Foundations of Quantum Mechanics in the Light of New Technology: Isqm-tokyo '05

Proceedings of the 8th International Symposium on

F

OF

IN THE LIGHT OF NEW TECHNOLOGY Edited by Sachio Ishioka • Kazuo Fujikawa

World Scientific

Proceedings of the 8th International Symposium on

FlNDflWOF QUANTUM MECHANICS •

liif HEW TECHNOLOGV ISOH^TOKVOOB

Proceedings of the 8th International Symposium on

OF IN THE LIGHT OF NEW TECHNOLOGY BON—n Advanced Research Laboratory Hitachi, Ltd., Hatoyama, Saitama, Japan 22-25 August 2005

Edited by

Sachio Ishioka Advanced Research Hitachi, Ltd., Japan

Laboratory

Kazuo Fujikawa Institute of Quantum Science Nihon University, Japan

\[p World Scientific NEW JERSEY

• LONDON

• SINGAPORE

• BEIJING

• SHANGHAI

• HONGKONG

• TAIPEI

•

CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

Proceedings of the 8th International Symposium (ISQM - Tokyo '05) FOUNDATIONS OF QUANTUM MECHANICS IN THE LIGHT OF NEW TECHNOLOGY Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-256-858-1

Printed in Singapore by Mainland Press

The Eighth International Symposium on Foundations of Quantum Mechanics (ISQM-Tokyo '05)

Vll

PREFACE The Eighth International Symposium on Foundations of Quantum Mechanics in the Light of New Technology (ISQM-TOKYO '05) was held on August 22-25, 2005 at the Advanced Research Laboratory, Hitachi, Ltd. in Hatoyama, Saitama, Japan. The symposium was organized by its own scientific committee under the auspices of the Physical Society of Japan, the Japan Society of Applied Physics, and the Advanced Research Laboratory, Hitachi, Ltd. Over 130 participants (23 from abroad) attended the symposium, and 30 invited oral papers, 7 contributed oral papers, and 37 poster papers were presented. Just as in the previous seven symposia, the aim was to link the recent advances in technology with fundamental problems in quantum mechanics. It provided a unique interdisciplinary forum where scientists from different disciplines, who would otherwise never meet each other, convened to discuss basic problems of common interest in quantum science and technology from various aspects and "in the light of new technology." Quantum Coherence, Decoherence, and Geometrical Phase was chosen as the main theme for the present symposium because of its importance in quantum science and technology. This topic was reexamined from all aspects, not only in terms of quantum computing, quantum information, and mesoscopic physics, but also in terms of the physics of precise measurement, spin related phenomena, and other fundamental problems in quantum physics. We were delighted that many active and eminent researchers in these fields accepted our invitation. We are now very happy to offer the fruits of the symposium in the form of the proceedings to a wider audience. As shown in the table of contents, the proceedings include a special lecture on Einstein by Professor C.N. Yang, which was really well-timed with the World Year of Physics 2005, and 63 refereed papers in ten sections: quantum information and entanglement, quantum computing; quantum-dot systems, anomalous Hall effect and spin-Hall effect, spin related phenomena, superconductivity in nano-systems, novel properties of carbon nanotubes, novel properties of nano-systems, precise measurements, and fundamental problems in quantum physics. We will mention just some of the important key words here to give the flavor of the proceedings: quantum computation and communication, qubits, quantum dots, spintronics, mesoscopic spins, Berry phase, nanowires, Josephson junctions, and vortices in high-temperature superconductors. We hope that the proceedings will not only be the record of the symposium but also serve as a good reference book for experts on quantum coherence and decoherence and as an introductory book for newcomers in this field. In conclusion, we thank the participants for their contribution to the symposium's success. Thanks are also due to all the authors who prepared manuscripts and to the referees who kindly reviewed the papers. We also thank the members of the Advisory Committee and Organizing Committee; without their invaluable assistance, the symposium would not have been a success. Finally, we would like to express our deepest gratitude to the Advanced Research Laboratory, Hitachi, Ltd. and its General Manager, Dr. Nobuyuki Osakabe, for providing us with financial support and an environment that was ideal for lively discussion. We also thank his staff members, in particular Mr. Yoshimasa Yamamoto and Ms. Maki Shinkai, for their efforts in making the symposium enjoyable as well as productive. March 2006 Sachio Ishioka Kazuo Fujikawa

IX

COMMITTEES

Chair: H. Fukuyama, Tohoku University

Advisory Committee: H. J. Kimble, California Institute of Technology S. Kobayashi, Tokyo University of Agriculture and Technology A. J. Leggett, University of Illinois at Urbana-Champaign J. E. Mooij, Delft University of Technology S. Nakajima, Superconductivity Research Laboratory, International Superconductivity Technology Center N. Osakabe, Advanced Research Laboratory, Hitachi, Ltd. F. Wilczek, Massachusetts Institute of Technology C. N. Yang, Tsinghua University A. Zeilinger, Vienna University

Organizing Committee: K. Fujikawa, Nihon University Y. lye, University of Tokyo N. Nagaosa, University of Tokyo Y. A. Ono, University of Tokyo F. Shimizu, University of Electro-Communications H. Takayanagi, NTT Basic Research Laboratories, NTT Corporation S. Ishioka, Advanced Research Laboratory, Hitachi, Ltd.

