Lecture Notes in Physics

Transcription

1 Lecture Notes in Physics Edited by H. Araki, Kyoto, J. Ehlers, MLinchen, K. Hepp, ZUrich R. Kippenhahn, ML~nchen, D. Ruelle, Bures-sur-Yvette H.A. WeidenmSIler, Heidelberg, J. Wess, Karlsruhe and J. Zittartz, K61n Managing Editor: W. Beiglb6ck 340 M. Peshkin A. Tonomura The Aharonov-Bohm Effect Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong

2 Authors M. Peshkin Physics Division, Argonne National Laboratory 9700 South Cass Avenue, Argonne, IL , USA A. Tonomura Advanced Research Laboratory, Hitachi, Ltd. Kokubunji, Tokyo 185, Japan ISBN Springer-Verlag Berlin Heidelberg NewYork ISBN Springer-Verlag NewYork Berlin Heidelberg 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing: Druckhaus Beltz, Hemsbach/Bergstr. Bookbinding: J. Sch&ffer GmbH & Co. KG., Gr~nstadt 2158/ Printed on acid-free paper

3 PREFACE The Aharonov-Bohm effect is a quantum-mechanical phenomenon wherein the motion of a charged particle is influenced by the existence of electromagnetic fields in regions which the particle does not enter. The influence of those remote fields is carried in the theory by the four-vector potential, which appears in the Hamiltonian and therefore in the Schroedinger equation. This phenomenon is counter-intuitive for many physicists because it has no classical analog and because it challenges the conventional perception that the physical quantities in electromagnetism are carried by the local Maxwell fields, not by the potentials. If confirmed by experiment, the Aharonov-Bohm effect raises fundamental questions about locality in quantum mechanics and in the electromagnetic interaction. If refuted, it requires either a drastic revision of supposedly fundamental ideas about quantum mechanics or a demonstration that some error has been made and standard quantum mechanics does not really imply the existence of the Aharonov-Bohm effect. Either way, it addresses questions about quantum mechanics in a multiplyconnected region that have been recognized as options in the theory but that have not been investigated by sufficiently sensitive experiments in the past. These considerations have stimulated a lively theoretical and experimental effort for the past thirty years, with almost every possibility represented and with much debate about the status of experiments and of calculations. Now the main issues appear to be clear. Almost everyone agrees that the Aharonov-Bohm effect is confirmed by experiment and that it is a genuine feature of standard quantum mechanics. In this treatise, we give an account of the experiments and of the fundamental theoretical questions that they illuminate. Our intended audience includes students who have learned the elements of quantum mechanics and physicists interested in fundamental questions. We have had great pleasure in exploring the new physics introduced by the Aharonov-Bohm effect and the old physics on which it sheds a new light, and we hope to transmit that pleasure to the reader. In Part One, Peshkin introduces the Aharonov-Bohm effect under the assumptions of standard quantum theory. The emphasis here is on the fundamental questions which are addressed directly by the experimental results and on other elementary aspects of the the theory that appear especially clearly in the present context. In Part Two, Tonomura gives a brief review of the diverse ideas that have been put forward during the protracted debate about the reality and meaning of the Aharonov-Bohm effect, followed by a detailed account of the experiments which finally settled most of those questions. The review is intended to give a flavor of the controversy rather than to do justice to every point of view. We thank Professor Huzihiro Araki of Kyoto University and Professor Mikio Namiki of Waseda University for their kind recommendations and for arranging to have this treatise published in Lecture Notes in Physics. Peshkin is indebted to Professor Harry J. Lipkin of the Weizmann Institute for contributions that cannot even be identified after decades of close collaboration. Tonomura thanks Professor Hiroshi Ezawa of Gakushuin University and Professor Mark P. Silverman of Trinity College, Hartford, for useful discussions during the preparation of this manuscript. March, 1989 Murray Peshkin Akira Tonomura

4 CONTENTS PART ONE: THEORY (MURRAY PESHKIN) INTRODUCTION... WHAT IS THE AHARONOV-BOHM EFFECT?... CLASSICAL THEORY... QUANTUM THEORY... BOUND STATE AHARONOV-BOHM EFFECT... THE CENTRAL ROLE OF QUANTIZED ANGULAR MOMENTUM SCATTERING STATE AB EFFECT LOCALITY AND CAUSALITY LESSONS FROM THE EXPERIMENT... APPENDIX A - ENERGY IN THE MAGNETIC FIELD... APPENDIX B - ELECTRIC AB EFFECT... APPENDIX C - TIME-DEPENDENT FLUX... APPENDIX D - EHRENFEST'S THEOREM... REFERENCES

5 VI PART TWO: EXPERIMENT (AKIRA TONOMURA) I. INTRODUCTION AHARONOV-BOHM EFFECT Electric AB Effect Magnetic AB Effect... 4] 2.3 Significance of AB Effect EARLY EXPERIMENTS Chambers Experiment M611enstedt and Bayh Experiment CONTROVERSY CONCERNING AHARONOV-BOHM EFFECT Early Discussions Increased Significance of AB Effect Controversy Since the Mid-1970s RECENT EXPERIMENTS Experiment Using Toroidal Magnet Experiment Using Solenoid Covered with Glass Tube Experiment to Test Possible Flux Quantization Experiments Concerning Electrostatic AB Effect Experiment Using Toroidal Magnet Covered with Superconductor CONCLUSIONS REFERENCES APPENDIX