Bose-Einstein Condensates and Atom Lasers Bose-Einstein Condensates and Atom Lasers Edited by Sergio Martellucci University of Rome "Tor Vergata" Rome, Italy Arthur N. Chester Hughes Research Laboratories, Inc. Malibu, California Alain Aspect Institut d’Optique Orsay, France and Massimo Inguscio University of Florence Florence, Italy Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow eBookISBN: 0-306-47103-5 Print ISBN: 0-306-46471-3 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com Preface Since the experimental demonstration in 1995 of Bose-Einstein condensation (BEC) in dilute atomic gases there has been an explosion of studies of the properties of this novel macroscopic quantum system. A matter wave analogous to the optical laser is becoming a reality. The purpose of this volume is to cover the methods used to produce these new samples of coherent atoms, to manipulate them and to study their properties. Emphasis has been given to anticipated developments of a new type of sources, more and more similar to the various lasers (pulsed, CW, mode locked...) and likely to produce a revolution similar to the laser revolution of 40 years ago! Recently there have been several new proposed applications of atom optics, and it is possible to foresee an increasing demand for atom lasers, sensors and associated instrumentation. Consequently, the chapters cover current developments in the basic techniques, materials and applications in the field of the generation of coherent beams of atoms. In October 1999, an international group of scientists convened in Erice, Sicily, for a meeting on the subject of "Bose-Einstein Condensates and Atom Lasers". This Conference was the 27th Course of the International School of Quantum Electronics, under the auspices of the "Ettore Majorana Centre and Foundation for Scientific Culture". This book presents the Proceedings of this Conference, providing a fundamental introduction to the topic as well as reports on recent research results. The aim of the Conference was to bring together some of the world's acknowledged scientists who have as a common link the use of instrumentation, techniques and procedures related to the fields of Bose-Einstein Condensates and Atom Lasers. Most of the lecturers attended all the lectures and devoted their spare hours to stimulating discussions. We would like to thank them all for their admirable contributions. v vi The Conference also took advantage of a very active audience; most of the participants were active researchers in the field and contributed with discussions and seminars. Some of these seminars are also included in these Proceedings. The Conference was an important opportunity to discuss the latest developments and emerging perspectives on the use of experimental techniques for Bose-Einstein Condensates and Atom Lasers. The Chapters in these Proceedings are not ordered exactly according to the chronology of the Conference, but they give a fairly complete accounting of the Conference lectures with the exception of the informal panel discussions. The contributions presented at the Conference are written as extended, review- like papers to provide a broad and representative coverage of the fields of Bose-Einstein Condensates and Atom Lasers. We did not modify the original manuscripts in editing this book, except to assist in uniformity of style. We are grateful to Prof. Carlo Bellecci for contributing to the secretarial organisation of the Conference, to our editor at Kluwer Academic/Plenum Publishers, Joanna Lawrence, for outstanding professional support. We also greatly appreciate the expert help from our assistants, Rosalia Caruso, Laura Cemoli, Maila Lanzini and the support of Eugenio Chiarati for much of the computer processing work. This International School was held under the auspices of Prof. Antonino Zichichi, Director of the "Ettore Majorana" Centre and Foundation for Scientific Culture, Erice, Italy. Finally, we acknowledge with gratitude the generous financial support of the organizations who sponsored the Conference: the Italian Ministry of Education, the Italian Ministry of University and Scientific Research, the Sicilian Regional Parliament, the Italian Research Group on Quantum Electronics and Plasma Physics (G. N. E. Q. P.) of the National Research Council (C.N.R.), the University of Rome "Tor Vergata", the I.N.F.M. (Florence), the French Embassy in Italy and the European Laboratory for Non Linear Spectroscopy (LENS). Arthur N. Chester Sergio Martellucci President and General Manager Professor of Quantum Electronics HRL Laboratories, LLC. University ofRome "TorVergata" Malibu, California (USA) Rome (Italy) Alain Aspect Massimo Inguscio Professeur à l'Ecole Politechnique Professor of Atomic Physics Directeur de Recherche CNRS University of Florence Orsay (France) Florence (Italy) May, 2000 Contents EXPERIMENTAL STUDIES OF BOSE-EINSTEIN CONDENSATES IN SODIUM W. Ketterle............................................................................................................1 MEASUREMENT OF THE RELATIVE PHASE BETWEEN TWO BOSE- EINSTEIN CONDENSATES