Sponsors: The Physical Society of Japan The Japan Society of Applied Physics Advanced Research Laboratory, Hitachi, Ltd.

XI

CONTENTS Preface

vii

Committees

ix

Opening Address H, Fukuyama

1

Welcoming Address N. Osakabe

3

Special Lecture Albert Einstein: Opportunity and perception C.N. Yang

Quantum Information and Entanglement Quantum optics with single atoms and photons H.J. Kimble

10

Quantum information system experiments using a single photon source Y. Yamamoto

16

Quantum communication and quantum computation with entangled photons A. Zeilinger

24

High-fidelity quantum teleportation and a quantum teleportation network for continuous variables N. Takei, A. Furusawa

29

Long lived entangled states H. Hdffner, F. Schmidt-Kaler, W. Hansel, C. Roos, P.O. Schmidt, M. Riebe, M. Chwalla, D. Chek-al-Kar, J. Benhelm, U.D. Rapol, T. Korber, C. Becher, R. Blatt,

33

Quantum non-locality using tripartite entanglement with non-orthogonal states J. V. Corbett, D. Home Quantum entanglement and wedge product H Heydari

38

42

xii

Analysis of the generation of photon pairs in periodically poled lithium niobate J. Soderholm, K. Hirano, S. Mori, S. Inoue, S. Kurimura Generation of entangled photons in a semiconductor and violation of Bell's inequality G. Oohata, R. Shimizu, K. Edamatsu

46 50

Quantum Computing Decoherence of a Josephson junction flux qubit Y. Nakamura, F. Yoshihara, K. Harrabi, J.S. Tsai

54

Spectroscopic analysis of a candidate two-qubit silicon quantum computer in the microwave regime J. Gorman, D.G. Hasko, D.A. Williams

60

Berry phase detection in charge-coupled flux-qubits and the effect of decoherence H. Nakano, S. Saito, H. Takayanagi, R. Fazio

64

Locally observable conditions for the successful implementation of entangling multi-qubit quantum gates H.F. Hofmann, R. Okamoto, S. Takeuchi

68

State control in flux qubit circuits: manipulating optical selection rules of microwave-assisted transitions in three-level artificial atoms Y.-X. Liu, J.Q. You, L.F. Wei, C.P. Sun, F. Nori The effect of local structure and non-uniformity on decoherence-free states of charge qubits T. Tanamoto, S. Fujita Entanglement-assisted estimation of quantum channels A. Fujiwara

72

76

80

Superconducting quantum bit with ferromagnetic 7t-Junction T. Yamashita, S. Takahashi, S. Maekawa

84

Generation of macroscopic Greenberger-Horne-Zeilinger states in Josephson systems T. Fujii, M. Nishida, N. Hatakenaka

88

Quantum-Dot Systems Tunable tunnel and exchange couplings in double quantum dots S. Tarucha, T. Hatano, M. Stopa

92

Xlll

Coherent transport through quantum dots S. Katsumoto, M. Sato, H. Aikawa, Y. lye Electrically pumped single-photon sources towards 1.3 um X. Xu, D.A. Williams, J.D. Mar, J.R.A. Cleaver

99 105

Aharonov-Bohm-type effects in antidot arrays and their decoherence M. Kato, H. Tanaka, A. Endo, S. Katsumoto, Y. lye

109

Nonequilibrium Kondo dot connected to ferromagnetic leads Y. Utsumi, J.Martinek, G. Schbn, S. Maekawa

113

Full counting-statistics in a single-electron transistor in the presence of strong quantum fluctuations Y. Utsumi

117

Anomalous Hall Effect and Spin-Hall Effect Geometry and the anomalous Hall effect in ferromagnets N.P. Ong, W.-L. Lee

121

Control of spin chirality, Berry phase, and anomalous Hall effect Y. Tokura, YTaguchi

127

Quantum geometry and Hall effect in ferromagnets and semiconductors N. Nagaosa

134

Spin-Hall effect in a semiconductor two-dimensional hole gas with strong spin-orbit coupling J. Wunderlich, B. Kaestner, K. Nomura, A.H. MacDonald, J. Sinova, T. Jungwirth Intrinsic spin Hall effect in semiconductors S. Murakami

140

146

Spin Related Phenomena Theory of spin transfer phenomena in magnetic metals and semiconductors A.S. Nunez, A.H. MacDonald

150

Spin filters of semiconductor nanostructures T. Dietl, G. Grabecki, J. Wrobel

159

XIV

Experimental study on current-driven domain wall motion T. Ono, A. Yamaguchi, H. Tanigawa, K. Yano, S. Kasai Magnetization reversal of ferromagnetic nano-dot by non local spin injection Y. Otani, T. Kimura Theory of current-driven domain wall dynamics G. Tatara, H. Kohno, J. Shibata, E. Saitoh Magnetic impurity states and ferromagnetic interaction in diluted magnetic semiconductors M. Ichimura, K. Tanikawa, S. Takahashi, G. Baskaran, S. Maekawa

