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Strong Field Single Ionization of Atoms and Small Molecules Strong field single ionization of atoms and small molecules: a hybrid anti-symmetrized coupled channels approach Naga Venkata Vinay Pramod Majety Munich 2015 Strong field single ionization of atoms and small molecules: a hybrid anti-symmetrized coupled channels approach Naga Venkata Vinay Pramod Majety PhD thesis Faculty of Physics Ludwig Maximilians University Munich Presented by Naga Venkata Vinay Pramod Majety from Vijayawada Munich, 25.08.2015 First examiner: Prof. Dr. Armin Scrinzi Second examiner: Prof. Dr. Regina de Vivie-Riedle Date of the examination: 06.10.2015 Contents Summary vii Zussamenfassung ix 1 Introduction 1 1.1 Background . .1 1.2 Re-collision imaging . .4 1.3 Photoionization . .6 1.4 Ab-inito modeling . .8 1.4.1 Simple models . .9 1.4.2 Popular ab-initio techniques . 10 1.5 Goal of the current work . 13 2 Cumulative thesis 15 2.1 The haCC approach . 16 2.1.1 Computation of observables . 23 2.2 Benchmarking tests . 25 2.3 Strong field ionization of small molecules . 27 2.3.1 Polarization effects . 28 2.3.2 Role of exchange interaction . 30 3 Full articles 33 3.1 Photoionization of few electron systems: a hybrid coupled channels ap- proach, New J. Phys. 17 (2015) 063002. 35 3.2 Mixed gauge in strong laser-matter interaction, J. Phys. B: At. Mol. Opt. Phys. 48 (2015) 025601. 53 3.3 Photoionization of noble gases: a demonstration of hybrid coupled channels approach. Photonics 2015, 2, 93-103. 63 3.4 Static field ionization rates for multi-electron atoms and small molecules. Submitted to J Phys B. 75 3.5 Dynamic exchange in the strong field ionization of molecules. Phys. Rev. Lett. 115, 103002 (2015) . 93 vi contents 4 Conclusions and outlook 99 5 Technical appendices 103 5.1 Derivation of matrix elements . 103 5.1.1 Overlap . 104 5.1.2 Single particle operators . 105 5.1.3 Two particle operators . 109 5.2 Two electron integrals . 113 5.2.1 Hartree term . 114 5.2.2 Standard exchange term . 115 2 IJ 5.2.3 Non-standard two-electron integral: αφb V f g φcφd ρabcd ...... 116 h j 2j i J 5.2.4 Non-standard two-electron integral: φaφb V f g φdβ ηabdN ...... 117 5.3 Interfacing with quantum chemistry . .h . .j . .j . .i . 118 5.4 The haCC code . 119 5.4.1 tRecX: a general pde solver . 120 5.4.2 Reconstructing the CI wavefunctions . 122 Bibliography 123 Acknowledgements 130 Summary In this thesis, strong field single ionization (SFI) of multi-electron atoms and small molecules is studied by developing a new non-perturbative multi-electron Schr¨odingerequation solver called the hybrid anti-symmetrized coupled channels (haCC) approach. SFI is the basis for several ultra-fast imaging techniques like molecular orbital tomog- raphy, high harmonic spectroscopy and laser induced electron diffraction. Analyzing these new techniques theoretically needs solving the non-perturbative multi-electron Schr¨odinger equation which in practice cannot be solved in full generality. Hence, for a long time these techniques were understood using single electron models. Recent experimental studies on angle dependent SFI of molecules CO and CO2 could not be explained by single electron models opening up a fundamental question on the role of multi-electron effects in SFI. In this context, a viable numerical method that goes beyond single electron models and that can systematically include multi-electron effects to examine their role is essential. For this purpose, the haCC technique was formulated and implemented in the form of a new C++ code. The method tackles the two important problems of solving the many electron Schr¨odingerequation: the multi-dimensionality by using a coupled channels formalism and the complexity arising from the multi-centered nature of a molecule by describing the ionizing electron with a hybrid single particle basis that consists of atom centered and origin centered functions. The method brings together a host of techniques in electronic structure theory and strong field physics: configuration interaction theory implemented in COLUMBUS quantum chemistry package, finite element technology, infinite range exterior complex scaling absorption technique, mixed gauge representations and the time dependent surface flux spectral analysis method. The key observables studied here are photo-electron spectra, angle dependent static field ionization rates and yields. The results obtained for the inert gas atoms conform with the existing knowledge that they behave as effective single electron systems. The new findings are in the case of molecules. The haCC calculations show that dynamic exchange and polarization are the important multi-electron effects in SFI of molecules. They also helped resolve long standing discrepancies between experiments and theory in angle dependent SFI of O2, CO and CO2. The calculations