Attosecond Electron Spectroscopy Theory and its Applications Justin Gagnon M¨unchen2010 Attosecond Electron Spectroscopy Theory and its Applications Justin Gagnon Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Justin Gagnon aus Halifax, Nova Scotia, Canada M¨unchen, den 3. Dezember 2010 Erstgutachter: Prof. Dr. Ferenc Krausz Zweitgutachter: Prof. Dr. Armin Scrinzi Tag der m¨undlichen Pr¨ufung:12. Januar 2011 Contents Contents vi List of Figures viii List of Tables ix Summary xiii Zusammenfassung xv List of Contributions xvii Introduction 1 1 Characterizing Attosecond Pulses 9 1.1 The RABITT Technique . .9 1.2 Gating the Attosecond Pulse Train . 11 1.2.1 Temporal Gating of the Attosecond Pulse Train . 14 1.2.2 Spectral Filtering of the Attosecond Pulse Train . 15 1.3 The Attosecond Streaking Measurement . 17 1.4 A Classical Trajectory Analysis of Streaking for Extracting the Attosecond Chirp . 21 1.5 The Semi-Classical Description of Attosecond Streaking . 30 1.6 The Attosecond FROG . 34 1.6.1 FROG Reconstruction . 36 1.6.2 The PCGPA . 44 1.6.3 The LSGPA . 46 1.6.4 A Comparison Between the LSGPA and the PCGPA . 49 1.7 The Robustness of Attosecond Streaking Measurements . 51 1.7.1 Streaking with a Single Isolated Attosecond Pulse . 53 1.7.2 Streaking with a Sequence of Two Attosecond Pulses . 58 vi Contents 2 Measuring Attosecond Electron Wave Parcels 67 2.1 The FROG Characterization of an Attosecond Electron Wave Parcel from a Streaking Measurement . 67 2.2 Laser-Dressed Scattering of an Attosecond Electron Wave Packet . 73 Conclusion 85 A Energy-Resolved Photoelectron Angular Distributions 87 A.1 The Coupled-Wave Lippmann-Schwinger Equation . 88 A.2 Bound-Free Transition Dipole Matrix Elements . 91 A.3 Scattering States for a Long Range Potential . 93 A.4 A Treatment of the Scattering Potential for Atoms and Molecules . 95 B A Little Bit of This and a Little Bit of That 99 B.1 The Obligatory Coordinate Transformations . 99 B.2 The Beloved Atomic Units . 101 B.3 A Simple Relation Between Bandwidth, Dispersion and Duration . 103 Bibliography 113 Acknowledgments 115 Personal Record 120 List of Figures 1 Schematic of the recollision process . .5 1.1 A RABITT measurement . 10 1.2 Recollision energies as a function of time for short and long driving laser pulses . 12 1.3 An attosecond streaking measurement . 19 1.4 The basic manifestations of the attosecond streaking effect . 20 1.5 Streaking effects for a gaussian attosecond pulse . 25 1.6 Streaking measurements with a non-gaussian XUV spectrum . 26 1.7 Illustration of the iCrap procedure for a cosine-like streaking field . 28 1.8 Illustration of the iCrap procedure for a sine-like streaking field . 29 1.9 Application of iCrap to very noisy spectrograms . 29 1.10 Comparison between the CVA and the TDSE . 33 1.11 The basic loop of the PCGPA and the LSGPA . 38 1.12 Characterization of an attosecond pulse from a spectrogram computed by numerical evaluation of the TDSE . 40 1.13 FROG retrieval of a sequence of two attosecond pulses from a streaking spectrogram . 41 1.14 The signal matrix assumed by the LSGPA . 47 1.15 Comparison between the LSGPA and the PCGPA . 50 1.16 Streaking spectrograms for various uncertainties in the parameters of an isolated attosecond pulse . 53 1.17 Attosecond FROG retrieval with uncertainty in the central energy . 55 1.18 Attosecond FROG retrieval with uncertainty in the bandwidth . 56 1.19 Attosecond FROG retrieval with uncertainty in the group-delay dispersion 56 1.20 Attosecond FROG retrieval with uncertainty in the timing for a single at- tosecond pulse . 57 1.21 Streaking spectrograms for various uncertainties in the parameters of a se- quence of two attosecond pulses . 59 1.22 Attosecond FROG retrieval with uncertainty in the relative intensity be- tween two attosecond pulses . 60 1.23 Attosecond FROG retrieval with uncertainty in the relative phase between two attosecond pulses . 61 viii List of Figures 1.24 Attosecond FROG retrieval with uncertainty in the relative timing between two attosecond pulses . 62 1.25 Fringe positions for different values of relative timing between two attosec- ond pulses . 63 1.26 Attosecond FROG retrieval with uncertainty in the timing for a sequence of two attosecond pulses . 64 2.1 FROG retrieval of an electron wave parcel . 70 2.2 Two-path interference of an electron emitted from a localized state . 74 2.3 Photoelectron spectra for right-going and left-going wave packets . 76 2.4 Comparison of TDSE and CVA photoelectron spectra for a spatially ex- tended system . 77 2.5 A wave parcel represented in position space . 78 2.6 The effect of a control field on the reflected wave parcel . 80 2.7 Comparison of TDSE and classically-adjusted photoelectron spectra for a spatially extended system . 82 B.1 Illustration of spherical and cylindrical coordinate vectors . 