Lecture Notes in Physics

Editorial Board R. Beig, Wien, Austria J. Ehlers, Potsdam, Germany U. Frisch, Nice, France K. Hepp, Zurich,¨ Switzerland W. Hillebrandt, Garching, Germany D. Imboden, Zurich,¨ Switzerland R. L. Jaffe, Cambridge, MA, USA R. Kippenhahn, Gottingen,¨ Germany R. Lipowsky, Golm, Germany H. v. Lohneysen,¨ Karlsruhe, Germany I. Ojima, Kyoto, Japan H. A. Weidenmuller,¨ Heidelberg, Germany J. Wess, Munchen,¨ Germany J. Zittartz, Koln,¨ Germany

3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Editorial Policy The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching -- quickly, informally but with a high quality. Manuscripts to be considered for publication are topical volumes consisting of a limited number of contributions, carefully edited and closely related to each other. Each contribution should contain at least partly original and previously unpublished material, be written in a clear, pedagogical style and aimed at a broader readership, especially graduate students and nonspecialist researchers wishing to familiarize themselves with the topic concerned. For this reason, traditional proceedings cannot be considered for this series though volumes to appear in this series are often based on material presented at conferences, workshops and schools (in exceptional cases the original papers and/or those not included in the printed book may be added on an accompanying CD ROM, together with the abstracts of posters and other material suitable for publication, e.g. large tables, colour pictures, program codes, etc.). Acceptance Aprojectcanonlybeacceptedtentativelyforpublication,byboththeeditorialboardandthe publisher, following thorough examination of the material submitted. The book proposal sent to the publisher should consist at least of a preliminary table of contents outlining the structureofthebooktogetherwithabstractsofallcontributionstobeincluded. Final acceptance is issued by the series editor in charge, in consultation with the publisher, only after receiving the complete manuscript. Final acceptance, possibly requiring minor corrections, usually follows the tentative acceptance unless the final manuscript differs significantlyfromexpectations(projectoutline).Inparticular,theserieseditorsareentitled to reject individual contributions if they do not meet the high quality standards of this series. The final manuscript must be camera-ready, and should include both an informative introduction and a sufficiently detailed subject index.

Contractual Aspects Publication in LNP is free of charge. There is no formal contract, no royalties are paid, and no bulk orders are required, although special discounts are offered in this case. The volumeeditorsreceivejointly30freecopiesfortheirpersonaluseandareentitled,asarethe contributing authors, to purchase Springer books at a reduced rate. The publisher secures the copyright for each volume. As a rule, no reprints of individual contributions can be supplied.

Manuscript Submission The manuscript in its final and approved version must be submitted in camera-ready form. Thecorrespondingelectronicsourcefilesarealsorequiredfortheproductionprocess,in particular the online version. Technical assistance in compiling the final manuscript can be provided by the publisher’s production editor(s), especially with regard to the publisher’s own Latex macro package which has been specially designed for this series.

Online Version/ LNP Homepage LNP homepage (list of available titles, aims and scope, editorial contacts etc.): http://www.springer.de/phys/books/lnpp/ LNP online (abstracts, full-texts, subscriptions etc.): http://link.springer.de/series/lnpp/ H. J. Carmichael R. J. Glauber M. O. Scully (Eds.)

Directions in Quantum Optics

A Collection of Papers Dedicated to the Memory of Dan Walls Including Papers Presented at the TAMU-ONR WorkshopHeld at Jackson, Wyoming, USA, 26--30 July 1999

13 Editors Howard J. Carmichael Department of Physics College of Arts and Sciences 1274UniversityofOregon Eugene, OR 97403-1274, USA RoyJ.Glauber Lyman Laboratory of Physics Harvard University Cambridge, MA 02138, USA Marlan O. Scully Department of Physics TexasA&MUniversity College Station, TX 77843-4242, USA

Library of Congress Cataloging-in-Publication Data applied for.

