This document is Sajad Azizi's doctoral thesis titled 'Three Aspects of Photoionization in Ultrashort Pulses.' The research was conducted under the supervision of Prof. Dr. Jan Michael Rost at the Max Planck Institute for the Physics of Complex Systems.:Contents
1 Introduction 1
1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Fundamental Concepts 5
2.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Introduction to strong field ionization . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 From the photoelectric effect to strong-field ionization . . . . . . . . . 6
2.3 Non-relativistic time-dependent Hamiltonian . . . . . . . . . . . . . . . . . . 10
2.3.1 Dipole approximation and choice of gauges . . . . . . . . . . . . . . . 11
2.3.2 Interaction of an electron with a classical field . . . . . . . . . . . . . 12
2.4 Ultrashort laser pulse shaping . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Fourier-limited pulse: Gaussian envelope . . . . . . . . . . . . . . . . . 17
2.4.2 Modulated pulse: sinusoidal phase modulation . . . . . . . . . . . . . 18
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Controlling Non-adiabatic Photoionization with Ultrashort Pulses 20
3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Introduction to non-adiabatic ionization . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Intuitive picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Mathematical picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Non-adiabatic ionization with tailored laser pulses . . . . . . . . . . . . . . . 25
3.3.1 Ionization by single Gaussian pulses . . . . . . . . . . . . . . . . . . . 26
3.3.2 Sensitivity of non-adiabatic photoionization to the modulation phase . 28
3.3.3 The role of the catalyzing state . . . . . . . . . . . . . . . . . . . . . . 31
3.3.4 Second-order perturbation theory . . . . . . . . . . . . . . . . . . . . . 32
3.3.5 Pulse optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Time-dependent Perturbation Theory for Ultrashort Pulses 37
4.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Introduction to time-dependent perturbation theory . . . . . . . . . . . . . . 39
4.2.1 Higher order time-dependent perturbation theory . . . . . . . . . . . . 42
4.2.2 Perturbation theory in shaped short laser pulse . . . . . . . . . . . . . 45
4.3 Application I: non-adiabatic ionization . . . . . . . . . . . . . . . . . . . . . . 47
4.3.1 Slowly varying envelope approximation . . . . . . . . . . . . . . . . . 50
4.3.2 Zero-photon transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.3 Zero-photon ionization probability . . . . . . . . . . . . . . . . . . . . 55
4.3.4 Oscillation in zero-photon transition . . . . . . . . . . . . . . . . . . . 58
4.4 Application II: interference stabilization . . . . . . . . . . . . . . . . . . . . . 59
4.4.1 Third-order time-dependent perturbation theory . . . . . . . . . . . . 61
4.4.2 Ionization probability and stabilization . . . . . . . . . . . . . . . . . . 62
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Molecular Photoionization Time Delay 65
5.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Introduction to time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.1 Time delay in scattering scenario . . . . . . . . . . . . . . . . . . . . 69
5.2.2 Asymptotic behavior of ⟨r⟩ . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Photoionization time delay from a scattering theory perspective . . . . . . . 74
5.3.1 Asymptotic solutions and scattering matrix . . . . . . . . . . . . . . . 75
5.3.2 Energy normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3.3 Boundary condition and final molecular wavefunction . . . . . . . . . 79
5.3.4 Matrix element and photoionization time delay . . . . . . . . . . . . . 81
5.3.5 Two-center system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4 Photoionization time delay from a wavepacket perspective . . . . . . . . . . 87
5.4.1 Partial time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4.2 Photoelectron wavepacket and photoionization time delay . . . . . . . 92
5.4.3 Anisotropic potential and half-collision checking . . . . . . . . . . . . 94
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 Conclusions and Outlook 97
A Renormalized Numerov Method 101
A.1 Introduction to Numerov method . . . . . . . . . . . . . . . . . . . . . . . . 103
A.1.1 Eigenvalue calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
A.2 Johnson renormalized Numerov method . . . . . . . . . . . . . . . . . . . . . 106
A.2.1 Proper initialization for extreme values of potential . . . . . . . . . . . 108
A.2.2 Matching point and bound states solutions . . . . . . . . . . . . . . . 110
A.2.3 Discretized continuum states solutions . . . . . . . . . . . . . . . . . . 111
A.2.4 Continuum states solutions . . . . . . . . . . . . . . . . . . . . . . . . 112
B Derivation of the Asymptotic Behavior of ⟨r⟩ 114
C Classical Time Delay 117
D Temporal Airy Pulse 119
E Numerical Details of Perturbation Theory 122
F Atomic Units
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:87936 |
| Date | 09 November 2023 |
| Creators | Azizi, Sajad |
| Contributors | Rost, Jan-Michael, Ketzmerick, Roland, Emmanouilidou, Agapi, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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