165 171

177

183

Geometrical effect on spin current in magnetic nano-structures M. Ichimura, S. Takahashi, S. Maekawa

187

Ferromagnetism in anatase Ti02 codoped with Co and Nb T. Hitosugi, T. Shimada, T. Hasegawa, G. Kinoda, K. Inaba, Y. Yamamoto, Y Furubayashi, Y. Hirose

191

Superconductivity in Nano-Systems Nonlinear quantum effects in nanosuperconductors C. Carballeira, G Teniers, V.V. Moshchalkov, A. Ceulemans Coalescence and rearrangement of vortices in mesoscopic superconductors A. Kanda, N. Shimizu, K. Tadano, Y. Ootuka, B.J. Baelus, F.M. Peeters, K. Kadowaki

194

200

Superconductivity in topologically nontrivial spaces M. Hayashi, T. Suzuki, H. Ebisawa, M. Kato, K. Kuboki

204

DC-SQUID ratchet using atomic point contact Y. Ootuka, H. Miyazaki, A. Kanda

208

Superconducting wire network under spatially modulated magnetic field H. Sano, A. Endo, S. Katsumoto, Y. lye

212

Simple and stable control of mechanical break junction for the study of superconducting atomic point contact H. Miyazaki, A.Kanda, Y. Ootuka, T. Yamaguchi

216

Critical currents in quasiperiodic pinning arrays: One-dimensional chains and Penrose lattices V. R. Misko, S. Savel'ev, F. Nori

220

XV

Macroscopic quantum tunneling in high-Tc superconductor Josephson junctions S. Kawabata

224

Novel Properties of Carbon Nanotubes Carbon nanotubes and unique transport properties: Importance of symmetry and channel number T. Ando

228

Optical processes in single-walled carbon nanotubes threaded by a magnetic flux J. Kono, S. Zaric, J. Shaver, X. Wei, S.A. Crooker, O. Portugall, G.L.J.A. Rikken, R.H. Hauge, R.E. Smalley

234

Non-equilibrium transport through a single-walled carbon nanotube with highly transparent coupling to reservoirs P. Recher, N. Y. Kim, Y. Yamamoto

242

Novel properties of Nano-systems Transport properties in low dimensional artificial lattice of gold nano-particles S. Saito, T. Arai, H. Fukuda, D. Hisamoto, S. Kimura, and T. Onai

246

First principles study of dihydride-chain structures on H-terminated Si(100) surface Y. Suwa, M. Fujimori, S. Heike, Y. Terada, T. Hashizume

250

Electrical property of Ag nanowires fabricated on hydrogen-terminated Si(l 00) surface M. Fujimori, S. Heike, T. Hashizume

254

Effect of environment on ionization of excited atoms embedded in a solid-state cavity M. Ando, C. Lee, S. Saito, Y. A. Ono

258

Development of universal virtual spectroscope for optoelectronics research: First principles software replacing dielectric constant measurements T. Hamada, T. Yamamoto, H. Momida, T. Uda, T. Ohno, N. Tajima, S. Hasaka, M. Inoue, N. Kobayashi

262

Quantum Nerast effect H Nakamura, N. Hatano, R. Shirasaki

266

xvi Precise Measurements Quantum phenomena visualized using electron waves A. Tonomura An Optical lattice clock: Ultrastable atomic clock with engineered perturbation H. Katori, M. Takamoto, R. Higashi, F.-L. Hong Development of Mach-Zehnder interferometer and "coherent beam steering" technique for cold neutron K. Taketani, H. Funahashi, Y. Seki, M. Hino, M. Kitaguchi, R. Maruyama, Y. Otake, H.M. Shimizu Surface potential measurement by atomic force microscopy using a quartz resonator S. Heike, T. Hashizume

270 276

282

286

Fundamental Problems in Quantum Physics Berry's phases and topological properties in the Born-Oppenheimer approximation K. Fujikawa

290

Self-trapping of Bose-Einstein condensates by oscillating interactions H. Saito, M. Ueda

294

Spinor solitons in Bose-Einstein condensates — Atomic spin transport J. Ieda

298

Spin decoherence in a gravitational field H. Terashima, M. Ueda Berry's phase of atoms with different sign of the g-factor in a conical rotating magnetic field observed by a time-domain atom interferometer A. Morinaga, H. Narui, A. Monma, T. Aoki

302

306

List of participants

309

Author Index

317

1 OPENING ADDRESS HIDETOSHIFUKUYAMA Chair of the Organizing Committee. ISQM-TOKYO '05 Institute for Materials Research, Tohoku University Sendai-shi, Miyagi 980-8577, Japan