Die Deutsche Bibliothek - CIP-Einheitsaufnahme Directionsinquantumoptics:acollectionofpapersdedicatedtothe memory of Dan Walls including papers presented at the TAMU ONR workshopheld at Jackson, Wyoming, USA, 26 - 30 July 1999 / H. J. Carmichael ... (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; HongKong;London;Milan;Paris;Singapore;Tokyo:Springer, 2001 (Lecturenotesinphysics;Vol.561) (Physics and astronomy online library) ISBN 3-540-41187-9 ISSN 0075-8450 ISBN 3-540-41187-9 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustra- tions,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Hei- delberg New York a member of BertelsmannSpringer Science+Business Media GmbH c Springer-Verlag Berlin Heidelberg 2001 Printed
in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such namesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreefor general use. Typesetting: Camera-ready by the authors/editors; Camera-data conversion by Steingraeber Satztechnik GmbH Heidelberg Cover design: design & production,Heidelberg Printed on acid-free paper SPIN: 10785652 55/3141/du-543210 Preface

Dan Walls was a notable presence in quantum optics almost from the begin- ning of the modern era of intense research in the field, right up to the time of his untimely death. In the 30 years that have passed since his PhD at Har- vard, he established a school of theoretical quantum optics in New Zealand, first at the University of Waikato and then at the University of Auckland, which gained an international reputation for its seminal contributions in the area of quantum fluctuations and noise, and as a leading center advancing and promoting the latest directions in quantum optics. Today his numerous students lead active research groups throughout New Zealand and Australia, and also in the United States. Dan is remembered by colleagues as an enthu- siastic collaborator, and as a generous host during their visits to New Zealand as guest scientists or participants at the summer meetings arranged by Dan Walls and John Harvey. To honor Dan’s achievements, and in recognition of the influence of his enthusiasm, insight, and generosity, on them individually and on quantum optics research more widely, a group of Dan Walls’ students and colleagues have assembled this collection of papers reviewing current research directions in quantum optics. At some stage in his career, Dan Walls contributed to each of the areas featured here. He was actively working on Bose–Einstein condensation right up until his last months, and we have included in this volume a completed, but unpublished, manuscript by Dan, Scott Parkins, and Atac Imamo˘glu,the theme of which is developed around three topical research areas – cavity QED, nonlinear optics, and quantum information; this paper looks in anticipation towards the next advances of high importance and impact, as was so often the case in Dan’s work. Recent developments in each of these areas are described in a number of the contributions. Other papers cover the areas of quantum interference, and the area of Dan’s most significant accomplishments, quantum noise processes. During the early part of Dan Walls’ career, travel out of New Zealand was not at all a small undertaking. Dan was, nevertheless, from the beginning, renowned as an international traveller and regular attendee at meetings in Europe and the United States. It is fitting that over this last year he has been recognized, through special sessions or symposia, at a number of international meetings. He was so recognized at the TAMU-ONR Workshop on Quantum VI Preface

Optics, held in Jackson, Wyoming in July of 1999. A number of the papers presented at that meeting are reproduced, in tribute, in this volume. We wish to express our thanks to all those who have contributed to this book, either as authors or in the refereeing of the papers. With no explicit direction from us, the range of the contributed papers provides a review of the latest developments across virtually the entire field of quantum optics. The standard of the papers is high, as we hoped it would be, and the work of the referees has helped us in that. We also extend our appreciation and thanks to Colleen Vande Voorde at the Oregon Center for Optics, for her management of the editorial communications with authors and referees, and for her help in compiling the numerous electronic files, producing a book of pleasant appearance and a suitable tribute to the memory of our colleague Dan Walls.

Eugene, Cambridge, College Station Howard Carmichael August 2000 Roy Glauber Marlan Scully List of Contributors

P. Alsing B.M. Caradoc-Davies University of New Mexico Physics Department Albuquerque High Performance University of Otago Computing Center Dunedin, New Zealand Albuquerque, NM 87131, USA [email protected] [email protected]

H.-A. Bachor H.J. Carmichael Department of Physics Oregon Center for Optics Faculty of Science and Department of Physics The Australian National University 1274 University of Oregon Canberra, ACT 0200, Australia Eugene, OR 97403–1274, USA [email protected] [email protected]

