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Modern Challenges in Quantum Optics Selected Papers of the First International Meeting in Quantum Optics Held in Santiago, Chile, 13-16 August 2000 1 3 Editors MiguelOrszag Dept.deF´ısica PontificiaUniversidadCato´licadeChile Casilla306Santiago22,Chile JuanCarlosRetamal Dept.deF´ısica UniversidaddeSantiagodeChile Avda.Ecuador,3493,correo2,Santiago,Chile Coverpicture:seecontributionbyE.Massoni,M.Orszaginthisvolume LibraryofCongressCataloging-in-PublicationData InternationalMeetinginQuantumOptics(1st:2000:Santiago,Chile) Modernchallengesinquantumoptics:selectedpapersoftheFirstInternational MeetinginQuantumOptics,heldinSantiago,Chile,13-16August2000/M.Orszag, J.C.Retamal(eds.). p.cm.--(Lecturenotesinphysics,ISSN0075-8450; 575)Includesbibliographicalreferences. ISBN3540419578(alk.paper) 1.Quantumoptics--Congresses.I.Orszag,Miguel,1944-II.Retamal,J.C.(Juan Carlos),1962-III.Title.IV.Series. QC446.15.16252000 535--dc21 ISSN0075-8450 ISBN3-540-41957-8Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustra- tions, recitation, broadcasting, reproduction on microfilm or in any other way, and storageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonly undertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrent version,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violations areliableforprosecutionundertheGermanCopyrightLaw.Springer-VerlagBerlinHei- delbergNewYork amemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.de (cid:1)c Springer-VerlagBerlinHeidelberg2001 PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks, etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuch namesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreefor generaluse. Typesetting:Camera-readybytheauthors/editors Camera-dataconversionbySteingraeberSatztechnikGmbHHeidelberg Coverdesign:design&production,Heidelberg Printedonacid-freepaper SPIN:10834150 57/3141/du-543210 Foreword Quantum optics, in a sense, is precisely as old as the quantum theory, that is to say 100 years old this year. The very first quanta, after all, and for a long time the only ones, were the indivisible units of radiation energy discovered by Planck. Those oddly constrained light waves were indeed quanta, and our coming to grips with their baffling particle-like behavior consumed another 27 years.Thatunderstandingwasnot,infact,fullyachieveduntilwellafterallthe particlesofmatterwereunderstoodtohavethesamedualnature.Thequantum mechanical theory of the atom, based on that duality, brought many dramatic successes, but it was only in 1927, after many of these, that Dirac was able to extend the theory to include light itself – and thus lay the true groundwork for quantum optics. ThedecadesthatfollowedprovidedmanyverificationsofDirac’sfundamental theory. Most of them involved the particle-like behavior of high-energy quanta in processes that never involved more than one or two quanta at a time. The calculationscouldbecarriedoutbythestandardmethodofperturbationtheory, which turned out to work quite well. Although light quanta are normally present in vast abundance, our interest inmulti-quantaphenomenawasslowindeveloping.Thefirsthintoftheneedfor a more comprehensive theory came from the photon correlation measurements of Hanbury Brown and Twiss in 1956. But it was not long before the brilliant and monochromatic beams of the laser began to change the optical landscape completely, revealing new worlds of experimental wonders. It was only in that context that we began to develop a range of mathematical tools sufficiently versatile to deal quantum mechanically with light of all intensities. And only thendidwebeginseriouslytoapplythename“quantumoptics”tosuchstudies. The ensuing years have seen the introduction of a vast range of new exper- imental techniques. These have been guided by ever more sophisticated theory, exploringinthemostintimatedetailthewaysinwhichlightinteractswithmat- ter. Isolated atoms, suspended in vacuum, can be made to perform many of the stunts that were hardly even imaginable as “thought experiments” a few years ago. Andnowithasbecomepossible,partlybyquantumopticalmeans,toreduce thetemperatureofatomicgasestosolowalevelthatthewave-likepropertiesof theatomsdominatetheirparticle-likeproperties.Wearewitnessinginthiswork VI Foreword the development of a remarkable new field of wave optics that we call for the moment “atom optics”. As the offspring of quantum optics, it possesses many resemblances to its parent field. It can be approached and understood by using many of the same mathematical tools. Itisthemostrecentadvancesintherelatedfieldsofquantumandatomoptics that concern us here, and their description in one form or another has occupied mostofthisconference.Butthereisanotherdevelopmentthatisworthpointing out at this meeting. The gospel of quantum mechanics, which was in its earliest dayslocalizedtothreeorfourcountriesofEurope,hasspreadgraduallyoverthe globeinthelastcentury,elicitingcontributionsfromtheUnitedStatesandmany countriesoftheNorthernHemisphere.Withinthelastseveralyearswehaveseen significantresearchinquantumopticsappearfromthesoutherncountriesaswell, and we can now point to contributions from groups in Argentina, Brazil, Chile, Colombia,PeruandUruguay,nottomentionAustraliaandNewZealand.Those groups are now advancing the gospel as well as spreading it. Cambridge, March 2001 Roy J. Glauber Preface QUANTUM OPTICS I was the 1st International Meeting in Quantum Optics held in Santiago, Chile, in 23-26 August, 2000 at the Pontificia Universidad Catolica de Chile. Justunder60participantsgatheredtogetherinSantiago,todiscussproblems in Non-Linear Optics, Quantum Information, Trapped Ions, Matter Waves and Fundamentals of Quantum Mechanics. TherewasastrongparticipationbyLatin-AmericanScientistsandstudents, inparticularfromBrazil,Chile,Argentina,Peru,UruguayandColombia,aswell as by Scientists from USA, Europe and Asia. New experimental and theoretical results were presented at the Conference. Prof. Walther talked about quantum phenomena of single trapped atoms and the experimental demonstration of pure Fock states in the micromaser. Prof. Eberly talked about quantum entanglement(not included here) and deter- mination of the localization of a single photon in a space time volume. Profes- sor Meystre referred to matter-wave amplification, Prof. Glauber talked about the Polarium Model( not included here) and coherent trapping. Prof. Kenkre