Good morning, ladies and gentlemen, and dear colleagues. On behalf of the Organizing Committee of this conference, I would like to welcome all of you to this International Symposium on Quantum Mechanics in the Light of New Technology, ISQM-TOKYO'05. This is the 8th of the series, which was started in 1983, when Professor Sadao Nakajima, then Director of the Institute for Solid State Physics, and Dr. Yasutsugu Takeda, then General Manager of Central Research Laboratory, Hitachi, Ltd., resonated in the idea to bridge between basic science and technology. Behind their decision, there was a beautiful experimental verification of the AharonovBohm effect by Dr. Akira Tonomura, who, as far as I understand, received many inspiring suggestions and warm encouragements from Professor C.N. Yang to carry out this very difficult experiment. Actually this experiment by Dr. Akira Tonomura was symbolic in demonstrating the fact that science and technology go hand in hand; namely, technological development can lead to further exploration of the mysteries of the nature and a new understanding of basic scientific facts leads to new technologies, or vice versa. Dr. Nakajima and Dr. Takeda had very good foresight when they started this activity. It is very fortunate for us to have Professor Nakajima here in this hall this morning, and we also expect to see Professor Yang later in the conference. As I said before, this is the 8th symposium of the series, and it is true that science and technology have undergone tremendous

changes during these years. This is clearly seen from the program of the first conference. We can see the titles, such as Aharonov-Bohm Effect, Theory of Measurement, Quantum Tunneling, EPR paradox, Quantum Logic, Philosophy of Quantum Mechanics, Quantum Optics, Quantum Hall Effect, and so on; so many talks addressed to very basic but at the same time very abstract subjects. At that time people just talked about these kinds of things without worrying about the difficulties of realizing quantum coherence over macroscopic scales. Because of that, it was not easy for experimentalists to have creative interactions with theorists. However, in this conference, many interesting experimental questions associated with the quantum coherence of not only electron waves but also of spins will be addressed. This trend will grow since scientific and technological interests are moving more and more toward materials on small scales, on the nano-scale, where obviously quantum coherence really manifests itself. It is my hope that this symposium will contribute to a deeper understanding of the properties of materials, which are governed by quantum mechanics, through stimulating discussion among colleagues who are interested in this subject but at the same time seldom meet each other because they are working in different fields. This conference, ISQM, is quite unique in that sense. As I mentioned, this is the 8th of the series. When you look at the Chinese character eight, you can see its top part has a narrow space but at the bottom there is a wider space. The

2

bottom part is called "Sue" in Japanese, meaning "Future." The character "Eight" shows that the future is wide, bright, and holds many possibilities. Because of this particular structure, the number eight is considered to be a very good number. Then why not expect a very bright future for materials science where quantum coherence plays a crucial role? I hope all of you enjoy this conference. Thank you very much for your attention.

3

WELCOMING ADDRESS NOBUYUKIOSAKABE Advanced Research Laboratory, Hitachi, Ltd. Hatoyama, Saitama 350-0395, Japan

Good morning, distinguished guests, ladies and gentlemen. On behalf of our laboratory, let me welcome you to Hatoyama and ISQMTOKYO '05. It is a great pleasure for us to host this event for you all here today. This symposium was initiated in 1983, as Professor Fukuyama explained. The motivation for Hitachi to host and sponsor the first ISQM came from Dr. Akira Tonomura's successful verification of the Aharonov-Bohm effect. In his study, new micro-fabrication technology developed in the semiconductor industry and an electron microscope technology developed at Hitachi were successfully combined to verify the important concept of the gauge field. In addition, through the strong thrust of Professor Chen Ning Yang, Hitachi decided to hold the first ISQM, i.e., the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology. The aim of the symposium has been to discuss the foundation of quantum mechanics achieved by using new technologies based on industrial innovation and to contribute to the scientific community in general. Twenty two years have past since then. The site of the symposium has moved from the Central Research Laboratory in Tokyo to the Advanced Research Laboratory, Hitachi, Ltd., here at Hatoyama. Many new areas in physics have been discussed over the years. Today those fundamental quantum phenomena are now being used in the world of technology. Single electron charges can now controlled to make new semiconductor memories to breakthrough the barrier of modern device performance. Quantum entanglement will be used to secure future communication.

Macroscopic quantum tunneling and coherence will be the basis for quantum computing. The foundation of quantum mechanics will leverage industrial companies. Thus, because of all these possibilities, we found enormous value in hosting and sponsoring the symposium here again. I hope all of you find the symposium rewarding. Before concluding, I would like to thank all the members of the Advisory and Organizing Committees for putting together such an exciting program. I also would like to thank all the invited speakers for coming to share their latest findings with the participants here. I very much look forward to hearing them. Thank you very much for your attention.

4 ALBERT EINSTEIN: OPPORTUNITY AND PERCEPTION CHEN NING YANG Huang Ji-Bei & Lu Kai-Qun Professor Tsinghua University, Beijing 100084, China, and Chinese University, Hong Kong

I The year 1905 has been called Albert Einstein's "Annus Mirabilis". It was during that year that he caused revolutionary changes in man's primordial concepts about the physical world: space, time, energy, light and matter.