R.J. Ballagh C.M. Caves Physics Department Center for Advanced Studies University of Otago Department of Physics Dunedin, New Zealand [email protected] and Astronomy University of New Mexico B. Berhane Albuquerque, NM 87131–1156, USA [email protected] School of Physics Georgia Institute of Technology Atlanta, GA 30332–0430, USA S. Chaturvedi [email protected] School of Physics University of Hyderabad N. Bloembergen Hyderabad, 500, 134, India Department of Physics [email protected] Harvard University Cambridge, MA 02138, USA G. Chen P. Brick Department of Mathematics Optical Sciences Center Texas A&M University University of Arizona College Station, TX 77843–3368 Tucson, AZ 85721, USA USA [email protected] [email protected] XII List of Contributors

Y.-T. Chough M. Fleischhauer Department of Physics Sektion Physik Korea Advanced Institute Universit¨at M¨unchen of Science and Technology 80333 M¨unchen, Germany Taejeon 305-701, South Korea [email protected]. [email protected] uni-muenchen.de

R. Cˆot´e Department of Physics M. Fliesser University of Connecticut Fachbereich Physik 2152 Hillside Road Universit¨at–GH Essen Storrs, CT 06269–3046, USA 45117 Essen, Germany [email protected] [email protected]

J.D. Cresser Department of Physics S.A. Fulling Macquarie University Department of Mathematics New South Wales 2109, Australia Texas A&M University [email protected] College Station, TX 77843–3368 USA D.G. Deppe [email protected] Department of Electrical and Computer Engineering Microelectronics Research Center H.M. Gibbs University of Texas Optical Sciences Center Austin, TX 78712-1084, USA [email protected] University of Arizona Tucson, AZ 85721, USA [email protected]. P. Deuar arizona.edu Centre for Laser Science Department of Physics University of Queensland V. Giovannetti Queensland 4072, Australia [email protected] Dipartimento di Matematica e Fisica and Unit´a INFM P.D. Drummond Universit´a di Camerino Department of Physics via Madonna delle Carceri University of Queensland 62032 Camerino, Italy Queensland 4072, Australia [email protected] [email protected]

C. Ell R. Graham Optical Sciences Center Fachbereich Physik University of Arizona Universit¨at–GH Essen Tucson, AZ 85721, USA 45117 Essen, Germany [email protected] [email protected] List of Contributors XIII

F. Haake [email protected]. Fachbereich Physik arizona.edu Universit¨at–GH Essen 45117 Essen, Germany M.I. Kolobov [email protected] Fachbereich Physik Universit¨at–GH Essen G.R. Hoy 45117 Essen, Germany Physics Department [email protected] Old Dominion University Norfolk, VA 23529–0116, USA E.S. Lee [email protected] Optical Sciences Center University of Arizona D.L. Huffaker Tucson, AZ 85721, USA Department of Electrical and [email protected] Computer Engineering Microelectronics Research Center H. Lee University of Texas California Institute of Technology Austin, TX 78712-1084, USA [email protected] Jet Propulsion Laboratory 4800 Oak Grove Drive MS 126-147 A.F. Hughes Pasadena, CA 91009-8099, USA 33 Woodlands Gate [email protected] Woodlands Way Putney, London SW15 2SY, UK [email protected] M. Lukin ITAMP A. Imamo˘glu Harvard–Smithsonian Center Department of Electrical and for Astrophysics Computer Engineering Cambridge, MA 02138, USA [email protected] and Department of Physics University of California Santa Barbara, CA 93106, USA U. Martini [email protected] Sektion Physik Universit¨at M¨unchen T.A.B. Kennedy 80333 M¨unchen, Germany School of Physics ullrich.martini@physik. Georgia Institute of Technology uni-muenchen.de Atlanta, GA 30332–0430, USA brian.kennedy@physics. K.-P. Marzlin gatech.edu Fachbereich Physik Universit¨at Konstanz G. Khitrova Postfach 5560 M674 Optical Sciences Center 78457 Konstanz, Germany University of Arizona [email protected]. Tucson, AZ 85721, USA uni-konstanz.de XIV List of Contributors

