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.
Author(s): Lampros A. A. Nikolopoulos
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 194
City: Bristol
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
