticalqualityoftheindividualspectra.Grayshadesin both subplots indicate the lowest electron binding energy (ionization potential) for the free, neutral, atomic Na fragments (Eb=5.14eV), which are generated in a molecular dissociation process when part of the wave packet tunnels through the A–X crossing. They approximately separate the plots into energy regions for (A,X)↵, transitions (left) and (A,X) transitions (right). The series of inner turns is plotted, to visualize an energy transfer within these spectra, observed for increasing oscillation numbers, as discussed below. The spectra for the outer turns and the crossings only show an intensity damping and spectral broadening due the broadening of the molecular wave packet for increasing oscillation numbers, therefore these spectra are not explicitly shown in ﬁgure 7.13.

79 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

The initial onset at t =6 fs (brown) in figure 7.13 should correspond to the the ground state spectrum of the NaI molecule as discussed earlier in subsection 7.1.3. The left peak doublet corresponding to the spin-orbit split ground state 2⇧ orbitals is significantly shifted to higher binding energies, compared to our previous measurements presented in figure 7.5 and to values from the literature and calculations, whereas the 2⌃ peak is visible around the expected 9.1eV, see table 7.2. The width of the cross-correlation function of pump and probe is around 100 fs, thus the spectrum around t =0fsisperturbedbytheearlydynamicsforshortpump–probetimede- lays. These dynamics can lead to a shift of the photoelectron peaks to higher binding energies for positive and for negative delays, hence, signals from already dynamically shifted spectra for small positive and negative delays govern the measured spectrum and can explain a shift of the photoelectron peaks obtained for two-color two-photon ionization. The black spectra for t =f<5192 fs and t =913 fs depict as the wave packet travels through the crossing, evolving to long or short distances, respectively. In this region, where the nature of the molecular bond changes from covalent (A potential) to ionic (X potential), an intra-molecular electron transfer takes place transforming the sys- + tem from covalent (Na I) to ionic (Na I)orviceversa.Therefore,theouterelectron localized around the Na atom is transfered to the I atom or vice versa. In the modeled spectrum, a minor peak as foot on the right of the main peak becomes visible (Eb 4.85eV), which arises from that part of the wave packet, which tunneled through the⇠ crossing and further propagates beyond on the A potential towards the asymptotic limit of infinite intra-molecular distances yielding free neutral Na atoms with lowest electron binding energy (ionization potential) of Eb=5.14 eV (gray shades). The broad peaks in the measured spectrum represent the modeled spectra for transitions to ↵, ion states (Eb=4.0–5.2eV) and the less intense transition to the final ion state (Eb=5.2–6.0eV). They are smeared out due to the width of the cross- correlation function and the combined bandwidth of pump and probe ( 100 fs and 0.1eV, respectively), leading to an averaging of the wave packet around⇠ the crossing.⇠ Therefore a clear distinction of photoelectrons from the trapped wave packet broadened and smeared out partly on the ionic X potential and partly on the covalent A potential and from electrons from the tunneled dissociating part of the wave packet is not possible, although a minor feature possibly arising from Na for long or infinite intra-molecular distances is visible in the spectra at the left edge of the gray shade indicating the atomic Na ionization potential. For the two depicted outer turns (green), at 539fs and 1660fs, model and measurement match. In the modeled spectra, on each side of the gray line, a major peak corresponding to the turn of the wave packet and a minor feature, indicating the dissociating part of the wave packet are visible. The two intense peaks for ionization at the outer turn are well visible in the measured spectra. They are asymmetric with a foot to the right, where the dissociating wave packet on the A potential is expected. However, the ionization eciency on the A potential is much smaller than on the X potential and therefore we conclude that the observed peak broadening

80 7.4 Coherent electronic and nuclear wave packet oscillations arises from the dispersed wave packet on the X potential being reflected at the outer barrier, associated to the smallest binding energies within the peaks rather than from dissociating parts of the wave packet outside the crossing. The blue spectra depict the first four inner turns (1110 fs, 2220 fs, 3321 fs and 4442 fs) and contain the most fascinating information, as the spreading out to the whole family of the spin-orbit split A potential curves is observed, as claimed in the model introduced in subsection 7.1.2. For all four depicted turns, the photoelectron intensity from the A↵ and A transitions in the range from 4.0–5.1 eV dominates the spectral distributions and the corresponding spectra are broadened to the full energy region, in which the photoelectron signals from the oscillating molecular wave packet are shifting for the respective molecular orbital. The first inner turn at 1110 fs shows a maximum for the distribution at high binding energies around 5 eV and six distinct peaks and shoulders in the electron intensity distribution are observed down to 4 eV, proving the initial claim, that all A potential curves are populated when the⇠ wave packet returns from the X potential through the crossing. This is additionally supported by the high degree of qualitative agreement between the measured spectrum and the modeled spectrum shown for the A↵ and A transitions. The model shows a broad distribution built up from several peaks, as well. A spreading out of the wave packet is motivated even on the high binding energy side for A transitions (Eb & 5.2 eV), where a broad spectral socket is seen as well, but here the signal intensity is not sucient to distinguish individual peaks. Again, distinct features around the expected photoelectron energy for free Na atoms (gray shades) are visible in all spectra shown for the inner turns. However, it is not possible from the spectra to clearly identify these features as arising from Na atoms — they might as well arise from the wave packet distributed on all potentials. Furthermore, the photoelectron spectra corresponding to the 2nd and later inner turns show an increasing population of the states corresponding to lower binding energies, which manifests in the center of mass of the spectral distributions shifting from right to left. For the 3rd and 4th inner turn, the spectral intensity maximum is observed at the low binding energy end of the spectral distribution for binding energies even lower than that for the outer turn. One could conclude from this finding that the wave packet more and more populates the highest lying of the A potential curves in each oscillation, which yields the lowest binding energies at the inner turn (see also figure 7.1). However, as mentioned before and visible in the TRPES maps in figure 7.9, the dispersed wave packet is broadened strong enough for longer delays, so that part of it is still or again evolving on the X potential during the inner turn of the main part of the wave packet. Furthermore, the photo-ionization cross-section for ionization from the ionic X potential is by orders of magnitude higher than for ionization from the covalent A potential curves, therefore already a small fraction of ionic nature in the molecular wave packet is amplified and becomes prominent in the photoelectron distribution. This is not reflected in the modeled spectra, as the model does not include any exchange of intensity between the potential curves. Such an exchange of wave packet

81 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

binding energy (eV) binding energy (eV) 4 4.5 5 5.5 6 4 4.5 5 5.5 6

(NaI)+ state: α , β γ (NaI)+ state: α , β γ 0.15

4th inner turn 4442 fs 0.14

3rd inner turn 3321 fs 0.13

2nd inner turn 2220 fs 0.89

2nd outer turn 1660 fs 0.16

1st inner turn 1100 fs 0.22 relative maximum intensity 1st crossing inwards 913 fs 1

1st outer turn 539 fs 0.23

1st crossing outwards 192 fs 0.1

inital onset 6 fs

7.5 8 8.5 9 9.5 7.5 8 8.5 9 9.5 total absorbed photon energy (eV) total absorbed photon energy (eV) (a) simpliﬁed model calculation (b) experiment

Figure 7.13: Simpliﬁed model photoelectron spectra (a) compared to experimental photoelectron spectra (b) at distinguished intra-molecular distances and the closest associated experimental pump–probe delay times. The respective situations to the distances and the associated delay times are indicated in the very left and right axis, respectively. The left y-axis in (b) gives the relative maximum intensity for the experimental spectra and straight lines mark the zero intensity level for each spectrum. For both subplots, the excited state binding energy for positive delays is shown in the top axis and the total absorbed photon energy in the bottom axis. The gray shades indicate the ionization potential of free, neutral Na fragments (Eb=5.14eV), generated when the wave packet tunnels through the crossing and approximately separate the plots into energy regions for (A,X)↵, transitions (left) and (A,X) transitions (right).

