Trapped Ions and Laser Cooling 111 

Selected publications of the Ion Storage Group of the Time and Frequency Division 

Edited by 

James C. Bergquist 

John J. Bollinger 

Wayne M. ltano 

David J. Wineland 

Time and Frequency Division 

Physics Laboratory 

National Institute of Standards and Technology 

Boulder, Colorado 80303-3328 

Supported in part by 

U.S. Office of Naval Research 

800 North Quincy 

Arlington, Virginia 2221 7 

April 1992 

U.S. DEPARTMENT OF COMMERCE, Barbara Hackman Franklin, Secretary 

TECHNOLOGY ADMINISTRATION, Robert M. White, Under Secretary for Technology 

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director 
National Institute of Standards and Technology Technical Note 

Natl. Inst. Stand. Technol., Tech. Note 1353, 204 pages (April 1992) 

CODEN: NTNOEF 

U.S. GOVERNMENT PRINTING OFFICE’ 

WASHINGTON: 1992 

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325 
PREFACE 

This collection of papers represents the work of the Ion Storage Group, Time and 

Frequency Division, National Institute of Standards and Technology from October 1988 to 

February 1992. It follows the collections of papers contained in NBS Technical Note 1086, 

Trapped Ions and Laser Cooling (June 1985) and NIST Technical Note 1324 Trapped Ions 

and Laser Cooling ZZ (September 1988). Although the primary goal of this work has been 

the development of techniques necessary for achieving high resolution spectroscopy, we have 

also been able to investigate related areas of research. 

Papers listed on page vii were published or prepared during the period October 1988 

to February 1992 but are not included here. They can be obtained on request. We intend to 

update this publication periodically to include new work. We hope this collection of papers 

will be useful to our colleagues in this and related fields. 

We acknowledge the important contributions of several colleagues to this collection. 

In particular, we thank Larry Brewer, Claude Cohen-Tannoudji, Jean Dalibard, Frank 

Diedrich, Frank Elsner, Sarah Gilbert, Jon Gilligan, Dan Heinzen, Dan Larson, Chuck 

Manney, Fred Moore, Mark Raizen, and Carl Weimer. We gratefully acknowledge the 

continued support of the U. S. Office of Naval Research and the support of the Air Force 

Office of Scientific Research through September 1991. 

James C. Bergquist 

John J. Bollinger 

Wayne M. Itano 

David J. Wineland 

Boulder, Colorado 

March 1992 

... 

111 
CONTENTS 

ADDITIONAL PUBLICATIONS 

LASER COOLING 

1. 

2. 

3. 

4. 

"Perpendicular Laser Cooling of a Rotating Ion Plasma in a Penning 

Trap," W. M. Itano, L. R. Brewer, D. J. Larson, D. J. Wineland, Phys. 

Rev. A 38, 5698 (1988). 

"Laser Cooling to the Zero-Point Energy of Motion," F. Diedrich, J. C. 

Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 

( 1 989). 

" Quantum-Limited Cooling and Detection of Radio-Frequency Oscillations 

by Laser-Cooled Ions," D. J. Heinzen and D. J. Wineland, Phys. Rev. A 

- 42, 2977 (1990). 

"Sisyphus Cooling of a Bound Atom," D. J. Wineland, J. Dalibard, and C. 

Cohen-Tannoudji, J. Opt. SOC. Am. B 9, 32 (1992). 

SPECTROSCOPY AND FREQUENCY STANDARDS 

1. "Hg' Single Ion Spectroscopy," J. C. Bergquist, F. Diedrich, W. M. 

Itano, and D. J. Wineland, in Laser Spectroscopv IX, ed. by M. S. Feld, 

J. E. Thomas, and A. Mooradian (Academic, San Diego, 1989), p. 274. 

2. "Frequency Standards in the Optical Spectrum," D. J. Wineland, J. C. 

