[1] Z.Ficek and M.R.B. Wahiddin, Quantum Optics: Fundamentals and Applications
(IIU Press, Kuala Lumpur, Malaysia, 2004).
[2] Z.Ficek and S.Swain, Quantum Interference: Theory and Experiments
(Springer, New York, Berlin 2005).
[3] Z.Ficek and R.Tanas, Quantum-Limit Spectroscopy
(Springer, New York, Berlin), in preparation, to be completed by March 2006.
BOOKS EDITED AND JOURNAL SPECIAL ISSUES EDITED
[1] Special Issue on Quantum Interference, edited by Z. Ficek and S. Swain,
Journal Modern Optics 49, No.1/2 (2002)
[2] Quantum Squeezing, edited by P.D. Drummond and Z. Ficek
(Springer, Berlin, 2004)
The book covers the background theory of quantum optics and stochastic methods with applications to atom optics. Various theoretical and experimental effects are discussed from first principles, and as clearly as possible, to introduce students to the main ideas of quantum optics and to teach the mathematical methods and techniques used by researches working in the fields of quantum and atom optics. Some of the key problems of quantum optics are also described, concentrating on the techniques, results and interpretations. No attempt has been made at a complete exploration of all the problems of quantum and atom optics, but it is hoped that the problems explored here will provide a useful starting point for those interested in learning more.
The field that encompasses the term "quantum interference" combines a number of separate concepts, and has a variety of manifestations in different areas of physics. In the sense considered here, quantum interference is concerned with coherence and correlation phenomena in radiation fields and between their sources. It is intimately connected with the phenomenon of non-separability (or entanglement) in quantum mechanics. On account of this, it is obvious that quantum interference may be regarded as a component of quantum information theory, which investigates the ability of the electromagnetic field to transfer information between correlated (entangled) systems. Since it is important to transfer information with the minimum of corruption, the theory of quantum interference is naturally related to the theory of quantum fluctuations and decoherence.
Since the early days of quantum mechanics, interference has been described as the real quantum mystery. Feynman, in his famous introduction to the lectures on the single particle superposition principle, referred in the following way to the phenomenon of interference: "it has in it the heart of quantum mechanics", and it is really 'the only mystery' of quantum mechanics. With the development of experimental techniques, it has been possible to carry out many of the early Gedanken experiments that played an important role in developing our understanding of the fundamentals of quantum interference and entanglement. Despite its long history, quantum interference still challenges our understanding, and continues to excite our imagination.
Quantum interference arises in some form or other in almost all the phenomena of quantum mechanics and its applications. Obviously, we have to be very selective in the topics we discuss here, and many important aspects are dealt with only briefly, or not at all. In writing the book our intention has been to concentrate on a systematic and consistent exposition of coherence and quantum interference phenomena in optical fields and atomic systems and to discuss the details of the most recent theoretical and experimental work in the field. We begin in Chap. 1 by discussing the basic principles of classical and quantum interference and summarizing some quite elementary concepts and definitions that are frequently used in the analysis of interference phenomena. The most important first- and second-order coherence effects are discussed including the welcher-weg problem, two-photon nonclassical interference, interferometric interaction-free measurements, and quantum lithography. We also discuss important experiments that confirm these basic interference predictions.
The mathematical formalism of quantum interference in atomic systems is developed in Chap. 2 for multi-level and multi-atom systems in free space and cavity environments. For our purposes, the master equation of an atomic system is derived in the Born-Markov and rotating-wave approximations. The relation of the source field operators to the atomic dipole operators and retardation effects are then discussed. In this way the correlation functions of the electric field and their relationship to the atomic dipole operators are developed as a basic formulation. The concept of superposition states is then introduced in Chap. 2B and applied to three-level systems in Vee and Lambda configurations. The concept of multi-atom entangled states is also introduced so that one can see the relation between quantum interference effects in multi-level and multi-atom systems. A full description of the quantum beats phenomenon and its relation to quantum interference phenomena is also included.
Chapter 3 discusses quantum interference effects induced by spontaneous emission and the experimental evidence of spontaneously induced quantum interference effects in a molecular multi-level system. This chapter includes a discussion of decoherence free subspaces and the role of decoherence in the formation of entanglement. A section on the effect of cavity and photonic bandgap materials on spontaneous emission from an atomic system is included here because these are examples of other practical systems to control and suppress spontaneous emission.
The subject of coherence effects in multi-level systems is treated in Chap. 4. The theory of two major quantum interference effects - coherent population trapping and electromagnetically induced transparency in simple three-level systems - are explored and described in terms of the density matrix elements of these systems. These processes depend on the creation of coherent superpositions of atomic states with accompanying loss of absorption. The chapter includes a general treatment of the spatial propagation of electromagnetic fields in optically dense media, and the absorption properties of coherently prepared atomic systems. This chapter also discusses applications of coherently prepared systems in the enhancement of optical nonlinearities in electromagnetically induced transparency.