82 7.5 Conclusion for this chapter intensity between the di↵erent potentials is not directly observable in a LIF experiment as performed by Zewail and coworkers, but only indirectly by a decrease in intensity of the ﬂuorescence signal in each oscillation. Hence, this ﬁnding shows the power of time- resolved photoelectron spectroscopy, where known phenomena can be investigated in greater detail and new previously ’invisible’ e↵ects in the dynamics of the electronic and nuclear coherent wave packet dynamics in molecules can be visualized.

7.5 Conclusion for this chapter

In this chapter time-resolved photoelectron spectroscopy was applied to visualize molecular wave packet dynamics in photo-excited NaI molecules by following the evolution of the valence electronic structure, arising from an oscillation of the intra- molecular distance of the atomic nuclei. The results from a TRPES experiment on NaI molecules for pumping with 3.87 eV (320 nm) photons and probing by ionization through 6.2 eV (200 nm) photons were presented and discussed in detail. The main oscillation frequency of the wave packet, the delay times for the wave packet evolving through the potential crossing region, and around the inner and outer turns and the time constant for the exponential damping of the wave packet oscillations, due to leakage through the crossing of the potentials, could be directly extracted from these delay scans. Furthermore, a spreading of the wave packet was observed. An indication was found, pointing to di↵erent speeds, with which the electronic wave packets corresponding to di↵erent excited state molecular orbitals follow the nuclear 320nm wave packet motion, as the oscillation period ⌧osc appears to be ⌧osc =22 14 fs shorter for the (A, X ) orbital than for the spin-orbit split (A, X )↵, orbitals.± Addi- tionally, this di↵erence in oscillation period seems to decrease for decreasing available 370nm energy, supported by ⌧osc =17 10 fs for a longer pump wavelength of 370 nm, determined from TRPES data measured± in an earlier test campaign at the same laser setup. Furthermore, a one-sided coupling of states corresponding to di↵erent degrees of excitation was visualized in a map of normalized delay scans and revealed that the high energy part of the wave packet oscillating in the A–X potential trap transfers to the higher excitation state B–X potential trap, giving rise to a wave packet beating in the B–X trap and opening a second decay channel for the system by dissociation to free fragments on the B potential, after tunneling through the B–X crossing. A coupling back, hence wave packet intensity being transfered from the B–X trap to the A–X trap was not observed. Simpliﬁed modeled photoelectron spectra for distinguished intra-molecular distances, corresponding to onset, crossing, inner and outer turns were compared to measured spectra for closest respective pump–probe delay times. The spectra for the inner turns were the most fascinating and motivated, that the whole family of spin-orbit split A potential states take part in the coherent electronic and nuclear wave packet

83 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI oscillations in A–X potential trap, as initially proposed within a simplified model for photoelectron spectral evolution. A transfer of photoelectron intensity to lower binding energies was observed within the spectral distributions for subsequent inner turns. We conclude, that each time the wave packet evolves through the crossing towards the inner turn, the higher lying spin-orbit split A potential states are more and more populated. The observed spreading out to many of the A potential curves has not been reported previously and to our knowledge, the coupling of A–X and B–X wave packet oscillations as well as the time di↵erences for the oscillation periods of di↵erent electronic orbitals was never observed experimentally before. In an experiment using laser- induced fluorescence, as in the pioneering work by the group around Zewail [3, 4], the observed signal depends on the optical coupling of the investigated potential and a higher lying fluorescing state and is measured as pump–probe delay time dependence scan of the fluorescence intensity. A two-dimensionality of the data set is introduced only by varying the coupling probe wavelength, but as the coupling constant to the fluorescing state is di↵erent for the individual states under investigation (A potential curve family, B or X potential) and as it depends, for example, on the symmetry of the coupled states, the low- or non-coupling states will be shaded for all probe wavelengths and at best be recognized as background to the main delay scan signal. In photoelectron spectroscopy, the measurement becomes intrinsically two-dimensional in energy and time within one scan of all pump–probe delay times. Therefore it is possible to determine contributions from all states at once for each delay step and thus none of the states are shaded, although one has to deal with di↵erent ionization cross-sections for the individual molecular states. Our finding of the spreading out of the molecular wave packet from a photo-excited NaI molecule to a whole family of spin-orbit split states, the coupling of the A–X and B–X potential traps and the observed oscillation period di↵erences are therefore an example, where the technique of time-resolved photoelectron spectroscopy (TRPES) can reveal deeper insights in the dynamics of a photo-excited molecular wave packet, than absorption techniques as laser-induced fluorescence spectroscopy, where shading of states and of information can occur. In contrast, the dynamic information from fluorescence or absorption delay scans is contained in delay scans from the TRPES data, as well, where the photoelectron intensity is plotted versus delay time for a defined photoelectron energy window.

Outlook

The VMI data additionally provides the ﬁrst two asymmetry parameters 2 and 4, from which the photoelectron angular distributions for two-photon ionization and thus basic asymmetry properties of the underlying electronic structure can be determined for each kinetic photoelectron energy at each delay step. The post processing and analysis of the angular resolved data is currently under way. The combination of both, energy and angular resolved photoelectron distributions can provide deeper in-