K. McNeil Canberra, ACT 0200, Australia Department of East Asian Studies [email protected] University of Waikato Hamilton, New Zealand S. Park [email protected] Optical Sciences Center University of Arizona P. Meystre Tucson, AZ 85721, USA Department of Physics [email protected] Optical Sciences Center University of Arizona S. Parkins Tucson, AZ 85721, USA Department of Physics pierre.meystre@optics. University of Auckland arizona.edu Auckland, New Zealand [email protected] G.J. Milburn R. Pike Special Research Centre for Physics Department Quantum Computer Technology Kings College and Department of Physics University of London University of Queensland Strand, London WC2R 2LS, UK Queensland 4072, Australia [email protected] [email protected] L. Plimak M.G. Moore Department of Chemical Physics Department of Physics The Weizmann Institute of Science Optical Sciences Center 76100 Rehovot, Israel University of Arizona [email protected] Tucson, AZ 85721, USA T.C. Ralph W.R. Munro Centre for Laser Science Centre for Laser Science Department of Physics Department of Physics University of Queensland University of Queensland Queensland 4072, Australia Queensland 4072, Australia [email protected] [email protected] M.D. Reid K. Nemoto Department of Physics Centre for Laser Science University of Queensland Department of Physics Queensland 4072, Australia University of Queensland [email protected] Queensland 4072, Australia [email protected] N. Robins Department of Physics E. Ostrovskaya Australian National University Optical Sciences Centre Canberra, ACT 0200, Australia Australian National University [email protected] List of Contributors XV

Y.V. Rozhdestvensky M.O. Scully Institute for Laser Physics Department of Physics S.I. Vavilov State Optical Institute and Institute for Quantum Studies Birzhevaya Line 12 Texas A&M University 199034, St. Petersburg, Russia College Station, TX 77843-4242, [email protected] USA and Max-Planck Institut f¨ur Quanten- P. Rungta optik, Munich, Germany Center for Advanced Studies [email protected] Department of Physics and Astronomy University of New Mexico C. Spiegelberg Albuquerque, NM 87131–1156, USA Optical Sciences Center [email protected] University of Arizona Tucson, AZ 85721, USA J. Ruostekoski [email protected] Abteilung f¨ur Quantenphysik Universit¨at Ulm 89069 Ulm, Germany M. Szymanska [email protected] Physics Department Cavendish Laboratory B.C. Sanders Theory of Condensed Matter Group Department of Physics Madingley Road Macquarie University Cambridge CB3 0HE, UK Sydney, New South Wales 2109 [email protected] Australia [email protected] V.V. Temnov C. Savage Fachbereich Physik Department of Physics Universit¨at–GH Essen Australian National University Canberra, ACT 0200, Australia 45117 Essen, Germany and [email protected] Institute of Applied Physics Russian Academy of Science B. Segev 46 Ul’yanov str. Department of Chemistry Nizhny Novgorod, 603600, Russia Ben-Gurion University of the Negev [email protected]. POB 653, Beer–Shiva 84105, Israel uni-essen.de [email protected]

A. Schenzle E. Timmermans Sektion Physik Theoretical Division (T-4) Universit¨at M¨unchen Los Alamos National Laboratory 80333 M¨unchen, Germany MS B-268, Los Alamos, NM 87545, axel.schenzle@physik. USA uni-muenchen.de [email protected] XVI List of Contributors

P. Tombesi via Madonna delle Carceri Dipartimento di Matematica e Fisica 62032 Camerino, Italy and Unit´a INFM [email protected] Universit´a di Camerino via Madonna delle Carceri H.M. Wiseman 62032 Camerino, Italy School of Science [email protected] Griffith University Nathan, Queensland 4111, Australia L. Tribe [email protected] Department of Physics Macquarie University Sydney, New South Wales 2109 W. Zhang Australia Centre for Lasers and Applications and Department of Physics D. Vitali Macquarie University Dipartimento di Matematica e Fisica Sydney, New South Wales 2109 and Unit´a INFM Australia Universit´a di Camerino [email protected] Contents

Part I Bose–Einstein Condensation

Density Oscillations in Trapped Bose Condensates at Finite Temperature M. Fliesser and R. Graham...... 3

Coherent Vortex Dynamics in Two and Three Dimensional Bose–Einstein Condensates R.J. Ballagh and B.M. Caradoc-Davies ...... 18