show that polarization at moderate intensities can be modeled using a few channel ansatz which is reassuring for further theoretical development. In the case of CO molecule it turns out that core polarization effects can reverse the maximum emission direction based on the intensity. Treating dynamic exchange, which refers to exchange interaction in the system beyond the initial and final states, accurately leads to a perfect agreement between theory and the experiment for the peak emission angles of O2 and CO2. viii Zussamenfassung In dieser Arbeit wird die Einfachionisation von Multielektronatomen und kleinen Molek¨ulen durch starke Felder studiert. Zu diesem Zweck wurde ein neuartiger Ansatz namens "hybrid anti-symmetrized coupled channels" (haCC) f¨urdie L¨osungder Multielektron- Schr¨odingergleichung entwickelt. Ionisation durch starke Felder (Strong Field Ionization - SFI) ist die Basis f¨ureinige neuartige Verfahren zur Abbildung von ultraschneller Kern- und Elektronenbewegung, wie zum Beispiel die Molek¨ulorbitaltomografie (molecular orbital tomography), Spektroskopie mittels Frequenzvervielfachung (high harmonic spectroscopy) und laserinduzierte Elektro- nenbeugung (laser induced electron diffraction). Die Analyse dieser Techniken erfordert die L¨osungder nicht-perturbativen Multielektron-Schr¨odingergleichung, was in der Praxis nicht im vollen Umfang m¨oglich ist. Daher wurden die Experimente bisher nur im Rah- men von Einelektronmodellen beschrieben. Neue winkelaufl¨osendeExperimente zur SFI von CO und CO2 Molek¨ulenkonnten jedoch so nicht erkl¨artwerden, was grundlegende Fragen ¨uber die Rolle von Multielektroneffekten in SFI aufwarf. In diesem Zusammenhang ist eine praktikable numerische Methode unerl¨asslich, die ¨uber das Einelektronmodel hinausgeht, systematisch Multielektroneffekte einschließt, und somit deren gezielte Untersuchung erm¨oglicht. Zu diesem Zweck wurde die haCC Methode formuliert und in Form eines neuen C++ Codes implementiert. Die Methode l¨ostdie beiden wichtigsten Probleme, welche sich bei der L¨osungder Multielektron-Schr¨odingergleichung stellen: die Hochdimensionalit¨atdurch einen Formalismus f¨urgekoppelte Ionisations-Kan¨ale und die fehlende sph¨arische Symmetrie eines Molek¨ulsdurch Verwendung einer hybriden Einelektron-Basis bestehend aus ursprungszentrierten und atomzentrierten Funktionen. Das Verfahren vereint mehrere Techniken aus den Bereich der Elektronenstruktur und der Physik starker Felder: Konfigurationswechselwirkung aus dem Quantenchemiepaket COLUMBUS, die Finite Elemete Methode, \komplexe Skalierung" (infinite range exterior complex scaling) als aborbierende Randbedingungen, nicht-standard gemischte Feldkop- plung (mixed gauge) und die Berechnung von Elektronspektren aus Oberfl¨achenfl¨ussen (time dependent surface flux). Als Observable betrachten wir Photoelektronenspektren, winkelabh¨angigestatische Fel- dionisationsraten und totale Ionisationswahrscheinlichkeiten. Es konnte best¨atigtwerden, dass Edelgasatome sich wie effektive Einelektronsysteme verhalten. Neue Erkenntnisse gibt es bei Molek¨ulen:die lange bestehenden Diskrepanzen zwischen Experiment und Theorie bei winkelabh¨angigerSFI von O2, CO und CO2 konnte erkl¨artund beseitigt werden. Dy- namische Austauschwechselwirkung (dynamic exchange) und Polarisationseffekte wurden als die wichtigsten Mehrelektroneffekte in SFI von Molek¨ulenidentifiziert. Zur Model- lierung von Polarisationseffekten bei moderaten Intensit¨atengen¨ugenwenige Kan¨ale,was beruhigend f¨urdie weitere theoretische Entwicklung ist. Im Fall des CO-Molek¨ulsk¨onnen Polarisationseffekte bei gewissen Intensit¨atendie Richtung maximaler Emission umkehren. x Ber¨ucksichtigung dynamischen Austauschwechselwirkung bei der Berechnung von winke- labh¨angigenIonisationsprofilen von CO2 und O2 bringt Theorie und Experiment in perfekte Ubereinstimmung.¨ 1 Introduction 1.1 Background Understanding motion of atoms and electrons on their natural time scales is the goal of ultrafast science. The time scales of motion associated with various degrees of freedom in a molecular system are related to their respective energies. Broadly, the rotational 12 dynamics happen on the picosecond (1ps = 10− s) timescale, the vibrational motion in 15 few tens to hundreds of femtoseconds (1fs = 10− s) and electron motion in attoseconds 18 (1as = 10− s) to a few femtoseconds. Taking snapshots of these dynamics on their natural time scales requires probes whose duration is smaller than these timescales [1]. Typical probes are light pulses, electron pulses or ion pulses. Charged particles repel each other and this makes it difficult to achieve very short duration pulses with them. Hence, for a number of applications in the femtosecond and attosecond domain, the pre- ferred choice is light probes. From the time the
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