84 7.5 Conclusion for this chapter sight into the intra-molecular electron transfer around the crossing, where the nature of the molecular bond between the Na atom and the I atom undergoes a transition + form covalent kind (Na I) to ionic kind (Na I)andanelectronistransferedbetween both atoms. It was reported in theoretical work by Arasaki et al. [84] that photoelectron angular distributions and their asymmetries can reveal at which of the atoms inside the molecule the electronic wave function was localized when the electron was ejected upon ionization. Therefore an accurate determination of the photoelectron angular distribution has the potential of revealing the degree of covalence or ionic- ity, respectively, at each photoelectron energy, allowing for a deeper distinction of the origin of the individual features in the photoelectron distributions. Moreover, this can enable the determination of the time scale for the intra-molecular exchange of a valence electron in the charge transfer process. During this campaign, we recorded electron and ion time-of-ﬂight pump–probe data for a series of pump wavelengths in the range of pmp=320–370nm (3.87–3.35eV) at the same experimental setup. The dataset is currently under analysis. Combining electron and ion data can reveal more details about the dynamics of the total molecular wave packet and correlate the time-resolved intensity of the ion species Na+ and (NaI)+ with respective features in the TRPES maps. Furthermore, the analysis of the variation of characteristic times, i.e. the oscillation period ⌧osc, the separation time of cross the wave packet appearing at the crossing ⌧sep and the di↵erence in oscillation pe- ↵, riod ⌧osc, observed for the molecular orbitals corresponding to (A,X) and (A,X) transitions, respectively, can shine new light on the understanding of the molecular dynamics in photo-excited NaI molecules and on the understanding of photo-excited molecular wave packet dynamics in general. To our knowledge quantum dynamics simulations of the electronic and nuclear wave packet dynamics in photo-excited NaI molecules, presented in this chapter, with inclusion of all spin-orbit split A and B potential curves has not been carried out yet. A comparison of the experimental data with an accurate simulation is highly desirable and can provide for deeper insights into the details of the dynamics observed in the experiment. It would be thrilling to see, if state-of-the-art theoretical and computational methods can reproduce the di↵erence in oscillation period ⌧osc. Furthermore quantum dynamics simulation can help to understand the dynamics of the coupling of the wave packets in the A–X and B–X potential traps. Hans O. Karlsson (Upp- sala University, Sweden) is currently working on a quantum mechanical wave packet dynamics simulation remodeling our TRPES experiment. Preliminary results without inclusion of the A potential splitting look very promising and yield qualitatively accurate spectra, as for example previously reported in [84]. However, the accurate inclusion of the spin-orbit splitting of the A potential curves and the coupling to the higher excited B state is non-trivial and the work is still under progress. Controlling natures elementary reactions, such as electron transfer in molecular bonds is an ultimate goal of modern science. Therefore, a next experimental step should be to perform a three pulse experiment, where an additional third laser pulse at individual time delay is used to control the molecular dynamics in the NaI molecule. For example

85 7 Coherent Nuclear and Electronic Wave Packet Dynamics in NaI

2 3 one could control the branching ratio for production of ground state I ( P /2 )orexcited 2 1 state I⇤ ( P /2 )duetothewavepacketleakageineachoscillationasproposedin theoretical work by Hosseini et al. [85]. This corresponds to controlling, which of the potential crossings A–X or B–X is preferred for tunnel ionization through the crossing and subsequent dissociation on either the A or B potential, respectively. Furthermore, it would be interesting to investigate if it is possible to control the dynamics around the crossing and hence the inter-atomic electron transfer, for example, in a way that almost the complete wave packet tunnels through the crossing, therefore forcing the system to dissociate and e↵ectively inﬂuencing the damping time constant observed in the delay scans.

Acknowledgement for this chapter

The presented campaign on the electronic and nuclear wave packet dynamics in NaI molecules was carried out in a collaboration with the Max-Born Institute (MBI), Berlin, Germany and Lund University, Sweden. The members in this collaboration are listed below, ﬁrst grouped by their aliations and second sorted alphabetically. The measurements were performed at the femtosecond laser laboratory at MBI. The extraction of the photoelectron kinetic energy distributions from the raw VMI images was performed by Linnea Rading and Per Johnsson. Further analysis of the experimental data as presented here was performed by the author of this thesis, Torsten Leitner. The data for the theoretical intra-molecular potentials and the expected binding energies were calculated by Michael Odelius, but the modeled spectral evolution was simulated and all plots were created by the author himself. Philippe Wernet supervised the whole project.

Experiment: Franziska Buchner, Andrea L¨ubcke, Arnaud Rouz´ee, Marc Vrakking – Max-Born In- stitute, Berlin, Germany Per Johnsson, Linnea Rading – Lund University, Sweden Torsten Leitner, Philippe Wernet – Helmholtz-Zentrum Berlin, Germany

Theory: Michael Odelius – Stockholm University, Sweden Hans O. Karlsson – Angstr¨om˚ Laboratory, Uppsala University, Sweden

86 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

It is well known that a CO group is eliminated in metal carbonyl compounds upon UV photolysis [100]. However, the precise nature of the elimination and especially the electronic structure dynamics during this photo-dissociation are not yet fully understood. For example, the story of characterizing Fe(CO)4 molecules created by elimination of one of the CO ligands of Fe(CO)5 (iron-pentacarbonyl) has been running since more than 40 years now [101]. The open questions are partly due to the fact that the experimental methods mainly employed so far, such as time-resolved ion time of ﬂight spectroscopy [102] are not unique in their interpretation. This is the case as in these experiments already the pump pulse creates ions and because the same ions arise from the various species during the decay sequence. The data presented here are the ﬁrst to characterize dynamics of the electronic structure of the intermediates. They can be seen as complementary to the structural characterization by time-resolved electron di↵raction [103].

. 100 fs 3.2 ps Fe(CO)5⇤ Fe(CO)4 ⇠ Fe(CO)3

CO CO

Figure 8.1: The photo-dissociation sequence of gas-phase Fe(CO)5⇤ after excitation of a Fe(CO)5 molecule by a UV photon. Two CO ligands are split o↵ on the way to stable Fe(CO)3.

The major time-scales involved in photo-dissociation of Fe(CO)5 in the gas phase have been determined in an ultrafast pump–probe transient ionization ion time-of- flight experiment by Trushin et al. [102]. They found that after pumping with 267 nm photons, two CO ligands are eliminated until the system has transformed to stable Fe(CO)3. It is furthermore claimed that only the first CO ligand is eliminated photo- chemically within a time of 100 fs, whereas the elimination of the second CO ligand arises from relaxing dissociation of the vibrationally hot intermediate Fe(CO)4 to final, stable Fe(CO)3 within 3.2 ps. This dissociation sequence is sketched in figure 8.1. To our knowledge, transient photoelectron spectra have never been determined for Fe(CO)5 photo-dissociation. This chapter presents the TRPES data on Fe(CO)5

87 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5 photo-dissociation, measured in a campaign at the free electron laser FLASH in Ham- burg in April and May/June 2011. The main scope hereby is the extraction of time scales for characterizing the dynamics in the dissociation sequence and the disentan- glement of the TRPES data in order to obtain photoelectron spectra for the daughter products of Fe(CO)5, especially for the short lived intermediate Fe(CO)4.

8.1 Rate model

There are two general temporal behaviors in gas-phase dissociation of Fe(CO)5:a step function, describing species, created or destroyed upon pumping and an exponential decay function, describing the temporal evolution of unstable species. The temporal evolution of products created from decaying species can be expressed as linear combinations of these two processes. For describing the real world, the evolution functions have to be convolved with the cross-correlation function of the pump and probe pulses to account for the ﬁnite time resolution in a real experiment. The general form of the convolution function for an impulse g(x)andaresponse h(x)isdescribedbytheconvolutionintegral: t f (t)= g(x)h(t x) dx . (8.1) Z 1 The impulse g(x)correspondstothecross-correlationfunctionofpumpandprobe pulses and is approximated as an area normalized Gaussian impulse with width w (FWHM): g(x)= 2ln2 exp 4ln2 x 2 . (8.2) ⇡w 2 w 2 q This leads to a convolved function, describing the evolution for instantaneous creation of a stable species upon pumping, where the response is a simple step function: 1 x 0 h(x)=✓(x)= 0 otherwise ⇢ = f (t)= 1 1+erf 2pln 2 t ,(8.3) ) s 2 w ⇣ ⇣ ⌘⌘ with the error function erf(x). Instantaneous destruction of a species is described by aconvolvedstep-downandreads1 fs (t). The response function for a decaying species is an exponential decay (lifetime ⌧, decay constant ↵ =1/⌧), multiplied by a step function ✓(x)toensurethatthedecaymathematicallystartsatt=0inorderto achieve a physically meaningful description and to maintain causality. Its convolution reads as: ↵x h(x)=✓(x) e ↵(t ) = f (↵, t)=e f (t 2), (8.4) ) d s with = ↵w 2/(16 ln 2) = w 2/⌧(16 ln 2).