How

for him to change the course of physics, an opportunity unmatched, perhaps, since the time of Newton. Such lucky opportunities occur very very infrequently. In E.T. Bell's Man of Mathematics, Lagrange (1736-1813) was quoted as having said:

could a 26-year-old clerk, previously unknown, cause such profound conceptual changes, and

Newton was assuredly the man of

thereby open the door to the era of modern

genius par excellence, but we must

scientific technological world?

No one, of

agree that he was also the luckiest: one

course, can answer that question. But one can,

finds only once the system of the world

perhaps, analyze some factors that were

to be established.

essential to his stepping into such a historic role.

Here Lagrange was referring to the words in Newton's introduction to the third and final volume of his great Principia Mathematica. I now demonstrate the frame of the system of the world. While Lagrange was obviously envious of Newton's lucky opportunity, we detect little sentiment of a similar nature in what Einstein

Fig. I Einstein as a Swiss patent clerk in 1905 when he revolutionizedfundamental physics through the creation of the special theory of relativity.

First of all, Einstein was extraordinary lucky: He was born at the right time, and was at the peak of his creative powers when the world of physics was shuddering from multiple crises. In other words, there was the lucky opportunity

had publicly said of Newton: Fortunate Newton, happy childhood of science... In one person he combined the experimenter, the theorist, the mechanic and, not least, the artist in exposition. He stands before us strong, certain, and alone...

5 Turning to Einstein's own times, he had the

one year before 1905 (In Physics for a New

opportunity to amend the system created by

Century, AIP publication on History, volume 5,

Newton more than 200 years ago. This lucky

1986):

opportunity was of course open also to all scientists of his time. Indeed electrodynamics

The principle of relativity, according to

in a moving system had been a subject of

which the laws of physical phenomena

intense discussions since the Michaelson-

should be the same, whether for an

Morley experiment, first performed 1881,

observer fixed, or for an observer

repeated with greater precision in 1887.

carried along in a uniform movement

Amazingly Einstein was already intensely

of translation; so that we have not and

interested in this topic while still a student in

could

Zurich.

discerning whether

He had written to his future wife

Milevain 1899:

not

have

any

means

of

or not we are

carried along in such a motion.

/ returned the Helmholtz 's volume and

This paragraph not only introduced the term

am now rereading Hertz's propagation

"relativity", but showed amazing insight which

of electric force

is absolutely correct philosophically. However,

because

I

with great care

didn't

understand

Poincare

did

not

understand

the

full

Helmholtz's treatise on the principle of

implication in physics of this paragraph: Later

least action in electrodynamics. I'm

paragraphs in the same speech showed that he

convinced more and more that the

failed to grasp the crucial and revolutionary

electrodynamics of moving bodies as it

idea of the relativity of simultaneity.

is presented today doesn't correspond to reality, and that it will be possible to present it in a simpler way. [From Albert Einstein/Mileva Marie,

Einstein was also not the first to write down the great transformation formula:

x'=y(x-vt), y'=y, z'=z

The love letters, Edited by Renn & Schulmann, Translated by Smith.] The search for this simpler way led, six years

1

later, to special relativity. Many other scientists were also deeply

Y

"Vl-v 2 /c 2

interested in the subject. Poincare (1854-1912), one of the two towering mathematicians at the time, was actively working on the same problem. Indeed the name relativity was not invented by Einstein. It was invented by Poincare. One reads in his speech delivered

which had already been given by Lorentz (1853-1928), after whom it was, and still is, named. But Lorentz also failed to grasp the revolutionary

idea

of

the

relativity

simultaneity. He wrote later in 1915:

of

6 The chief cause of my failure was my

To have a free perception, one must

clinging to the idea that only the

simultaneously be close to the subject under

variable t can be considered as the true

investigation, and yet be able to examine it at a

time and that my local time t' must be

distance. Indeed the often used term distant

regarded as no more than an auxiliary

perception shows the necessity of maintaining

mathematical quantity.

a

[Cf. Pais' biography of Einstein, p. 167]

discernment. But distant perception alone is

certain

distance

in

any

penetrating

not enough. It must be matched by a detailed I.e. Lorentz had the mathematics, but not the

close-up understanding of the problem at hand.

physics, and Poincare had the philosophy, but

It is the ability to freely adjust, assess and

also not the physics. It was the 26-year-old

compare the close-up and distant views that

Einstein who dared to question mankind's

constitutes free perception.

primordial concept about time, and insisted

metaphor, we might say that Lorentz had failed

that simultaneity is relative, thereby opening

because he had only a close-up view, while

the door to the new physics of the microscopic

Poincare had failed because he had only a

world.

distant perception.

Pursuing this

Almost all physicists today agree that it

The great Chinese esthetician ^ % ?§

was Einstein who had created special relativity.

(1897-1986) had emphasized the importance of

Is that fair to Poincare and Lorentz? To discuss

"psychical distance" in artistic and literary

this question let us quote from A. N.

creativity. I think that idea is very much the

Whitehead [in The Organization of Thought,

same as the distant perception discussed above,

Greenwood Press, 1974, p. 127]:

but in another area of intellectual activity. In the brilliant definitive scientific biography of

To come very near to a true theory and

Einstein, Subtle is the Lord, by Pais, the author

to grasp its precise application, are two

chose one word to describe Einstein's character:

very different things, as the history of

apartness, and quoted at the beginning of

science teaches us.