Material on the implementation of quantum interference is included in Chap. 6. This chapter also discusses the phase control of quantum interference and extremely large values (superbunching) of the second-order correlation functions. Methods for producing quantum interference effects in three-level systems with perpendicular transition dipole moments is considered to show how one can get around the well-known difficulty of finding atomic or molecular systems with parallel transition dipole moments. This chapter concludes with a fairly detailed description of Fano profiles, laser-induced continuum structures and population trapping in photonic bandgap materials.
In Chap. 5 the theory of subluminal and superluminal propagation of a weak electromagnetic field in coherently prepared media is formulated and accompanied with many examples of the experimental observation of slow and fast light, and the storage of photons. The concept of polaritons is then introduced in terms of atomic and field operators.
The subject of quantum interference in a superposition of field states is considered in Chap. 7. The phase space formalism is described and quantum interference effects in phase space for several field states are discussed. Examples of the experimental reconstruction of Wigner functions and of the production of single-photon states are also included.
The final chapter discusses quantum interference effects with cold atoms. This includes the subjects of diffraction of cold atoms, interference of two Bose-Einstein condensates, collapses and revivals of an atomic interference pattern and interference experiments in coherent atom optics.
Since this book is based to a large extent on the combined work of many earlier contributors to the field of quantum interference, it is impossible to acknowledge our debts on an individual basis. We should, however, like to express our thanks to Peng Zhou who, during his stay at The Queen's University of Belfast, carried out some of the work on control of decoherence and field induced quantum interference presented in Chaps. 3 and 6.
We are greatly appreciative of the help and suggestions received from many colleagues, including Ryszard Tanas, Helen Freedhoff, Peter Drummond, Bryan Dalton, Shi-Yao Zhu, Christoph Keitel, Josip Seke, Gerhard Adam, Andrey Soldatov, Joerg Evers, Terry Rudolph and Uzma Akram. We are also grateful to Alexander Akulshin, Immanuel Bloch, Dmitry Budker, Milena D'Angelo, Juergen Eschner, Edward Fry, Christian Hettich, Alexander Lvovsky, Steven Rolston, and Lorenz Windholz for sending us originals of the reproduced figures of their experimental results.
The concept of squeezing is intimately related to the idea of vacuum fluctuations, once thought to place an absolute limit to the accuracy of measurement. However, vacuum fluctuations are not unchangeable. By recognizing that these quantum fluctuations always occur in two complementary observables, physicists have been able to make an intriguing trade-off. Reduced fluctuations in one variable can be realized - at the expense of increased fluctuations in another, according to Heisenberg.
This Heisenberg `horse-trade' - originally predicted by theorists - was first accomplished experimentally by R. Slusher in 1985. Since then, the various techniques and applications of quantum squeezing have metamorphosed into a central tool in the wider field of quantum information. This book is a summary of the main ideas, methods and applications of quantum squeezing, written by those responsible for some of the chief developments in the field.
The book is divided into three parts, to recognize that there are three areas in this research. These are the fundamental physics of quantum fluctuations, the techniques of generating squeezed radiation, and the potential applications.
Part I of the book, giving the fundamentals, is arranged as follows. Chapter 1 introduces the basic ideas about what squeezing of quantum fluctuations is from the quantized free-field perspective. This chapter establishes the definitions and notations used throughout. Chapter 2 explains how to quantize radiation in a dielectric, which is the basic technique that is used to make squeezed radiation. Chapter 3 explains how to quantize interfaces, where squeezed light is input or output through the dielectric boundaries.
Part II treats methods of generating quantum squeezed radiation. Chapter 4 starts with the most commonly used techniques in which squeezed radiation is generated using nonlinear optics. This covers both intra-cavity parametric squeezing and fiber soliton squeezing. Chapter 5 describes how lasers with the right kind of pumping may produce squeezed light, typically with squeezing in the intensity. Chapter 6 explains how various feedback techniques can be used to also produce non-classical radiation, and describes the distinction between in-loop' and out-of-loop' or external squeezing.
Part III treats the applications of squeezed radiation. In Chap. 7 the ideas of using squeezed and anti-bunched radiation sources forimproved communications and measurement are introduced. Chapter 8 details applications to spectroscopy of two-level atoms, including the possibility of sub-natural-linewidth spectroscopy. Chapter 9 extends this treatment to the spectroscopy of three-level atoms, in which anomalous inversions and pumping rates may be observed. Chapter 10 explains how entangled squeezed light can be used to carry out tests of quantum-mechanics and cryptography, based on the original entangled state proposal of Einstein, Podolsky and Rosen.
We emphasize that this is a rapidly changing research field, and the areas of applications, in particular, are the most rapidly changing of them all. While every effort is made to reference the most recent publications, not every development could be covered, for space reasons. However, it is hoped that the fundamental physics issues treated here will be of use to researchers and students in quantum information and related research fields.