88 8.1 Rate model

From these mathematical considerations, a rate model can be formulated as a set of equations describing the time evolution Nx (t)forthenumberofentitiesofall species occurring in the dissociation sequence of photo-excited Fe(CO)5, presented in table 8.1. The rate model starts with Fe(CO)5 which is instantaneously transformed to highly unstable, excited state Fe(CO)5⇤ upon pumping and a two-stage chain via Fe(CO)4 to stable Fe(CO)3 begins, where the total number of molecules of all Fe(CO)x species has to be conserved: N (t)=1, t (8.5) x 8 x=5,5 ,4,3 X⇤

The decay of the unstable species Fe(CO)5⇤ and Fe(CO)4 is characterized by their lifetimes ⌧5 and ⌧4 (or the respective decay constants ↵5 and ↵4). In each decay ⇤ ⇤ step, corresponding to a reduction of the number of ligands to the central Fe atom, afreeCOmoleculeiscreated.Thenon-convolvedequationsandthecorresponding convolutions are listed in table 8.1 for each species.

species inﬁnite time resolution ﬁnite resolution (convolved) Fe(CO) N (t) 1 ✓(t) 1 f (t) 5 5 s ↵ t 5⇤ Fe(CO)5⇤ N5⇤ (t) ✓(t) e fd (↵5⇤ , t)

↵4 t ↵ t Fe(CO) N (t) ✓(t) A (e e 5⇤ ) A (f (↵ , t) f (↵ , t)) 4 4 d 4 d 5⇤ Fe(CO) N (t) 1 N N N = 3 3 5 5⇤ 4 ↵ t ↵4 t ✓(t)[1 (1 A)e 5⇤ Ae ] f (t) (1 A)f (↵ , t) Af (↵ , t) s d 5⇤ d 4 CO N (t) (1 N N )+N = co 5 5⇤ 3 ↵ t ↵4 t ✓(t)[2 (2 A)e 5⇤ Ae ] 2 f (t) (2 A)f (↵ , t) Af (↵ , t) s d 5⇤ d 4 ↵ =1/⌧ , A = ↵ /(↵ ↵ ) x x 5⇤ 5⇤ 4

Table 8.1: Rate model equations for the Fe(CO)5 photo-dissociation sequence. Note that A 1 for the decay times ⌧5 100 fs and ⌧4 3.2 ps reported in [102]. ⇡ ⇤⇡ ⇡

Figure 8.2 shows the evolution of the species following the rate model equations for initial photo-excitation of all Fe(CO)5 molecules in the sample, where a cross- correlation width of w=400fs(FWHM), as approximately available ( 200 fs) in our ± experiment at FLASH and decay times ⌧5 =100 fs and ⌧4=3.2 ps, reported in [102], ⇤ are assumed. The model plot shows that the fast decaying species Fe(CO)5⇤ (light blue trace) never reaches more than about 20% of relative content and vanishes very rapidly and will thus hardly be observable with our limited time resolution. Furthermore, the experiment described in the following is based on photoelectron spectroscopy, where complex photoelectron spectra are measured for each time delay, which are a mix of the overlapping individual spectra from all species and therefore

89 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

1 0.9 0.8 0.7 Fe(CO)5 0.6 Fe(CO)5* 0.5 Fe(CO)4 Fe(CO)3 0.4 0.5*CO relative content 0.3 0.2 0.1 0

−1 0 1 2 3 4 5 6 7 delay (ps)

Figure 8.2: Rate model for Fe(CO)5 photo-dissociation for a cross-correlation width of w= 400 fs (FWHM), as available in the present experiment and decay times ⌧5 =100 fs and ⌧4=3.2 ps, reported in [102]. The (brown) trace, describing the ⇤ production of free CO molecules is multiplied by 0.5 for better visualization, as two CO molecules are created during the dissociation sequence, leading to a maximum relative content of 2.

hard to disentangle, as the photoelectron peaks, especially for the Fe(CO)x molecules lie closely next to each other. Additionally, not all Fe(CO)5 molecules will be photo- excited, yielding a strong background in the signal from these unpumped molecules. Therefore, delay scan traces extracted for deﬁned photoelectron energy windows from the experimental data will be a weighted superposition of the traces for all species depicted in ﬁgure 8.2 and listed in table 8.1. The general form of a delay scan trace from our experiment reads:

fgeneral(c0, cs , c4, c5⇤ , ↵4, ↵5⇤ , w, t)=c0 +cs fs (t)+c4fd (↵4, t)+c5⇤ fd (↵5⇤ , t), (8.6) depending on a total of 7 parameters: the width w of the pump–probe cross-correlation,

↵4 and ↵5⇤ (or the respective lifetimes ⌧x )characterizingthedecaystepsandthepa- rameters c0, cs , c4, c5⇤ R describing a constant background and the weights of the superposition. 2

The very fast ﬁrst decay step from excited Fe(CO)5⇤ to Fe(CO)4 will hardly be observable in a superposed delay scan trace extracted from our limited time resolution experimental data, as its contributions vanish very fast and as the relative content does never exceed about 20%. Therefore the delay scan traces can be approximately described by only 5 free parameters, enabling easier ﬁtting of the model to experimental data sets:

f (c , c , c , ↵ , w, t) c + c f (t)+c f (↵ , t). (8.7) mix 0 s 4 4 ⇡ 0 s s 4 d 4

90 8.2 Experiment

However, this approximated fit function is still not unique to a high degree, meaning that di↵erent sets of fit parameters can yield almost equal delay traces, with di↵erent mixing parameters cx and time scales ↵4 and w. Thus, not all fit results give reasonable values for any delay scan trace and one always has to be careful about what is fitted, especially when extracting time scales for the cross-correlation width w and the decay constant ↵4 from the data. Furthermore, in time-resolved pump– probe photoelectron spectroscopy, some of the photoelectron peaks undergo dynamic energy shifts, therefore not only the decay of a species, but as well the shift of the corresponding photoelectron peak(s) out of or into the respective delay scan energy window influence and alter the time scales estimated from a fit of the delay scan trace. This shifting of photoelectron peaks relative to the selected energy window corresponds to a non-linear and unknown time-dependence of the mixing parameters cx in equation (8.7). This can result in widened fitted cross-correlation widths w and shifted fitted values for the position of t=0 along the delay axis. Additionally taking into account the arguments given above, one sees that the mixing parameters do not evidently correlate with the real amount of contributions from the individual species in the spectra, but are just a set of motivated, but still artificial model parameters. However, for carefully selected energy regions, where one is aware of the dynamics in the spectra or at best where contributions from one electronic state of one of the species dominates the photoelectron spectrum, it is possible to determine time scales, which characterize the dynamic processes happening in Fe(CO)5 photo-dissociation.

