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1、 This page intentionally left blank 3 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the Universitys objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town
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3、tnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York c ? Oxford University Press 2008 The moral rights of the authors have been asserted Database right Oxford University Pre
4、ss (maker) First published 2008 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed w
5、ith the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same
6、condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 9780198508861 Printed in Great Britain on acid-free paper by Biddles Ltd., Kings Lynn, Norfolk This book is dedicated to our wives: Florence Chiao and Hillegonda Garrison. Without their unfailing support an
7、d almost infi nite patience, the task would have been much harder. This page intentionally left blank Contents Introduction1 1The quantum nature of light3 1.1The early experiments5 1.2Photons13 1.3Are photons necessary?20 1.4Indivisibility of photons24 1.5Spontaneous down-conversion light source28 1
8、.6Silicon avalanche-photodiode photon counters29 1.7The quantum theory of light29 1.8Exercises30 2Quantization of cavity modes32 2.1Quantization of cavity modes32 2.2Normal ordering and zero-point energy47 2.3States in quantum theory48 2.4 Mixed states of the electromagnetic fi eld55 2.5 Vacuum fl u
9、ctuations60 2.6 The Casimir eff ect62 2.7Exercises65 3Field quantization69 3.1Field quantization in the vacuum69 3.2The Heisenberg picture83 3.3Field quantization in passive linear media87 3.4Electromagnetic angular momentum100 3.5Wave packet quantization103 3.6Photon localizability106 3.7Exercises1
10、09 4Interaction of light with matter111 4.1Semiclassical electrodynamics111 4.2Quantum electrodynamics113 4.3Quantum Maxwells equations117 4.4Parity and time reversal118 4.5Stationary density operators121 4.6 Positive- and negative-frequency parts for interacting fi elds122 4.7Multi-time correlation
11、 functions123 4.8The interaction picture124 4.9Interaction of light with atoms130 ?Contents 4.10Exercises145 5Coherent states148 5.1Quasiclassical states for radiation oscillators148 5.2Sources of coherent states153 5.3Experimental evidence for Poissonian statistics157 5.4Properties of coherent stat
12、es161 5.5Multimode coherent states167 5.6Phase space description of quantum optics172 5.7Gaussian states187 5.8Exercises190 6Entangled states193 6.1EinsteinPodolskyRosen states193 6.2Schr odingers concept of entangled states194 6.3Extensions of the notion of entanglement195 6.4Entanglement for disti
13、nguishable particles200 6.5Entanglement for identical particles205 6.6Entanglement for photons210 6.7Exercises216 7Paraxial quantum optics218 7.1Classical paraxial optics219 7.2Paraxial states219 7.3The slowly-varying envelope operator223 7.4Gaussian beams and pulses226 7.5The paraxial expansion228
14、7.6Paraxial wave packets229 7.7Angular momentum230 7.8Approximate photon localizability232 7.9Exercises234 8Linear optical devices237 8.1Classical scattering237 8.2Quantum scattering242 8.3Paraxial optical elements245 8.4The beam splitter247 8.5Y-junctions254 8.6Isolators and circulators255 8.7Stops
15、260 8.8Exercises262 9Photon detection265 9.1Primary photon detection265 9.2Postdetection signal processing280 9.3Heterodyne and homodyne detection290 9.4Exercises305 Contents? 10 Experiments in linear optics307 10.1Single-photon interference307 10.2Two-photon interference315 10.3Single-photon interf
