Quantum Optics in Phase Space

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book.

Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect.

Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields.

Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

What is Quantum Optics?
Ante
The Wigner Function
Quantum States in Phase Space
Waves á la WKB
WKB Wave Functions and Berry's Phase
Interference in Phase Space
Applications of Interference in Phase Space
Wave Packet Dynamics
Quantization of the Radiation Field
Quantum States of the Radiation Field
Phase Space Functions
Optical Interferometry
Atom-Field Interaction
Dynamics of Jaynes-Cummings-Paul Model
State Preparation and Entanglement
The Paul Trap
Damping and Amplification
Atom Optics in Quantized Light Fields
Wigner Functions in Atom Optics
Appendix
Time Dependent Operators -
Derivation of Equations Determining the Moyal Function -
Energy Wave Functions of Harmonic Oscillator -
Method of Stationary Phase -
Radial Equation -
Airy Function -
Asymptotic Expansion of the Poisson Distribution -
Area of Overlap -
P-Distributions -
Homodyne Detection Kernel -
Effective Hamiltonian -
Spontaneous Emission -
A Model for the Square Root of a Delta Function -
Bessel Functions

- Recipient of the Max Planck Research Award 2002

This book starts with a description of the quantization of the radiation field, phase space distribution functions, density operators and quantum mechanical beam splitters. Next, the measurement of phase-space distribution functions based on homodyne detector is discussed. It then goes on to treat semiclassical quantum mechanics. The next chapters cover interaction between atoms and quantized light fields, quantum theory of damping, quantum theory of the micromaser and concludes with atom optics in quantized lights fields. To keep the text as clear as possible some derivations of results are contained in appendices. Those seeking a modern and compact introduction to the theoretical aspects of quantum optics will greatly profit from this book. The aim has been to make the subject as transpa