With four parameters I can ﬁt an elephant, and with ﬁve I can make him wiggle his trunk.

John von Neumann

8.2 Experiment

The experimental setup used at FLASH is described in detail in chapter 5. In brief: An experimental chamber, equipped with a magnetic bottle electron spectrometer was mounted to the PG2 beamline at FLASH. The monochromator unit in the beamline was tuned to 123 eV photon energy (10.1 nm) and 0.1 eV bandpass, resulting in monochromatized probe pulses fluctuating in the range from approximately a few tens of nJ to µJpulsesandafocalspotsizeofabout280µminhorizontaland400 µminverticaldirectionattheinteractionregion.ThethirdharmonicofaTi:Sapphire laser system is generated, delivering 267 nm pump pulses to the interaction zone with afocalspotsizeofabout400µmindiameter,shorterthan80fsFWHM in duration and attenuated to 25 µJpulseenergy.Adelaystageinthelaserpathallowsforvarying the relative arrival time of pump and probe pulses over a total range of 9 ns. A metal tube just underneath the interaction volume serves as sample gas inlet. For detecting photoelectrons, a magnetic bottle time-of-flight electron spectrometer is installed. The photoelectron time-of-flight distributions are determined from a micro channel

91 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5 plate (MCP) in current mode and stored to the FLASH data storage system via a network connected 10 bit digitizer system. The electron spectrometer was calibrated with the additionally recorded photoelectron spectrum from pure CO molecules (see figure 8.4). The binding energies for the CO photoelectron peaks are: 5 – 14.01 eV, 1⇡ –16.91eVand4 –19.72eV[59]. The intensity of the FLASH pulses is highly stochastic and can vary by orders of magnitude from shot to shot. Therefore, the photoelectron intensities for di↵erent delays cannot be directly compared, even after time sorting (see chapter 5)and binning of the data in time slots up to 200 fs wide (half the cross-correlation width). Hence, the data for each delay time slot has to be individually normalized. The most physical normalization is normalizing the photoelectron spectra to the incoming pulse intensity, but unfortunately, no shot-to-shot resolved pulse intensity data is available after the monochromator at the PG2 beamline at FLASH. Therefore an area norm was applied to the spectra for each time slot, where each spectrum is divided by its total sum along all photoelectron energies. This norm assumes, that the total intensity in the spectra is preserved for all delays. The area normalized data set will be further referenced as Znorm. An approximate value for time zero (t =0)withanaccuracyof 500 fs could be determined from the experimental signal by stepwise comparing the± photoelectron spectra for a series of nested delay time intervals on a LeCroy digital oscilloscope. Time zero could be further ascertained with an accuracy of 70 fs, by a fit of equation (8.7) to a delay scan (integrated photoelectron intensity± vs. delay time) in a region of interest (ROI) of E [12.2–13.2]eV, where the fastest feature in the normalized b 2 data set Znorm is observed [see also figure 8.4, ROI (2)]. The delay scan is depicted in figure 8.3. Furthermore, a cross-correlation width of w=400 200 fs (FWHM)is extracted from the fit, arising from the pulse widths and from the± relative timing jitter of the FEL (see chapter 5).

0.8

0.6

0.4

intensity (a.u.) 0.2

−3 −2 −1 0 1 2 3 4 5 6 7 delay (ps)

Figure 8.3: Integrated photoelectron intensity versus delay time for the fastest feature in the TRPES data for E [12.2–13.2] eV to determine t =0(accuracy 70 b 2 ± fs) and to estimate the width of the pump–probe cross-correlation function w = 400 200 fs. ±

92 8.2 Experiment

8.2.1 Di↵erence spectra

The photoelectron spectrum for Fe(CO)5 was extracted by averaging the data for long negative delays, Znorm(t < -2 ps), and a TRPES map of di↵erence spectra D was obtained by subtracting the Fe(CO)5 spectrum from the data set Znorm separately for each delay time slot. Figure 8.4 gives an overview of the data recorded for the valence region up to Eb=23eV. The photoelectron spectra for pure Fe(CO)5, spectra from pure CO, separately recorded at the same setup and di↵erence spectra for selected delays are shown and labeled with the corresponding valence orbitals. The Fe(CO)5 spectrum is plotted downwards for comparison with the negative contents in the di↵erence spectra, visualizing the depletion of Fe(CO)5 in the interaction zone. A shift to lower binding energies is suggested for the Fe 3d peaks at binding energies below 10eV, and the creation of CO molecules during the dissociation sequence is clearly⇠ observed in the spectra around 14.0eV, 16.9eV and 19.7eV.

5σ 1π 4σ

(1) (2) (3) intensity

+6.0 ps +3.0 ps +1.0 ps difference spectra +0.0 ps −3.0 ps

CO (σ+π) Fe 3d CO (σ+π)

Fe(CO) 5 6 8 10 12 14 16 18 20 22 binding energy (eV)

Figure 8.4: Comparison of Fe(CO)5 and CO photoelectron spectra with pump–probe di↵erence spectra for the valence energy region and selected delays. (see text for a description)

93 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

Further more all ROIs, referenced in this chapter are indicated in the plot: (1) the scaling ROI, see next subsection 8.2.2, (2) the fastest dynamic feature for calculating the cross-correlation function, see above, and (3) the ROI for characterizing the creation of CO and at the same time the decay of transient Fe(CO)4, see section 8.3.

8.2.2 Relative amount of non-excited Fe(CO)5 in the data

For determination of the relative amount of photo-excited Fe(CO)5 molecules in the interaction volume, the integrated photoelectron intensity in a scaling ROI Eb [9.7– 10.0] eV was extracted versus delay time. The scaling ROI was chosen at a position2 in the Fe(CO)5 photoelectron spectrum, where the corresponding Fe 3d photoelectron peak splits to lower and higher binding energies and therefore the signal in the scaling ROI disappears as Fe(CO)5 disappears [see also figure 8.4, ROI (1) and figure 8.7, ROI (1)]. Figure 8.5 shows the delay scan with a fit of equation (8.7)andvisualizesthetime evolution of the relative content of non-excited Fe(CO)5 molecules in the interaction volume. The plot clearly shows that within 1 ps all initially pumped Fe(CO)5 molecules have dissociated to daughter products. Note that for this energy region the width of the negative step arises from the ultrafast (sub time resolution) Fe(CO)5⇤ decay perturbed by the experimental time resolution.

102

100

content (%) 98 5

94 relative Fe(CO) 92 −3 −2 −1 0 1 2 3 4 5 6 7 delay (ps)

Figure 8.5: Depletion of the content of signals from non-excited Fe(CO)5 molecules in the data set. Approximately 6% of the Fe(CO)5 molecules in the interaction region were pumped in this experiment.