16、erence revisited333 10.4Tunneling time measurements337 10.5The meaning of causality in quantum optics343 10.6Interaction-free measurements345 10.7Exercises348 11 Coherent interaction of light with atoms350 11.1Resonant wave approximation350 11.2Spontaneous emission II357 11.3The semiclassical limit3
17、69 11.4Exercises379 12 Cavity quantum electrodynamics381 12.1The JaynesCummings model381 12.2Collapses and revivals384 12.3The micromaser387 12.4Exercises390 13 Nonlinear quantum optics391 13.1The atomic polarization391 13.2Weakly nonlinear media393 13.3Three-photon interactions399 13.4Four-photon i
18、nteractions412 13.5Exercises418 14 Quantum noise and dissipation420 14.1The world as sample and environment420 14.2Photons in a lossy cavity428 14.3The inputoutput method435 14.4Noise and dissipation for atoms442 14.5Incoherent pumping447 14.6 The fl uctuation dissipation theorem450 14.7Quantum regr
19、ession454 14.8Photon bunching456 14.9 Resonance fl uorescence457 14.10 Exercises466 15 Nonclassical states of light470 15.1Squeezed states470 15.2Theory of squeezed-light generation485 15.3Experimental squeezed-light generation492 15.4Number states495 15.5Exercises497 16 Linear optical amplifi ers49
20、9 ?Contents 16.1 General properties of linear amplifi ers499 16.2 Regenerative amplifi ers502 16.3 Traveling-wave amplifi ers510 16.4 General description of linear amplifi ers516 16.5 Noise limits for linear amplifi ers523 16.6Exercises527 17 Quantum tomography529 17.1Classical tomography529 17.2Opt
21、ical homodyne tomography532 17.3Experiments in optical homodyne tomography533 17.4Exercises537 18 The master equation538 18.1Reduced density operators538 18.2The environment picture538 18.3Averaging over the environment539 18.4Examples of the master equation542 18.5Phase space methods546 18.6The Lin
22、dblad form of the master equation556 18.7Quantum jumps557 18.8Exercises576 19 Bells theorem and its optical tests578 19.1The EinsteinPodolskyRosen paradox579 19.2The nature of randomness in the quantum world581 19.3Local realism583 19.4Bells theorem589 19.5Quantum theory versus local realism591 19.6
23、Comparisons with experiments596 19.7Exercises600 20 Quantum information601 20.1Telecommunications601 20.2Quantum cloning606 20.3Quantum cryptography616 20.4Entanglement as a quantum resource619 20.5Quantum computing630 20.6Exercises639 Appendix AMathematics645 A.1Vector analysis645 A.2General vector
24、 spaces645 A.3Hilbert spaces646 A.4Fourier transforms651 A.5Laplace transforms654 A.6Functional analysis655 A.7Improper functions656 Contents? A.8Probability and random variables659 Appendix BClassical electrodynamics661 B.1Maxwells equations661 B.2Electrodynamics in the frequency domain662 B.3Wave
25、equations663 B.4Planar cavity669 B.5Macroscopic Maxwell equations670 Appendix CQuantum theory680 C.1Diracs bra and ket notation680 C.2Physical interpretation683 C.3Useful results for operators685 C.4Canonical commutation relations690 C.5Angular momentum in quantum mechanics692 C.6Minimal coupling693
26、 References695 Index708 This page intentionally left blank Introduction For the purposes of this book, quantum optics is the study of the interaction of indi- vidual photons, in the wavelength range from the infrared to the ultraviolet, with ordi- nary mattere.g. atoms, molecules, conduction electro
27、ns, etc.described by nonrela- tivistic quantum mechanics. Our objective is to provide an introduction to this branch of physicscovering both theoretical and experimental aspectsthat will equip the reader with the tools for working in the fi eld of quantum optics itself, as well as its applications.
