Über die Autorin bzw. den Autor

Paul R. Berman & Vladimir S. Malinovsky

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"This book is special in that it covers certain topics from several viewpoints. Many are presented, compared, discussed, and described in terms of their similarities and differences. I think this is beautifully done! The writing is clear, precise, and concise, and the well-done citations to other parts of the text lead the reader along logical paths to a significant conclusion."--Harold Metcalf, State University of New York, Stony Brook

"This book gives a very detailed and comprehensive treatment of theoretical quantum optics. It provides a consistent and thorough look at the whole field and will be a valuable reference."--Richard Thompson, Imperial College, London

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"This book is special in that it covers certain topics from several viewpoints. Many are presented, compared, discussed, and described in terms of their similarities and differences. I think this is beautifully done! The writing is clear, precise, and concise, and the well-done citations to other parts of the text lead the reader along logical paths to a significant conclusion."--Harold Metcalf, State University of New York, Stony Brook

"This book gives a very detailed and comprehensive treatment of theoretical quantum optics. It provides a consistent and thorough look at the whole field and will be a valuable reference."--Richard Thompson, Imperial College, London

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Principles of Laser Spectroscopy and Quantum Optics

PRINCETON UNIVERSITY PRESS

Contents

Preface.................................................................................................................xv1 Preliminaries.........................................................................................................12 Two-Level Quantum Systems.............................................................................................173 Density Matrix for a Single Atom......................................................................................564 Applications of the Density Matrix Formalism..........................................................................835 Density Matrix Equations: Atomic Center-of-Mass Motion, Elementary Atom Optics, and Laser Cooling.....................996 Maxwell-Bloch Equations...............................................................................................1207 Two-Level Atoms in Two or More Fields: Introduction to Saturation Spectroscopy........................................1368 Three-Level Atoms: Applications to Nonlinear Spectroscopy-Open Quantum Systems........................................1599 Three-Level Atoms: Dark States, Adiabatic Following, and Slow Light...................................................18410 Coherent Transients..................................................................................................20611 Atom Optics and Atom Interferometry..................................................................................24212 The Quantized, Free Radiation Field..................................................................................28013 Coherence Properties of the Electric Field...........................................................................31214 Photon Counting and Interferometry...................................................................................33915 Atom–Quantized Field Interactions..............................................................................35816 Spontaneous Decay....................................................................................................37517 Optical Pumping and Optical Lattices.................................................................................40218 Sub-Doppler Laser Cooling............................................................................................42219 Operator Approach to Atom–Field Interactions: Source-Field Equation............................................45320 Light Scattering.....................................................................................................47421 Entanglement and Spin Squeezing......................................................................................492Problems................................................................................................................505References..............................................................................................................506Bibliography............................................................................................................507Index...................................................................................................................509

Chapter One

1.1 Atoms and Fields

As any worker knows, when you come to a job, you have to have the proper tools to get the job done right. More than that, you must come to the job with the proper attitude and a high set of standards. The idea is not simply to get the job done but to achieve an end result of which you can be proud. You must be content with knowing that you are putting out your best possible effort. Physics is an extraordinarily difficult "job." To understand the underlying physical origin of many seemingly simple processes is sometimes all but impossible. Yet the satisfaction that one gets in arriving at that understanding can be exhilarating. In this book, we hope to provide a foundation on which you can build a working knowledge of atom–field interactions, with specific applications to linear and nonlinear spectroscopy. Among the topics to be discussed are absorption, emission and scattering of light, the mechanical effects of light, and quantum properties of the radiation field.

This book is divided roughly into two parts. In the first part, we examine the interaction of classical electromagnetic fields with quantum-mechanical atoms. The external fields, such as laser fields, can be monochromatic, quasi-monochromatic, or pulsed in nature, and can even contain noise, but any quantum noise effects associated with the fields are neglected. Theories in which the fields are treated classically and the atoms quantum-mechanically are often referred to as semiclassical theories. For virtually all problems in laser spectroscopy, the semiclassical approach is all that is needed. Processes such as the photoelectric effect and Compton scattering, which are often offered as evidence for photons and the quantum nature of the radiation field can, in fact, be explained rather simply with the use of classical external fields. The price one pays in the semiclassical approach is the use of a time-dependent Hamiltonian for which the energy is no longer a constant of the motion.

Although the semiclassical approach is sufficient for a wide range of problems, it is not always possible to consider optical fields as classical in nature. One might ask when such quantum optics effects begin to play a role. Atoms are remarkable devices. If you place an atom in an excited state, it radiates a uniquely quantum-type field, the one-photon state. One of the authors (PRB) is a former student of Willis Lamb, who claimed that it should be necessary for people to apply for a license before they can use the word photon. Lamb was not opposed to the idea of a quantized field mode, but he felt that the word photon was misused on a regular basis. We will try to explain the distinction between a one-photon field and a photon when we begin our discussion of the quantized radiation field.

The field radiated by an atom in an excited state has a uniquely quantum character. In fact, any field in which the average value of the number operator for the field (average number of photons in the field) is less than or on the order of the number of atoms with which the field interacts must usually be treated using a quantized field approach. Thus, the second, or quantum optics, part of this book incorporates a fully quantized approach, one in which both the atoms and the fields are treated as quantum-mechanical entities. The advantage of using quantized fields is that one recovers a Hamiltonian that is perfectly Hermitian and independent of time. The most common quantum optics effects are those associated with spontaneous emission, scattering of external fields by atoms, quantum noise, and cavity quantum electrodynamics. There is another class of problems related to quantized field effects involving van der Waals forces and Casimir effects, but we do not discuss these in any detail.

1.2 Important Parameters

Why did the invention of the laser cause such a revolution in physics? Laser fields differ from conventional optical sources in their coherence properties and intensity. In this book, we look at applications that exploit the coherence properties of lasers, although complementary textbooks could be written in...