The normalized spectrum of Fe(CO)5 is scaled according to the ﬁt function and subtracted from the normalized TRPES data set Znorm for each delay time, yielding anewdatasetofscaleddi↵erences Dscaled, free of contributions from Fe(CO)5, enabling an approximation of photoelectron spectra for the transient Fe(CO)4 and stable Fe(CO)3 daughter products, presented in section 8.4, ﬁgures 8.7 and 8.8. Additionally, the scaling ROI could be manually optimized by ensuring that there are no negative di↵erences in Dscaled. A note on the scaling region of interest: The borders for the scaling ROI where manually varied throughout the whole negative di↵erence regions in the unscaled

94 8.3 Decay of transient Fe(CO)4 and creation of free CO di↵erences D, figure 8.4. The finally chosen ROI was the only one, where a scale could be extracted without yielding negative di↵erences in the scaled di↵erence map Dscaled. As this ROI is not at the edge of the corresponding Fe 3d peak in the Fe(CO)5 spectrum, see figure 8.4, ROI (1), but in between, we can conclude that the Fe 3d peak splits to both sides for the daughter products of Fe(CO)5. Furthermore, the scale is perturbed by the edges of the new peaks, reaching into the scaling ROI window, which leads to a slight overcompensation for non-excited Fe(CO)5 in the spectra within the strength of this perturbation.

8.3 Decay of transient Fe(CO)4 and creation of free CO

The dynamics of the dissociation sequence can be identified and characterized from the photoelectron fingerprint of the CO molecules, created in each decay step. Fig- ure 8.6 shows a fit of equation (8.7)toadelayscanextractedfromthedatafor Eb [16.6–17.3]eV, where the strongest CO peak occurs in the valence band photo- electron2 spectra [see also figure 8.4, ROI (3)], and at the same time, there is no or only very few signal of any of the Fe(CO)x species expected, as this energy region lies in a gap in the photoelectron spectrum of Fe(CO)5. This gap even increases for the daughter species.

0.8

0.6

0.4

intensity (a.u.) 0.2

−3 −2 −1 0 1 2 3 4 5 6 7 delay (ps)

Figure 8.6: Integrated photoelectron intensity versus delay time for E [16.6–17.3] eV, b 2 describing the dynamics of the dissociation sequence with the help of a ﬁnger- print in the photoelectron spectra from the CO molecules, created in each decay step.

The initial creation of CO molecules upon pumping is reflected in the initial step in the data, as motivated by the rate model, figure 8.2. This process is much faster than the time resolution, therefore no reliable time scale can be determined from the step for the formation of the first CO molecule created during the transition of photo- excited Fe(CO)5⇤ to transient Fe(CO)4. The life time for the exponential growth of CO molecules corresponds to the exponential decay time of the transient Fe(CO)4

95 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

molecules, which decay to stable Fe(CO)3, producing the second CO molecule. This decay time is determined from the ﬁt to ⌧4 =3.2 1.7 ps, hence nicely matching the 3.2 ps determined from ultrafast pump–probe transient± ionization ion time-of-ﬂight experiments, previously reported by Trushin et al. [102].

8.4 Transient photoelectron spectra

Figure 8.7 compares, the Fe(CO)5 spectrum, extracted for t < -2 ps (blue) and averaged scaled di↵erence spectra, estimated from Dscaled for t=1 0.2 ps, dominated by photoelectrons from transient Fe(CO) (green) and for t=6.5± 0.2 ps, where 4 ± the spectrum is dominated by photoelectrons from Fe(CO)3 (yellow). For comparison, the photoelectron spectrum from free CO molecules (gray), recorded during the same campaign is plotted in the top panel. A shifting and splitting of the Fe 3d peaks is visible for binding energies below 12 eV and the growth of photoelectron content from CO molecules is observed around⇠ 14.0eV, 16.9eV and 19.7eV.

∆ t = 6.5 ± 0.2 ps Fe(CO) + CO 3

∆ t = 1.0 ± 0.2 ps Fe(CO) + CO 4 intensity

∆ t < −2 ps scaling ROI Fe(CO) 5 CO (σ+π) Fe 3d

6 8 10 12 14 16 18 20 22 binding energy (eV)

Figure 8.7: Scaled di↵erence photoelectron spectra at selected delays for initial Fe(CO)5, transient Fe(CO)4 and stable Fe(CO)3 molecules. (see text for a detailed description)

96 8.4 Transient photoelectron spectra

In order to obtain transient photoelectron spectra for the daughter species Fe(CO)4 and Fe(CO)3, the spectra for free CO molecules have to be subtracted from the scaled di↵erences Dscaled for estimating a data set DCOfree of transient, Fe(CO)x only photoelectron distributions. The general time dependence of the amount of photoelectrons from CO molecules has been determined in section 8.3, figure 8.6. Furthermore, the CO spectrum has to be multiplied by an additional delay time independent scale to account for di↵erent photo-ionization eciencies for probing of CO or Fe(CO)x molecules, respectively, before subtracting it, scaled by the fit function for CO creation (figure 8.6), separately for each delay time from the scaled di↵erences Dscaled, yielding a data set DCOfree, free of contributions from CO molecules and non-excited Fe(CO)5 and therefore containing the evolution of the transient photoelectron spectra during the photo-dissociation of Fe(CO)5 to Fe(CO)3. However, as the additional scaling due to the individual photo-ionization eciency is not determinable from the data, its value relies on an educated guess. The main criterion for this guess is to maintain a comparable background signal for binding energies corresponding to the right most CO peak and higher, hence for Eb & 19eV, as no signals arising from any of the Fe(CO)x species are expected for these photoelectron energies. Figure 8.8 gives an overview of the resulting transient spectra for Fe(CO)4 (green), estimated from D for t=1 0.2 ps and Fe(CO) (yellow), t=6.5 0.2 ps, and COfree ± 3 ± compares them to the Fe(CO)5 spectrum (blue), extracted for t < -2 ps and the spectrum from free CO molecules (gray). In figure 8.9, calculated photoelectron spectra are shown for Fe(CO)5, Fe(CO)4 and Fe(CO)3 molecules. The spectra were calculated by Michael Odelius (Stockholm Uni- versity, Sweden) [94] with a partial density of states (PDOS) numerical method. This method does not deliver accurate absolute binding energies, therefore the calculated spectra where shifted such that the lowest peaks from experiment and calculation match. Furthermore, a comparison with the measured spectra shows, that the relative peak distances are not reproduced, as well. In both, the measured and the calculated spectra, a shifting of the photoelectron peaks to lower binding energies is observed for each elimination of a CO ligand and the gross shape of the calculated spectra matches the experimental data. The outermost Fe 3d peak, at lowest binding energy undergoes a shift from 8.1 eV for Fe(CO)5 to 7.6 eV for Fe(CO) and Fe(CO) and an additional feature⇠ at around 10.6 eV shows ⇠ 4 3 up for Fe(CO)4 and Fe(CO)3 in the measurement, as the right peak of the Fe 3d peak doublet at 9.6 eV splits into two peaks at lower and higher binding energies of 8.5 eV and 10.6eV,⇠ respectively, after the elimination of the first CO ligand. The calculated⇠ spectra⇠ suggest this splitting as well, but with both new peaks shifted to lower binding energies, with respect to the Fe(CO)5 spectrum. The method of subtracting non-photo-excited Fe(CO)5 from the spectra by using a scaling ROI and furthermore, the subtraction of CO by using a scale obtained from an educated guess is not fully reliable, especially in the region for Eb>12 eV, where contributions from bound and free CO molecules dominate the spectra. Therefore the spectra for Fe(CO)4 and Fe(CO)3 for this energy region, depicted in figure 8.8,