Chapter 3:

Everything of

importance has been said before by somebody who did not discover it.

Apart ...4. Away from others in action or function; separately, independently,

Lorentz and Poincare indeed did seize the

individually.

lucky opportunity of the time, and had worked

f Oxford English Dictionary]

very hard on one of the main problems, the electrodynamics in a moving system. But they

Indeed,

apartness,

distance,

and

free

both missed the crucial key point. They missed

perception are related concepts, referring to an

because they had "clung" to old concepts, as

essential element in all human creativity, in

Lorentz himself later had said. Einstein did not

science, in art, and in literature.

miss because he had a freer perception of the meaning of space-time.

Another

historic

achievement

of

Einstein's in 1905 was his paper "0« a

7 the

papers of 1916-1917 established the value of

generation and conversion of light" written in

the momentum of the light quantum, leading

March of that year. Historically this paper

later to the epoch-making understanding of the

launched the revolutionary idea of light as

Compton effect in 1924.

heuristic point

of

view

concerning

quanta with discrete energy hv. The constant h had already been introduced by Planck in 1900

The

history

of

the

birth

of

the

in his bold theoretical study of black body

revolutionary idea of the light quanta can be

radiation. In subsequent years, however, Planck

summarized as follows:

got cold feet, and began to hedge. In stepped Einstein in 1905, who not only did not hedge,

1905 Einstein's paper on E= hv

but pushed forward courageously with his

1916 Einstein's paper on P=E/c

"heuristic point of view" of light quanta. That

1924 Compton effect

this courageous push was not

generally

appreciated can be gathered from the following

Throughout these years, before the Compton

sentences in a document written by Planck,

effect was established in 1924, Einstein was

Nernst, Rubens and Warburg, eight years later

alone in his insightful perception, at a time

in 1913, when they proposed Einstein for

when entrenched conviction about waves was

membership

sacred to the whole physics community.

in

the

prestigious

Prussian

Academy: In sum, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may sometimes have

missed

the

target

in

his

speculations, as, for example, in his hypothesis

of light-quanta,

cannot

Fig. 2 Einstein giving a lecture in 1922 at the College de France in Paris.

really be held too much against him, for it is not possible to introduce really new ideas even in the most exact science without sometimes taking a risk [From Pais, Subtle is the Lord, 1982,p.382] Here the ridiculed "hypothesis of light-quanta" referred to Einstein's bold proposal of 1905 mentioned above. Despite such general derision, Einstein pushed further ahead, and in

II Between 1905 and 1924 Einstein's main research interests were focused on the general theory of relativity. As a scientific revolution general relativity is unique in the history of mankind. The grandeur of its conception, its beauty, its sweeping scope, its spawning the awesome science of cosmology, and the fact that it was conceived and executed by one

8 single person, reminds me of the act of creation in the old testament. (And I wonder whether Einstein himself had thought of this comparison.)

Fig. 3 Einstein in his study in his home on Haberlandstrafie in Berlin.

Of course, one would also naturally think of

other

scientific

revolutions,

such

as

Newton's Principia, special relativity, and quantum

mechanics.

Some

differences:

Newton's work had grandeur, had beauty, had sweeping scope. Yes. But he had before him the works of Galileo, of Kepler and of earlier mathematicians and philosophers. He was not alone at the time in searching for the law of gravity.

Special

relativity

and

quantum

mechanics were both profound revolutions. But

Ill General relativity represented the geometrization of the gravitational field. It quite naturally led to Einstein's push for the geometrization of the electromagnetic field. Thus was born his idea to formulate an overall geometrization of all forces of nature, a unified field theory, which gradually evolved into his main research effort during the latter part of his life. The last seminars that he gave, for example, were in 1949-1950 at the Institute for Advanced Study in Princeton, and the subject was his latest attempt to incorporate the field strengths F,,v of the electromagnetic field into an unsymmetrical metric g,,v. This attempt, as well as his earlier attempts in the same direction, was also unsuccessful. As a consequence of this lack of success, and also because of the fact that, starting in the late 1920s, he directed his attention almost exclusively to this search, neglecting such newly developing fields as solid state physics and nuclear physics, he was often criticized, even ridiculed. His devotion to the unified field theory was called an obsession. An example of this criticism is what I. I. Rabi (1898-1988) had said in 1979 at the Einstein centennial in Princeton:

they were hot topics worked on by many people at the time. Neither was the creation of a single person.

When you think of Einstein's career from 1903 or 1902 on to 1917, it was

For general relativity, Einstein did not seize

an extraordinarily rich career, very

any opportunity. He created the opportunity.

inventive, very close to physics, very

Alone, through deep perception, he conceived

tremendous insights; and then, during

the problem and after seven or eight years of

the period on which he had to learn

lonely struggle produced a new system of the

mathematics, particularly differential

world of unimaginable beauty. It was an act of

geometry in various forms, he changed.

pure creation.

