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Exploring the Quantum This page intentionally left blank Exploring the Quantum Atoms, Cavities and Photons Serge Haroche Professeur, Collège de France Jean-Michel Raimond Professeur, Université P. et M. Curie et Institut Universitaire de France 1 OXPORD UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. 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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 with 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 the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Printed in Great Britain on acid-free paper by Biddies Ltd., www.biddles.co.uk ISBN 0-19-850914-6 978-0-19-850914-l(Hbk) 1 3 5 79 10 8 6 42 To Claudine, Julien and Judith Fabienne, Yves and Marie This page intentionally left blank Foreword The counter-intuitive aspects ofquantumphysics were illustratedin the earlydays of the theory by famous thought experiments, from the Einstein and Bohr photon box to Schro¨dinger’s cat. Modern versions of these experiments, involvingsingle particles – electrons, atoms or photons – have now been actually realized in many laboratories aroundthe world.Bymanipulatingthese simplesystems inacontrolledenvironment, physicists directly unveil the strange features of the quantum. State superpositions, entanglement and complementarity define a novel quantum logic which can be har- nessed for informationprocessing, raising great hopes for applications. This book describes a class of such thought experiments which have come of age. Selecting among a vast and fast expanding domain of research, we have chosen to analyse in detail experiments performed with atoms and photons in high-Q cavities as well as related ones, dealing with ions in traps or cold atoms in optical lattices. In these apparently disparatedomains,the sameunderlyingphysics is atwork:two-level spin-like systems are interacting with quantum harmonic oscillators. We believe that a description of these real ‘spin-spring’ experiments provides a more concrete illustration of quantum concepts than that given by abstract discus- sions about idealized experiments. Although the latter are simpler to analyse and are certainly here to stay in introductory courses of quantum mechanics, real ‘thought experiments’ should in our view become central in the teaching of modern quantum physicsatanintermediateoradvancedlevel.Theeffortstocarryouttheseexperiments in laboratories have been largely triggered by the hopes placed in the development of quantum information for practical applications in communication and computing. Conversely, this fast expanding field of research is bound to have an increasing influ- ence on the teaching and learning of quantum concepts. Dealing with real systems necessarily involves a description of the interaction of these systems with their unavoidable environment, in other words a discussion of re- laxation and decoherence. These phenomena are described by a formalism (density operator or stochastic Monte Carlo approach) which replaces the simple state de- scriptionofelementary quantumphysics. Mastering this approach andunderstanding decoherence provideadeepunderstandingofoneimportantaspectofthequantum,its relation to classical physics. Thought experiments have been invented at the dawn of thequantumagetoillustratethepuzzlingfeaturesofthequantum–classicalboundary. Itisthusnosurprisethatanunderstandingofthemodernversionoftheseexperiments must also address this important issue. Startingfromthesimplegoaltodescribe experimentsillustrativeofbasicquantum viii laws, we have thus been led to widen our perspective, ending up with a book which presents a comprehensive discussion of many important issues in modern physics. It combines a fundamental approach, based on an analysis of quantum concepts and of useful theoretical tools, with a detailed analysis of experiments, including a brief overviewofthevarioustechnologicaldevelopmentswhichhavemadetheseexperiments possible. In balancing these theoretical and applied points of view, we have tried to conveyatthesametimethestrangebeautiesofthequantumandthedifficultieswhich had tobe overcome to unveilthem, and possibly to harness them for achieving useful tasks. This book is intended for students at the undergraduate or graduate level, with anelementary knowledgeofquantummechanics. Wehavenot assumed that they had been previously exposed to a detailed discussion of concepts such as entanglement, non-locality, decoherence or measurement theory, which we have chosen to expose fromscratch. At the same time, we hope that our work willalso be useful to teachers in the field of quantum optics and quantum information science. We have attempted to present many examples of physical situations which are computed in detail, and which could be easily turned into instructive problem sets for students. The many connexions and comparisons we make between atom–cavity, ion trap and cold atomexperiments mightalso be useful to scientists workingin these various fields of quantum optics. Reading this book might suggest to them new perspectives fortheir work,as writingithashelped us tosharpen our understandingandto design new experiments. Finally,theorists in quantum information science might learn here aboutsome of the challenges that experimenters have to address in order to put their bright ideas into practice. The material of this book is based on the lectures on quantum information we haverespectively givenatCollègede France from2001to 2006,andat EcoleNormale Supérieure (ENS) from 2003 to 2006. The atom–cavity experiments which are at the heart ofthe bookdiscussions have been carried outby our research team atENS. We are indebted to all the colleagues, students, postdocs and visitors who have worked withusovertheyears.WeshouldmentioninparticularMichelBrune,whohasplayed an essential role in all these experiments and who has provided precious advice to improve the manuscript. Our ENS colleagues Jean Dalibard and Yvan Castin have been consulted on some aspects of cold atomphysics and we are glad to acknowledge theirilluminatinginput.Specialthanks goalsotoLuizDavidovichandNicimZagury, from the Federal University of Rio de Janeiro, whose theoretical insights have been precious to design new experiments. We have devoted the last chapters of the book to the description of experiments performedinotherlaboratories,mainlyinBoulder,Innsbruck,MunichandMainz.We thankD.Wineland,D.Leibfried,R.Blatt,C.RoosandI.Blochforhelpfuldiscussions andforcriticalreadingofpartsofthemanuscript.Weareofcourse responsibleforany approximation or error remaining in the description of their work. Finally and fore- most,wethankClaudineandFabiennefortheirconstantsupportandencouragement. Serge Haroche and Jean-Michel Raimond Paris, May 2006 Contents 1 Unveiling the quantum 1 1.1 One century of quantum physics 4 1.2 Emergence of the microscopic world 10 1.3 Thought experiments comingof age 14 1.4 Aims and outline of this book 20 2 Strangeness and power of the quantum 25 2.1 The superposition principle and the wave function 26 2.2 Quantum interference and complementarity 34 2.3 Identical particles 42 2.4 Entanglement and non-locality 52 2.5 The quantum–classical boundary 68 2.6 Tamingthe quantum to process information 83 3 Of spins and springs 101 3.1 The field oscillator 106 3.2 Coupled field modes 126 3.3 The spin system 143 3.4 Couplinga spin and a spring: the Jaynes–Cummings model 151 4 The environment is watching 163 4.1 Quantum description of open systems 165 4.2 Quantum maps: the Kraus sum representation 173 4.3 The Lindblad master equation 178 4.4 Quantum Monte Carlo trajectories 189 4.5 Damped spin–spring system: from Rabito Purcell 203 4.6 Kicking a spring with spins: the micromaser 208 4.7 Collective coupling of N spins to a spring: superradiance 220 5 Photons in a box 231 5.1 A short history of cavity QED 232 5.2 Giant atom in a cavity:an ideal cavity QED situation 251 5.3 Two experiments unveiling the quantum in a cavity 272 5.4 An atom–photon entanglingmachine 278 6 Seeing light in subtle ways 297 6.1 Complementarity at quantum–classical boundary 299