97 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

∆ t = 6.5 ± 0.2 ps Fe(CO) 3

∆ t = 1 ± 0.2 ps Fe(CO) 4 intensity

∆ t < −2 ps Fe(CO) CO (σ+π) 5 Fe 3d

6 8 10 12 14 16 18 20 22 binding energy (eV)

Figure 8.8: Suggested valence photoelectron spectra for the dominating Fe(CO)x species at selected delays. Scaled CO spectra were additionally subtracted from the scaled di↵erences Dscaled. (see text for a detailed description)

Fe 3d CO (σ+π)

Fe(CO) 3

Fe(CO) intensity 4

Fe(CO) 5

6 8 10 12 14 16 18 20 22 binding energy (eV)

Figure 8.9: Calculated valence photoelectron spectra for Fe(CO)5,Fe(CO)4 and Fe(CO)3.

98 8.5 Conclusion for this chapter show structures and reveal a reshu✏ing, shifting, creation and destruction of states and suggest a gross shape for the valence spectra, but are neither good to determine reliable values for the peak shifts, nor to reliably determine how many new states are where visible in the spectra. The variations in the valence electron spectra show as electronic states in the valence electronic structure shift and new states are generated under the influence of a changing ligand field due to elimination of CO ligands, hence breaking of molecular bonds and therefore transfer of charge between the CO ligands and the central Fe atom during the photo-dissociation process. Furthermore, the peak shifts can reveal information about the degree of localization of the molecular orbitals and where they are localized. In order to accurately disentangle the spectra for the participating Fe(CO)x species and the CO molecules and in order to better understand the dynamics observed, accurate molecular dynamics simulations are desired for comparing theory and experiment. For example, if a numerical method can reproduce the measured Fe(CO)5 photoelectron spectra with high accuracy, this method most likely leads to accurate spectra for the daughter species and the resulting spectra can be utilized to improve the educated guess for CO subtraction, as well as to extract a more accurate scale for subtraction of non-excited Fe(CO)5 content in the data set. Furthermore, the area normalization, applied to the acquired spectra leads to perturbations, which can only be overcome by either recording spectra for as much time as needed to overcome the highly fluctuating nature of the FLASH pulses by sheer statistical averaging or by measuring the incoming intensity of FLASH for each shot, hence enabling the reliable intensity normalization. However, the presented spectra already show the power of TRPES for determining photoelectron spectra of transient species in ultrafast photo-dissociation processes in complex molecules of in this case 11 atoms, but it is as well illustrated that the methods for data acquisition , the light source and the on-line determination of the light’s properties are still to be improved.

8.5 Conclusion for this chapter

This chapter presented a scheme for disentangling complex TRPES data from UV photo-dissociation of Fe(CO)5. Photo-excited Fe(CO)5⇤ in gas-phase decays in two steps to Fe(CO)3 via intermediate Fe(CO)4. In each decay step, a CO ligand is split o↵,thereforetherecordeddatasetcontainscontributionsfromtheFe(CO)x species, as well as from the created free CO molecules. Furthermore, only a minor fraction of the sample gas ( 6%) was photo-excited upon pumping in this experiment. ⇠ In order to extract the main time characteristic of the dissociation sequence, delay scans were extracted for selected photoelectron energy regions and fitted according to afitfunctionmotivatedbyaratemodel,describingthedecaysequence.Duetothe limited time resolution in the experiment, no reliable time scale for the elimination of the first CO ligand could be estimated, but the time constant for the second

99 8 Transient Electronic Structures in Photo-Dissociation of Fe(CO)5

CO ligand elimination, related to the decay time for the transition from Fe(CO)4 to Fe(CO)3 was determined to 3.2 1.7 ps, in agreement with previously published results [102]. Furthermore, a scaling± region of interest was identified, describing the time evolution of non-excited Fe(CO)5 molecules in the data and therefore enabling subtraction of content from non-excited sample molecules from the recorded data set –thefirststeptotransientphotoelectronspectra.Inasecondstep,thecontributions from the created free CO molecules were subtracted from the TRPES data, yielding transient Fe(CO)4 and final, stable Fe(CO)3 photoelectron spectra. The gross shape and qualitative dynamics of these transient spectra are in reasonable agreement with theoretical spectra calculated with a PDOS method. A shifting of the valence peaks and creation of a new peak for the Fe 3d region was identified and furthermore, ashiftingandcreationofvariousnewpeaksduringthedissociationsequencewas observed for the CO (+⇡)orbitalregion.However,forsubtractionoftheCOcontent, it was necessary to introduce an artificial scaling to the photoelectron spectra for free CO molecules, only motivated by an educated guess. Therefore, no concrete numbers for characterizing the dynamics in the orbitals corresponding to bound CO ligands were extracted. Nevertheless, to our knowledge, this was the first time that Fe(CO)x especially Fe(CO)4 photoelectron spectra were determined experimentally. In order to improve the disentangling procedure, accurate state-of-the-art simulations for the photoelectron spectra of Fe(CO)5, Fe(CO)4 and Fe(CO)3 are desired. Knowing, what is expected from theory can provoke new ideas of how and where to look in the data. Furthermore, these calculations might help to improve the subtraction procedures on the way to transient, Fe(CO)x only spectra. In general, it turned out that the intrinsic timing jitter of FLASH is to large to resolve processes as fast as 100 fs and below (see chapter 5). Additionally, the pulses from FLASH underly an intrinsic spectral jitter, which at the PG2 beamline, upon monochromatization, translates to a shot-to-shot jitter of the probe pulse intensity by several orders of magnitudes. Hence, the spectra for the individual pump–probe delay times have to be normalized before being compared. There is no shot-to-shot intensity measurement installed after the monochromator at the PG2 beamline at FLASH, thus the most physical, relative intensity preserving normalization of each spectrum to the respective shot-to-shot intensity is not possible. Therefore, an area normalization was applied to the spectra, scaling all spectra by their area and thus assuming that the total photoelectron intensity in the recorded photoelectron energy window stays constant for all delay times. Hence, another perturbation is introduced by the lack of a suitable normalization scheme.

100 8.5 Conclusion for this chapter

Acknowledgement for this chapter

The presented campaign on transient electronic structures during photo-dissociation of Fe(CO)5 was carried out in a larger collaboration at the free-electron laser facility FLASH at the DESY site in Hamburg, Germany. The members in this collaboration are listed below, ﬁrst grouped by their aliations and second sorted alphabetically. The project was lead and the evaluation of the experimental data was performed by the author of this thesis, Torsten Leitner. The theoretical photoelectron spectra were calculated and provided by Michael Odelius. Philippe Wernet supervised the project. All other members of the collaboration greatly supported the campaign during planning and performing the experiment and in numerous discussions thereafter.