He changed his mind.

That great

9 originality for physics was altered...

So, Einstein did change. He himself was keenly

Was Rabi right? Did Einstein change? The answer is, Einstein did change. Evidence

aware

of

this

change.

In

the

Autobiographical Notes, published when he was 70 years old, we read:

for this change can be found in his Herbert Spencer lecture of 1933 bearing the title On the

... and it was not clear to me as a

Method of Theoretical Physics:

student that the approach to a more profound knowledge of the basic

... the axiomatic basis of theoretical

principles of physics is tied up with

physics

the

cannot

experience

be extracted from

but

must

be

freely

intricate

mathematical

methods. This dawned upon me only gradually after years of independent

created... Experience

most

may

suggest

the

scientific work.

appropriate mathematical concepts, but they most certainly cannot be deducedfrom it... But the creative principle resides in mathematics.

In a certain sense,

therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed. One may or may not agree with these very concise statements, but one has to agree that they powerfully and emphatically describe Einstein's perception in 1933 about how to do fundamental theoretical physics, a perception that represents a profound change from his earlier days.

Fig. 4 Einstein in Princeton

It is evident that in this passage the independent scientific work was his long struggle to formulate general relativity during the period 1908-1915. That long struggle had changed him. Did he change for the better? Rabi would say: no, his changed perception had become a futile obsession. We would say: yes, his changed perception has altered the future course of development of fundamental physics: Einstein's perception had permeated the very soul of the research in fundamental theoretical physics in the 50 years since Einstein's death, serving as a lasting testimonial to his courageous, independent, obstinate and perceptive greatness.

10 Q U A N T U M OPTICS W I T H SINGLE ATOMS A N D P H O T O N S

H. J. K I M B L E Norman

Bridge Laboratory of Physics MC California Institute of Technology Pasadena, CA 91125 USA

12-33

Across a broad front in physics, an important advance in recent years has been the increasing ability to observe and manipulate the dynamical processes of individual quantum Systems. Within this context, an important physical system has been a single atom strongly coupled to the electromagnetic field of a high-Q cavity within the setting of cavity quantum electrodynamics (cavity QED). Another promising possibility is provided by the cooperative interaction of light with an atomic ensemble for writing and reading single quanta. Here, I present a brief overview of recent advances in the Quantum Optics Group at Caltech related to optical interactions with single photons and atoms and to applications in quantum information science.

Keywords: Quantum information; Quantum optics; Cavity QED.

1. Introduction

the external and internal degrees of freedom for one atom strongly coupled to an Because of several advantages, Quantum Opoptical cavity, the generation of entangletics continues to play an important role in ment among multiple cavities, and the labothe new science of Quantum Information, ratory realization of fault-tolerant protocols including for realizations of scalable quanfor quantum-state transformations. Much of tum networks and for investigations of quanour research within the arena of cavity QED tum dynamics of single quantum systems 1'2. is applicable to a broad spectrum of topics Research in the Quantum Optics Group at in Quantum Information Science, including Caltech addresses these themes by utilizing fundamental primitives for general quantumstrong coupling in optical physics to control state synthesis and new protocols for the renonlinear optical interactions atom by atom versible transfer of quantum states between and photon by photon. One application of different types of physical systems. this research is the implementation of a rudiThe second front for our research inmentary quantum network, as illustrated in volves the collective interactions of ensemFigure 1 3 ' 4 . bles of cold atoms with single photons. Here, We are approaching the problem of conwe are developing the laboratory capabilitrol of optical interactions on two different ties to implement the quantum network profronts. The first is within the setting of cavtocols described in Ref. 5 , including for ity quantum electrodynamics (cavity QED) entanglement-based quantum cryptography with single atoms strongly coupled to the and teleportation of quantum states. We fields of high quality optical resonators. Alhave also developed a theoretical protocol to though the prospects for quantum informarealize a "heterogeneous" quantum network tion processing via cavity QED are quite by entangling one atom in a cavity-QED syspromising, several major scientific and tech- tem with a remotely located atomic ensemnical advances are required for the robust im- ble. plementation of sophisticated quantum netWithin this broad setting, recent laboraworks. These challenges include control of

11

Quantum Node

Quantum Channel

iiQ

Fig. 1. The "quantum internet" composed of quantum nodes and quantum channels. The nodes are shown schematically as small quantum processing units based upon interactions in cavity QED, here illustrated with five atoms trapped inside a Fabry-Perot cavity (but which might incorporate atomic ensembles as well). Quantum channels distribute entanglement via photons in fibers, with the interface between light and matter made by way of quantum-state exchange protocols developed in Refs. 3 ' 4 .

tory advances include (1) the observation of the vacuum-Rabi spectrum for an individual atom trapped in an optical cavity 6 , (2) the attainment of photon blockade for an optical cavity containing a single trapped atom 7 , (3) a new experiment in cavity QED to achieve strong coupling of a single atom to the field of an ultrahigh-Q toroidal microresonator 8 , (4) the generation of single photons from excitation stored in an atomic ensemble 9 ' 1 0 ' n and (5) the observation of measurement-induced entanglement between remote atomic ensembles 12 . A brief summary of each of these activities follows.

by the atom into the cavity mode is likely to be repeatedly absorbed and re-emitted at the single-quantum Rabi frequency 2g before being irreversibly lost into the environment. This oscillatory exchange of excitation between atom and cavity field results from a normal mode splitting in the eigenvalue spectrum of the atom-cavity system, which is manifest in emission and absorption spectra. The splitting has been dubbed the vacuum-Rabi splitting and serves as the hallmark of strong coupling in cavity QED.