talked about oscillations between coupled Bose-Einstein condensates and also did some beautiful sketches of several participants (included in this volume), Prof. Becker addressed the topic of above- threshold ionization and harmonic generation, Prof. Marangos gave us an interesting talk on Electromagnetically Induced Transparency, Prof. Swain referred to the quantum interference effects in fluorescence and Prof. Kaige talked about QND measurements in trapped ions. From the Southern Hemisphere there were talks about dwell time and tun- neling, quite relevant for several recent experiments on ” superluminal effects” (Prof.M.Nussezweig),quantumerrorcorrection(AldoDelgadoet.al.),manipu- lationofmotionalstates(Prof.Zaguryet.al.),ion-trappedlasersandsqueezing( Prof. Orszag et. al.), decoherence and state protection (Prof. Davidovich), ra- diation pressure and decoherence(Professor Maia Neto et al.),and many more exciting results. The Conference took place during the Chilean Winter, in a relaxing atmo- sphere with a beautiful background of the snow covered Andes Cordillera. It was a good opportunity to establish new collaborations and contacts. VIII Preface The editors would like to thank the participants for providing their papers promptly after the Conference and also the following organizations who pro- vided financial or other forms of support: Pontificia Universidad Catolica de Chile(PUC), Universidad de Santiagode Chile (USACH), Conicyt(Fondecyt), Consortium of the Americas for Interdisciplinary Science(UNM), Centro Lati- noamericano de Fisica(CLAF), The Abdus Salam International Centre for The- oretical Physics(Trieste), Fundacion Andes, United Airlines. Finally, Ms. Carolina Leon was a great help in the local organization and also we would like to thank Ms. Marta Montoya for her support in all the local events as well as the general organization of this Conference. Santiago, Miguel Orszag February 2001 Juan Carlos Retamal Table of Contents Part I Trapped Ions and Cavity QED Generation of Fock States in the One-Atom Maser H. Walther........................................................ 3 1 Introduction ................................................... 3 2 The One-Atom Maser and the Generation of Fock-States Using Trapping States ............................. 4 3 Dynamical Preparation of Number States in a Cavity ............... 7 4 Preparation of Fock States on Demand............................ 9 5 Conclusion .................................................... 12 References ........................................................ 13 Coherent Manipulation of Two Trapped Ions with Bichromatic Light E. Solano, R.L. de Matos Filho, N. Zagury............................ 14 1 Introduction ................................................... 14 2 Dispersive Interaction........................................... 15 2.1 The model ................................................ 15 2.2 Bell states ................................................ 18 2.3 Reliable teleportation ...................................... 19 2.4 Wigner function of the collective motion ...................... 21 3 Selective Interaction ............................................ 22 4 Resonant Interaction............................................ 25 4.1 Conditional vibrational displacement ......................... 25 4.2 Motional Schro¨dinger’s cat states ............................ 26 4.3 Motional squeezed states ................................... 27 5 Conclusions.................................................... 27 6 Acknowledgments .............................................. 27 References ........................................................ 28 Quantum Nondemolition Measurement and Quantum State Manipulation in Two Dimensional Trapped Ion W. Kaige, S. Maniscalco, A. Napoli, A. Messina....................... 29 X Table of Contents 1 Introduction ................................................... 29 2 Description of the Model ........................................ 31 3 Properties of the Model ......................................... 32 4 QND Measurement of Vibrational Quanta ......................... 35 5 Quantum State Manipulation .................................... 36 5.1 Generation of a bimodal Fock state .......................... 36 5.2 Generation of entangled superposition of Fock states ........... 38 5.3 Generation of a pair coherent state........................... 39 6 Conclusion .................................................... 41 References ........................................................ 41 Phonon-Photon Translation with a Trapped Ion in a Cavity E. Massoni, M. Orszag ............................................ 43 1 Introduction ................................................... 43 2 The Model for a Phonon-Photon Translator ....................... 44 3 Information Transfer............................................ 46 4 Numerical Simulation ........................................... 49 5 Discussion..................................................... 52 6 The Model for an Ion Trap Laser Producing Transfer of Squeezing.... 53 7 Semiclassical Aproximation ...................................... 56 8 Numerical Results .............................................. 58 References ........................................................ 61 Part II Quantum Interference, Entanglement, Decoherence and Quantum Computing Decoherence, Pointer Engineering and Quantum State Protection A.R.R. Carvalho, P. Milman, R.L. de Matos Filho, L. Davidovich ....... 65 1 Introduction ................................................... 65 2 Strategy for Quantum State Protection ........................... 66 3 Application to a Trapped Ion .................................... 67 3.1 Hamiltonian of the system .................................. 67 3.2 Master equation for the center-of-mass motion................. 68 3.3 Effect of random fields ..................................... 70 3.4 Protection of superpositions of Fock states .................... 72 3.5 Protection of a qubit ....................................... 73 3.6 Protection of approximate phase eigenstates................... 74 3.7 Superpositions of coherent states ............................ 74 3.8 Protection of squeezed states ................................ 76 4 Conclusion .................................................... 76 References ........................................................ 78