99 List of Tables B.1 Transformations between rectangular, cylindrical and spherical coordinates 100 B.2 Orthogonal unit vectors x^, y^, z^, ρ^, φ^, ^r, θ^ in rectangular, cylindrical and spherical coordinates . 100 B.3 Common differential operators in rectangular, cylindrical and spherical co- ordinates . 100 B.4 Physical constants in SI and atomic units . 101 B.5 Atomic units of fundamental physical quantities with their values in SI units 102 x List of Tables I've had enough of someone else's propaganda. I'm for truth, no matter who tells it. I'm for justice, no matter who it's for or against. Malcolm X Summary Since the original prediction and demonstration of attosecond pulses, attosecond physics has entrenched itself in the ultrafast sciences, and promises to advance a wide range of scientific disciplines. It has the potential to provide key developments and insights in several research areas, such as atomic physics, quantum chemistry, biology and medicine. At present, engaging in this novel field of research is rather prohibitive, due to the high costs of cutting-edge technology and a steep learning curve. After all, playing with attosecond pulses is tantamount to playing with the shortest events ever made by man! Nonetheless, these are just typical growing pains of a new and exciting research area, and will eventually subside to make attosecond science accessible to a broad research community. In the meanwhile, as this promising field is taking its baby steps, it is the responsibility of those working at the cutting edge to propose novel experiments, and develop the tools and models that will be used in the future, as the field matures. Attosecond science comprises two frontiers: (i) the generation and characterization of increasingly intense, energetic, short and isolated attosecond pulses; and (ii) the design of experiments to probe physical systems on the attosecond time scale, the holy grail being the attosecond pump-attosecond probe time-resolved spectroscopic measurement. The second frontier offers a deeper understanding of the temporal behavior of the microcosm, but relies on advancements made in the first one. At present, both of these frontiers heavily rely on the attosecond streaking technique, which consists in energy-resolving photoelectrons ejected by an attosecond extreme ultraviolet pulse, in the presence of a phase-stabilized and temporally synchronized near-infrared field. Although it was originally devised as a means to characterize attosecond pulses, this measurement technique has even produced new discoveries in atomic and solid-state physics, due to pioneering experiments by M. Drescher, A. Cavalieri, G. Sansone, M. Schultze, and others, and has inspired novel theories of laser-dressed photoionization by V. S. Yakovlev, A. Scrinzi, O. Smirnova, M. Y. Ivanov and others. In the first part of this thesis, I focus on new methods I developed [II,III,IV,XII] for the analysis of attosecond streaking measurements [I,V,VI,VII,IX,XI]. One of these methods [XII], based on a formalism I devised based on electron trajectories in a laser field, can directly recover the chirp of an attosecond pulse from a set of streaked photoelectron spectra. Next, I describe a robust optimization algorithm [II,III,IV], based on a formalism due to M. Kitzler et al., that can completely recover the temporal profile of an attosecond pulse with an arbitrary shape. This optimization algorithm was used to characterize the xiv Summary field of ∼ 80 as pulses [I], the shortest on record, and to uncover a delay of ∼ 20 as between the photoemissions from the 2s and 2p sub-shells of neon [VII]; both experiments were performed here at the Max Planck Institut f¨urQuantenoptik in 2008 and 2010, respectively. Moreover, during the course of this work, it was established [VIII] by V. S. Yakovlev et al. that the attosecond streaking technique generally measures a quantity that is related to the photoelectron wave packet, not the attosecond light pulse. Only when the energy- resolved dipole response, given by the bound-free transition matrix elements, is nearly constant can we take the electron wave packet as a replica of the attosecond pulse. In light of this finding, I show that the attosecond streaking technique provides a means to measure and even time-resolve the energy-dependent phase of transition dipole matrix elements. Finally, I consider the laser-dressed scattering of an attosecond photoelectron wave packet [X]. I show that the scattering of a photoelectron, emitted by an attosecond pulse from a localized state in a spatially extended system, can be influenced by a near-infrared laser field. Measuring the photoelectron spectrum reveals an interference pattern which is affected by the intensity of the near-infrared field. To describe these effects, I introduce a model based on classical trajectories that quantitatively predicts laser-dressed photoelec- tron spectra for such a spatially-extended system.