Elements of Photoionization Quantum Dynamics Methods

Description

The dynamics of quantum systems exposed to ultrafast (at the femtosecond time-scale) and strong laser radiation has a highly non-linear character, leading to a number of new phenomena, outside the reach of traditional spectroscopy. The current laser technology makes feasible the probing and control of quantum-scale systems with fields that are as strong as the interatomic Coulombic interactions and time resolution that is equal to (or less than) typical atomic evolution times. It is indispensable that any theoretical description of the induced physical processes should rely on the accurate calculation of the atomic structure and a realistic model of the laser radiation as pulsed fields. This book aims to provide an elementary introduction of theoretical and computational methods and by no means is anywhere near to complete. The selection of the topics as well as the particular viewpoint is best suited for early-stage students and researchers; the included material belongs in the mainstream of theoretical approaches albeit using simpler language without sacrificing mathematical accuracy. Therefore, subjects such as the Hilbert vector-state, density-matrix operators, amplitude equations, Liouville equation, coherent laser radiation, free-electron laser, Dyson-chronological operator, subspace projection, perturbation theory, stochastic density-matrix equations, time-dependent Schrödinger equation, partial-wave analysis, spherical-harmonics expansions, basis and grid wavefunction expansions, ionization, electron kinetic-energy and angular distributions are presented within the context of laser-atom quantum dynamics. PRELIMS.pdf Prologue Acknowledgments Author biography Lampros Nikolopoulos Glossary of symbols CH001.pdf Chapter 1 Introduction CH002.pdf Chapter 2 Quantum dynamics 2.1 Hilbert vector states 2.1.1 Iterative expansion 2.1.2 Basis expansion 2.2 Subspace dynamics 2.3 von Neumann (density) matrix states 2.3.1 IP iterative expansion 2.4 Homework problems References CH003.pdf Chapter 3 Atomic potentials 3.1 Central field 3.2 Harmonic oscillator 3.3 Homework problems References CH004.pdf Chapter 4 Laser pulses 4.1 Classical electrodynamics 4.2 Laser pulses in the paraxial approximation 4.3 Coherent and partially coherent fields 4.4 Homework problems References CH005.pdf Chapter 5 Quantum systems in laser fields 5.1 Atomic TDSE in the dipole approximation 5.2 Time-dependent perturbation theory 5.3 Driven quantum oscillator 5.4 Homework problems References CH006.pdf Chapter 6 Amplitude coefficient equations 6.1 Two-level systems 6.2 Ionization 6.2.1 Single-photon ionization 6.3 Resonant excitation and (auto-)ionization 6.4 Homework problems References CH007.pdf Chapter 7 Density-matrix element equations 7.1 Resonant ionization 7.2 Ionization in stochastic fields 7.2.1 Averaged equations for resonant auto-ionization 7.3 Homework problems References CH008.pdf Chapter 8 Matrix elements of atomic operators 8.1 Atomic operators on the angular basis 8.1.1 Central-field Hamiltonian and dipole operators 8.1.2 Molecular diatomic potential 8.2 Inversion symmetry (parity) 8.3 Plane waves as a momentum basis 8.4 One- and two-electron ionization amplitudes 8.5 Homework problems References CH009.pdf Chapter 9 TDSE of hydrogen-like atoms in laser fields 9.1 Spectral and angular basis formulation 9.1.1 Spectral basis 9.1.2 Angular basis 9.2 Calculation of observables 9.3 Practical considerations 9.4 Homework problems References CH010.pdf Chapter 10 Space division of a one-dimensional TDSE 10.1 Time-independent potential 10.2 Time-dependent potential 10.3 Homework problems References CH011.pdf Chapter 11 Quantum mechanics of vector- and matrix-states 11.1 Vectors and operators 11.2 Statistical matrix state (or density matrix) 11.2.1 Density-state operator 11.3 Position representation 11.4 Degenerate systems 11.5 Homework problems References CH012.pdf Chapter 12 Technicalities 12.1 Radial atomic Schrödinger equation 12.1.1 Calculation of radial eigenstates 12.1.2 Box-normalization of the continuum states 12.1.3 Free boundary conditions 12.2 Time-propagation methods 12.3 B-spline polynomial basis References APP1.pdf Chapter A.1 Solutions of the Laplace operator A.1.1 Spherical harmonics, angular basis of ∇2 A.2 Integro-differential calculus formulas A.3 Operator and (matrix) algebraic functionals References