Quasicondensate Droplet Formation in Hydrogen R. Cˆot´e ...... 28 Polarization Decay in a BCS Paired Fermi Gas B. Berhane and T.A.B. Kennedy ...... 41 A Model of a Pumped Continuous Atom Laser N. Robins, C. Savage, and E. Ostrovskaya ...... 50 The BEC Near a Feshbach Resonance: A Superfluid of Mutually Coherent Condensates† E. Timmermans ...... 60 Collisional and Collapse Dynamics of a Twin Bose–Einstein Condensate with Negative ScatteringLength W. Zhang, K.-P. Marzlin, L. Tribe, and B.C. Sanders ...... 70 Schr¨odingerCat State of a Bose–Einstein Condensate in a Double-Well Potential J. Ruostekoski ...... 77

Part II Quantum Interference and Atom Optics

A Historical Perspective on LasingWithout Inversion † N. Bloembergen and G. Khitrova ...... 91 VIII Contents

The Coherent-Path Approach to Forward Scattering of Recoil-Free Resonant Gamma Radiation† G.R. Hoy ...... 107

Parametric Amplification of Coupled Atomic and Optical Fields† M.G. Moore and P. Meystre ...... 116

Quantum and QED Effects on Reflection from an Atomic Mirror† B. Segev ...... 126 Atom Wave Lithography via Adiabatic Passage in Multilevel Systems Y. Rozhdestvensky and L. Plimak ...... 136

Part III Quantum Information

Qudit Entanglement P. Rungta, W.J. Munro, K. Nemoto, P. Deuar, G.J. Milburn, and C.M. Caves ...... 149 Grover’s Algorithm for Multiobject Search in Quantum Computing† G. Chen, S.A. Fulling, H. Lee, and M.O. Scully ...... 165 New Tests of Macroscopic Local Realism M.D. Reid ...... 176 Teleportation Criteria: Form and Significance T.C. Ralph ...... 187 Quantum Information ProcessingBased on Cavity QED with Mesoscopic Systems† M. Lukin, M. Fleischhauer, and Atac Imamo˘glu...... 193 Quantum State Protection UsingAll-Optical Feedback P. Tombesi, V. Giovannetti, and D. Vitali ...... 204

Part IV Cavity QED and Nonlinear Optics

Single-Photon Nonlinear Optics and Quantum Control S. Parkins, D. Walls, and A. Imamo˘glu ...... 217 Contents IX

Normal-Mode Couplingof Excitons and Photons in Nanocavities – Toward the Quantum Statistical Limit† E.S. Lee, S. Park, P. Brick, C. Ell, C. Spiegelberg, H.M. Gibbs, G. Khitrova, D.G. Deppe, and D.L. Huffaker ...... 230

Cavity QED with Many Atoms U. Martini and A. Schenzle ...... 238

The Photonic Band Gap Laser: The Role of Spontaneous Emission in the Theory of Solid-State Lasers and LEDs R. Pike, A. Hughes, and M. Szymanska ...... 250

Superradiant and Subradiant Behavior of the Overdamped Many-Atom Micromaser V.V. Temnov, M.I. Kolobov, and F. Haake ...... 261

Bifurcations to Cooperative States in Arrays of Coupled Nonlinear Optical Oscillators K. McNeil ...... 271

Part V Quantum Noise Processes

Nonlinear Quantum Fluctuations in the Parametric Amplifier P.D. Drummond and S. Chaturvedi ...... 283 Quantum Phase Transitions in a Linear Ion Trap G.J. Milburn and P. Alsing...... 303 Quantum Noise Transfer Functions: A Practical Tool in Quantum Optics H.-A. Bachor and T.C. Ralph ...... 313 Self-Consistency of Thermal Jump Trajectories Y.-T. Chough and H.J. Carmichael ...... 333 Complementarity in Spontaneous Emission: Quantum Jumps, Staggers and Slides H. Wiseman ...... 347 Ergodicity of Quantum Trajectory Detection Records J.D. Cresser ...... 358

Paper presented at the TAMU–ONR Workshop on Quantum Optics †