Strong coupling in cavity QED as evidenced by the vacuum-Rabi splitting provides enabling capabilities for quantum information science. Against this backdrop, 2. Vacuum-Rabi spectrum for experiments in cavity QED have made great "one-and-the-same" atom strides over the past two decades to achieve A cornerstone of optical physics is the in- strong coupling. However, without exception teraction of a single two-level atom with prior experiments related to the vacuumthe electromagnetic field of a high quality Rabi splitting in cavity QED have required resonator. Of particular importance is the averaging over trials with many atoms (> 103 regime of strong coupling, for which the fre- to 105 atoms) to obtain quantitative spectral quency scale g associated with reversible evo- information, even if individual trials involved lution for the atom-cavity system exceeds the only single atoms. By contrast, the implerates (7, K) for irreversible decay of atom mentation of complex algorithms in quantum and cavity field, respectively. In the do- information science requires the capability main of strong coupling, a photon emitted

12

Fig. 2. A single atom is trapped inside an optical cavity in t h e regime of strong coupling by way of an intracavity F O R T driven by the field £FORT 6 - The transmission spectrum T\(wp) for the atom-cavity system is obtained by varying the frequency u>p of the probe beam £p and recording the output with singlephoton detectors. Cooling of the radial atomic motion is accomplished with the transverse fields Q4, while axial cooling results from Raman transitions driven by the fields £FORT> ^Raman- An additional transverse field JJ3 acts as a repumper during probe intervals.

for repeated manipulation and measurement of an individual quantum system. With this goal in mind, we have employed the experimental arrangement shown in Fig. 2 and have succeeded in recording a complete probe spectrum for "one-and-thesame" atom 6 . The vacuum-Rabi splitting has thereby been measured in a quantitative fashion for each atom in a sequence by way of a protocol that represents an important milestone in the development of cavity QED. Our experiment provides a critical first step towards more complex tasks in quantum information science, including, significantly, the realization of quantum networks. An essential component of this work is a new Raman scheme that we have developed for cooling atomic motion along the cavity axis, which leads to inferred atomic localization A z a i i a i ~ 33 nm.

3. Photon blockade Sufficiently small metallic and semiconductor devices at low temperatures exhibit "Coulomb blockade," whereby charge transport through the device occurs on an electron-by-electron basis. In 1997, Imamoglu et al. proposed that an analogous effect might be possible for photon transport through an optical system by employing photon-photon interactions in a nonlinear optical cavity 13>14. In this scheme, strong dispersive interactions cause the presence of a "first" photon within the cavity to block the transmission of a "second" photon, leading to an ordered flow of photons in the transmitted field. Although there is by now an extensive literature on photon blockade, this effect had not been previously observed. In Ref. 7 we reported the first observation of photon blockade by examining the light transmitted by an optical cavity containing one atom strongly coupled to the cavity field, as il-

13

Fig. 3. The upper panels illustrate the level structure used for implementation of the photon-blockade effect, while the lower panel offers a simple diagram of the experiment 7 . (a) Level diagram showing the lowest energy states for a two-state atom of transition frequency U>A coupled (with single-photon Rabi frequency go) to a mode of the electromagnetic field of frequency wc, with u ^ = u c = « o . Two-photon transmission is suppressed for a probe field uip (arrows) tuned to excite the transition |0) —> |1, —), u>p = u>o — go. leading to sub-Poissonian statistics for the transmitted field, g' 2 '(0) < 1. (b) Eigenvalue structure for t h e {F = 4,mjj) «-» (F' = 5',m'F) transition in atomic Cesium coupled to two degenerate cavity modes ly,z- Although the eigenvalue structure is now much more complex than in (a), two-photon transmission is likewise blocked for excitation tuned to the lowest eigenstate (arrows), again leading to a more orderly flow of photons for the transmitted field (relative to the incident Poissonian photon stream), (c) Simple schematic of our experiment.

lustrated in Fig. 3. For coherent excitation at the cavity input, we investigated the photon statistics for the cavity output by way of measurements of the intensity correlation function g^(r), which demonstrate the manifestly nonclassical character of the transmitted field. Explicitly, we found (2) 5 (2)(0) = (0.13 ±0.11) < 1 with c/ (0) < # * 2 ) ( T ) , SO that the output light is both subPoissonian and antibunched. Further, we observed that