28、In order to keep the text to a manageable length, we have not attempted to provide a detailed treatment of the various applications considered. Instead, we try to connect each application to the underlying physics as clearly as possible; and, in addition, supply the reader with a guide to the curren
29、t literature. In a fi eld evolving as rapidly as this one, the guide to the literature will soon become obsolete, but the physical principles and techniques underlying the applications will remain relevant for the foreseeable future. Whenever possible, we fi rst present a simplifi ed model explainin
30、g the basic physical ideas in a way that does not require a strong background in theoretical physics. This step also serves to prepare the ground for a more sophisticated theoretical treatment, which is presented in a later section. On the experimental side, we have made a serious eff ort to provide
31、 an introduction to the techniques used in the experiments that we discuss. The book begins with a survey of the basic experimental observations that have led to the conclusion that light is composed of indivisible quantacalled photonsthat obey the laws of quantum theory. The next six chapters are c
32、oncerned with building up the basic theory required for the subsequent developments. In Chapters 8 and 9, we emphasize the theoretical and experimental techniques that are needed for the discussion of a collection of important experiments in linear quantum optics, presented in Chapter 10. Chapters 1
33、1 through 18 contain a mixture of more advanced topics, including cavity quantum electrodynamics, nonlinear optics, nonclassical states of light, linear optical amplifi ers, and quantum tomography. In Chapter 19, we discuss Bells theorem and the optical experiments performed to test its consequences
34、. The ideas associated with Bells theorem play an important role in applications now under development, as well as in the foundations of quantum theory. Finally, in Chapter 20 many of these threads are drawn together to treat topics in quantum information theory, ranging from noise suppression in op
35、tical transmission lines to quantum computing. We have written this book for readers who are already familiar with elementary quantum mechanics; in particular, with the quantum theory of the simple harmonic oscillator. A corresponding level of familiarity with Maxwells equations for the clas- ?Intro
36、duction sical electromagnetic fi eld and with elementary optics is also a prerequisite. On the mathematical side, some profi ciency in classical analysis, including the use of partial diff erential equations and Fourier transforms, will be a great help. Since the number of applications of quantum op
37、tics is growing at a rapid pace, this subject is potentially interesting to people from a wide range of scientifi c and engineering backgrounds. We have, therefore, organized the material in the book into two tracks. Sections marked by an asterisk are intended for graduate-level students who already
38、 have a fi rm understanding of quantum theory and Maxwells equations. The unmarked sections will, we hope, be useful for senior level undergraduates who have had good introductory courses in quantum mechanics and electrodynamics. The exerciseswhich form an integral part of the textare marked in the
39、same way. The terminology and notation used in the book arefor the most partstandard. We employ SI units for electromagnetic quantities, and impose the Einstein summa- tion convention for three-dimensional vector indices. Landaus hat notation is used for quantum operators associated with material pa
40、rticles, e.g. ? q, and ? p, but not for similar operators associated with the electromagnetic fi eld. The expression c-numberalso due to Landau is employed to distinguish ordinary numbers, either real or com- plex, from operators. The abbreviations CC and HC respectively stand for complex conjugate
41、and hermitian conjugate. Throughout the book, we use Diracs bra and ket notation for quantum states. Our somewhat unconventional notation for Fourier transforms is explained in Appendix A.4. 1 The quantum nature of light Classical physics began with Newtons laws of mechanics in the seventeenth centu
42、ry, and it was completed by Maxwells synthesis of electricity, magnetism, and optics in the nineteenth century. During these two centuries, Newtonian mechanics was extremely successful in explaining a wide range of terrestrial experiments and astronomical ob- servations. Key predictions of Maxwells
43、electrodynamics were also confi rmed by the experiments of Hertz and others, and novel applications have continued to emerge up to the present. When combined with the general statistical principles codifi ed in the laws of thermodynamics, classical physics seemed to provide a permanent foundation fo
44、r all future understanding of the physical world. At the turn of the twentieth century, this optimistic view was shattered by new ex- perimental discoveries, and the ensuing crisis for classical physics was only resolved by the creation of the quantum theory. The necessity of explaining the stabilit
45、y of atoms, the existence of discrete lines in atomic spectra, the diff raction of electrons, and many other experimental observations, decisively favored the new quantum mechanics over Newtonian mechanics for material particles (Bransden and Joachain, 1989, Chap. 4). Thermodynamics provided a very
46、useful bridge between the old and the new theories. In the words of Einstein (Schilpp, 1949, Autobiographical Notes, p. 33), A theory is the more impressive the greater the simplicity of its premises is, the more diff erent kinds of things it relates, and the more extended is its area of applicabili
47、ty. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown (for the special attention of those wh
48、o are skeptics on principle). Unexpected features of the behavior of light formed an equally important part of the crisis for classical physics. The blackbody spectrum, the photoelectric eff ect, and atomic spectra proved to be inconsistent with classical electrodynamics. In his characteristicallybo
49、ld fashion, Einstein (1987a) proposed a solution to these diffi culties by off ering a radically new model in which light of frequency is supposed to consist of a gas of discrete light quanta with energy ? = h, where h is Plancks constant. The connection to classical electromagnetic theory is provided by the assumption that the number density of light quanta is proportional to the intensity of the light. We will follow the current usage in which light quanta are called photons, but this terminology must be used with some
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