Members of the Collaboration: Tommaso Mazza, Michael Meyer, Paul Radcli↵e–European XFEL, Hamburg, Ger- many Stefan D¨usterer – DESY, Hamburg, Germany Michael Odelius – Stockholm University, Sweden Martin Beye, Alexander F¨ohlisch, Kristjan Kunnus, Torsten Leitner, Simon Schreck, Philippe Wernet – Helmholtz-Zentrum Berlin, Germany

101

9 Conclusion

The main objective of this thesis was to visualize ultrafast processes in molecules by means of time-resolved photoelectron spectroscopy (TRPES) and contribute to the grand challenge of understanding chemistry on a fundamental level. “Methods and Instruments” used for performing TRPES experiments were introduced in Part I. Especially the implementation and operation of the HHG based TRPES setup at HZB was explained in detail. The HHG source provides monochromatized VUV pulses of 120fs duration and up to 30eV photon energy for probing. Furthermore, the realization of a high-temperature sample evaporation source to enable the investigation of the electronic dynamics in the gas-phase for a wider range of materials, and two existing TRPES setups, at the Max-Born-Institute in Berlin and at the free electron laser FLASH in Hamburg have been presented. Schemes have been detailed for accurate timing in pump–probe experiments at FLASH, where the photon pulses underly a large intrinsic shot-to-shot arrival time jitter. In Part II, “Experiments”, three separate experimental campaigns on investigating the electronic structures of molecules and the dynamics therein were presented: Polariza- tion dependence in two-color two-photon ionization (chapter 6), coherent nuclear and electronic wave packet dynamics in photo-excited NaI molecules (chapter 7)andthe determination of the transient electronic structures during photo-dissociation in the gas-phase of the metal-carbonyl Fe(CO)5 (chapter 8). In all three gas-phase experiments the power of TRPES for investigating molecules on their fundamental time and length scales could be demonstrated. The polarization dependence in two-color two-photon ionization was linked directly to the asymmetry of the electronic structure via the asymmetry parameter for photoelectron angular distributions, 2, as the main free parameter in a theoretical approximation. The model is in good agreement for most of the experimental data. The break down of the model when hitting a photo-absorption resonance points towards necessary extensions of the model and shows that there is still a lot to learn and understand about two-photon ionization processes and their dependence on symmetry properties. The experiment on the coherent wave packet oscillations in NaI, which have been earlier investigated in great detail with femtosecond transition state spectroscopy by laser-induced ﬂuorescence by A.Zewail and coworkers [3, 4], showed that TRPES enables to reveal deeper insight, even for well investigated systems. The general time scales characterizing the oscillations have been extracted from the data and a hint, pointing to di↵erent evolution speeds for di↵erent molecular electron orbitals

103 9 Conclusion was identified. Further, the coherent superposition of a single molecule on several branches of a spin-orbit split intra-molecular potential, corresponding to the molecule co-existing in several intra-molecular distances, could be shown and a transfer of molecular wave packet population between two excitation levels of the NaI molecule was clearly visualized. Hence, it was demonstrated how TRPES resolves electronic dynamics in molecules even on a scale, where quantum mechanical e↵ects do play an important role. Finally, the results from a TRPES campaign at the free electron laser FLASH in Ham- burg on the step-wise photo-dissociation of a complexer molecule, Fe(CO)5, with a total of 11 atoms were presented. After photo-excitation, the Fe(CO)5 molecules decay to the short-lived transient Fe(CO)4, which is vibrationally hot and decays within 3.2 ps to stable Fe(CO)3 molecules. In each decay step, one of the ligands is split of⇠ and free CO molecules are created. The stepwise creation of CO molecules was confirmed with the time resolved photoelectron data and the lifetime of the Fe(CO)4 intermediate was determined. Furthermore, the valence photoelectron distributions for initial Fe(CO)5, transient Fe(CO)4 and final Fe(CO)3 molecules could be extracted from the data. To our knowledge, this was the first time that photoelectron distributions, for Fe(CO)4 and Fe(CO)3 were determined experimentally. However, it was also found that the achievable time resolution at FLASH is not sucient for revealing the very early transient dynamics occurring within 100 fs, when the photo-excited ⇠ Fe(CO)5⇤ molecules decay to Fe(CO)4 and a photo-induced breaking of the bond between the Fe center and one of the CO ligands takes place.

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112 Acknowledgement

I want to thank every one whom I had the great pleasure to work with on the presented projects and everyone who supported me during the last years, while working on this thesis. At first I would like to thank Dr. Philippe Wernet who supervised this thesis and provided great tips and directions for my research. I am very grateful for his patience and for ecient (and work-intense) proofreading of every last bit of this thesis, for his ideas and criticism and fast support, especially during the final spurt. I want to thank Prof. Dr. Dr. h.c. Wolfgang Eberhardt for giving me the opportunity to work at the Helmholtz-Zentrum Berlin and for examining this thesis. I thank Prof. Dr. Alexander Föhlisch, head of the institute G-I2 at HZB, for his great support and for examining this thesis. I am thankful for the great, friendly and helpful working environment at HZB. I want to cordially thank all colleagues from HZB and all further collaborators whom I have worked with during this thesis. Here’s an unordered and by far incomplete list: Mateusz Ibek for great times working together, great support in endless aligning ! sessions and lots of meaningful discussions about science, society and far beyond Rolf Mitzner and Torsten Quast for keeping the laser up and running ! Jérôme Gaudin, Olaf Schwarzkopf and Kai Godehusen for introducing me to the ! HHG setup and supporting my first steps in the world of laser and x-ray optics Michael Odelius for providing insight into simulating the molecular world and for ! supporting our experiments with various computer simulations Michael Meyer for his friendly support and our fruitful collaborations for the beamtime ! on Fe(CO)5 and on the polarization dependence in two-color photo-ionization Mathias Richter and Andrej Sorokin for the ecient collaboration on determining the ! absolute flux of the HZB HHG source and the reliability of semiconductor photodiodes Franziska Buchner, Andrea Lübcke, Arnaud Rouzée, Marc Vrakking, Per Johnsson, ! Linnea Rading and Hans Karlsson for enabling and performing the experiments on wave packet dynamics in NaI Tommaso Mazza, Paul Radcli↵e, Stefan Düsterer, Simon Schreck, Kristjan Kunnus ! and Martin Beye, who greatly supported the beamtime on Fe(CO)5 at FLASH Kerstin Kalus and Tino Noll for the design of the sample source ! Christian Kalus for great vacuum support ! I am indebted to Atoosa Meseck for inspiring and infecting me with her passion for science. I want to thank all my fellow PhD colleagues at HZB for nice Stammtisch evenings after the monthly seminar and for the good times at the yearly Klausurtagung. I especially thank Stephan Werner and Ruslan Ovsyannikov for the traditional ’co↵ee and cigarette’ breaks. Benjamin Pitt, Wilson Quevedo, Benjamin Riedl, Christian Sußner, Ralph Schwarz and Ju- lia Weinhold gave helpful criticism on language and lay out – thank you! I am very grateful to Nils Krebs, a really good friend, a fellow scientist and a dialog partner, for driving discussions from serious science all the way to utopia land and back again. My greatest and warmest gratitude goes to my parents for their infinite support and en- couragement throughout my entire life. Last but not least, I thank Johanna for her incomparable ability to motivate and strengthen me at any time. Thank you . . .

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