D. S. Hall............................................................................................................31 INTERTWINED BOSE-EINSTEINCONDENSATES D. S. Hall............................................................................................................43 COHERENT ATOM OPTICS WITHBOSE-EINSTEIN CONDENSATES K. Helmerson.......................................................................................................55 NON-LINEAR ATOM OPTICS WITH BOSE-EINSTEIN CONDENSATES K. Helmerson.......................................................................................................65 MOMENTUM DISTRIBUTION OF A BOSE CONDENSED TRAPPED GAS S. Stringari, L. Pitaevskii, D. M. Stamper-Kurn, and F. Zambelli..........................77 ATOM OPTICS WITH BOSE-EINSTEIN CONDENSATES S. Burger, K. Bongs, K. Sengstock, and W. Ertmer..................................................97 vii viii Contents GENERATING AND MANIPULATING ATOM LASER BEAMS T. Esslinger, I. Bloch, M.Greiner,and T. W. Hänsch............................................ 117 MULTIPLE 87RB CONDENSATES AND ATOM LASERS BY RF COUPLING F. Minardi, C. Fort, P. Maddaloni, and M. Inguscio............................................. 129 THEORY OF A PULSED RF ATOM LASER J. Schneider, and A. Schenzle................................................................................. 141 THE ATOMIC FABRY-PEROT INTERFEROMETER I. Carusotto, and G. C. La Rocca ........................................................................... 153 RF-INDUCED EVAPORATIVE COOLING AND BEC IN A HIGH MAGNETIC FIELD P. Bouver, V. Bover, S. C. Murdoch, G. Delannoy, Y. Le Coq, A. Aspect, and M. Lécrivain ................................................................................... 165 DISSIPATIVE DYNAMICS OF AN OPEN BOSE-EINSTEIN CONDENSATE F. T. Arecchi, J. Bragard, and L. M. Castellano .................................................... 187 NON-GROUND-STATE BOSE-EINSTEIN CONDENSATION V. S. Bagnato, E. P. Yukolova, and V. I. Yukalov...................................................201 TOWARDS A TWO SPECIES BOSE-EINSTEIN CONDENSATE E. Arimondo............................................................................................................213 ATOM INTERFEROMETRY WITH ULTRA-COLD ATOMS M. Kasevich...........................................................................................................231 CLASSICAL AND QUANTUM JOSEPHSON EFFECTS WITH BOSE-EINSTEIN CONDENSATES A. Smerzi.................................................................................................................249 JOSEPHSON QUBITS FOR QUANTUM COMPUTATION G. Falci, R.Fazio, E. Paladino, and U. Weiss ......................................................265 ADDRESSING SINGLE SITES OF A CO -LASER OPTICAL LATTICE 2 F. S. Cataliotii, R. Scheunemann, T. W. Hänsch, and M. Weitz .............................275 Contents ix SCISSORS MODE AND SUPERFLUIDITY OF A TRAPPED BOSE-EINSTEIN CONDENSED GAS O. M. Maragò, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, and C. J. Foot ...................................................................285 EXPERIMENTS WITH POTASSIUM ISOTOPES C. Fort...............................................................................................................291 EQUILIBRIUMSTATE AND EXCITATIONS IN TRAPPEDFERMI VAPOURS A. Minguzzi, and M. P. Tosi................................................................................. 301 PHOTO ASSOCIATIVE SPECTROSCOPY OF Cs 2 C. Drag, B. Laburthe Tolra, D. Comparat, A. Fioretti, A. Crubellier, O. Dulieu, F. Masnou-Seeuws, S.Guibal, and P. Pillet......................................... 313 INDEX ...........................................................................................................323 Experimental Studies Of Bose-Einstein Condensates In Sodium W. KETTERLE Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 1. INTRODUCTION 1.1 Bose-Einstein Condensation in a Gas When a gas of bosonic atoms is cooled below a critical temperature T , a c large fraction of the atoms condenses into the lowest quantum state. This phenomenon was first predicted by Albert Einstein in 19251 and is a consequence of quantum statistics. Atoms at temperature T and mass m can be regarded as quantum-mechanical wavepackets which have an extension on the order of a thermal de Broglie wavelength When atoms are cooled to the point where is comparable to the interatomic separation, the atomic wavepackets "overlap" and the indistinguishability of particles becomes important. At this temperature, bosons undergo a quantum-mechanical phase transition and form a Bose-Einstein condensate, a coherent cloud of atoms all occupying the same quantum state. The relation between the transition temperature and the peak atomic density n is given by With the realization of Bose-Einstein condensation (BEC) in dilute atomicgases2-6, several long-standinggoals were achieved. First, by cooling atoms into the lowest energy state, one exerts ultimate control over the motion and position of atoms, limited only by Heisenberg's uncertainty Bose-Einstein Condensates and Atom Lasers Edited by Martcllucci et al., Kluwer Academic/Plenum Publishers, 2000 1