Bergquist, W. M. Itano, F. Diedrich, and C. S. Weimer, in The Hvdrogen 

Atom, Ed. by G. F. Bassani, M. Inguscio, and T.W. Hhsch (Springer 

Verlag, Berlin, Heidelberg, 1989), p. 123. 

3. "Progress at NIST toward Absolute Frequency Standards Using Stored 

Ions," D. J. Wineland, J. C. Bergquist, J. J. Bollinger, W. M. Itano, 

D. J. Heinzen, S. L. Gilbert, C. H. Manney, and M. G. Raizen, IEEE 

Trans. Ultrason. Ferroelec. Freq. Contr. 3, 515 (1990). 

4. "A 303-MHz Frequency Standard Based on Trapped Be' Ions," J. J. 

Bollinger, D. J. Heinzen, W. M. Itano, S. L. Gilbert, and D. J. Wineland, 

IEEE Trans. Instrum. Meas. 40, 126 (1991). 

Page 

Vlll 

... 

TN- 1 

TN-10 

TN-14 

TN-32 

TN-43 

TN-47 

TN-5 8 

TN-67 

V 
5. "Single Ion Optical Spectroscopy," J. C. Bergquist, W. M. Itano, F. 

Elsner, M. G. Raizen, and D. J. Wineland, in Light Induced Kinetic 

Effects o n Atoms. Ions and Molecules, ed. by L. Moi, S. Gozzini, C. 

Gabbanini, E. Arimondo, and F. Strumia (ETS Editrice, Pisa, 1991), p. 

291. 

6. "Linear Trap for High-Accuracy Spectroscopy of Stored Ions," M. G. 

Raizen, J. M. Gilligan, J. C. Bergquist, W. M. Itano, and D. J. Wineland, 

J. Mod. Opt. 3, 233 (1992). 

FUNDAMENTAL TESTS 

1. 

2. 

3. 

4. 

5. 

6. 

"Test of the Linearity of Quantum Mechanics by rf Spectroscopy of the 

'Be+ Ground State," J. J. Bollinger, D. J. Heinzen, W. M. Itano, S. L. 

Gilbert, and D. J. Wineland, Phys. Rev. Lett. 63, 1031 (1989). 

"Quantum Optics of Single, Trapped Ions," W. M. Itano, J. C. Bergquist, 

F. Diedrich, and D. J. Wineland, in Coherence and 0 uantum &tics VI, 

ed. by J. H. Eberly, L. Mandel, and E. Wolf (Plenum, New York, 1990) 

p. 539. 

"Quantum Zeno Effect," W. M. Itano, D. J. Heinzen, J. J. Bollinger, and 

D. J. Wineland, Phys. Rev. A 41, 2295 (1990). 

"Reply to 'Comment on the Quantum Zen0 effect'," W. M. Itano, D. J. 

Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A a, 5168 

(1991). 

"Search for Anomalous Spin-Dependent Forces Using Stored-Ion 

Spectroscopy," D. J. Wineland, J. J. Bollinger, D. J. Heinzen, W. M. 

Itano, and M. G. Raizen, Phys. Rev. Lett. 62, 1735 (1991). 

"Atomic Physics Tests of Nonlinear Quantum Mechanics," J. J. Bollinger, 

D. J. Heinzen, W. M. Itano, S. L. Gilbert, and D. J. Wineland, Atomic 

Physics 12 (proc. 12th International Conference on Atomic Physics), ed. 

by J. C. Zom and R. R. Lewis (Amer. Inst. of Physics Press, New York, 

1991), p. 461. 

TN-70 

TN-79 

TN-89 

TN-93 

TN-98 

TN- 104 

TN- 106 

TN-110 

vi 
NONNEUTRAL PLASMA STUDIES 

1. Toulomb Clusters of Ions in a Paul Trap," W. M. Itano, J. C. Bergquist, TN- 130 

and D. J. Wineland, Proc. Workshop on Crystalline Ion Beams, Wertheim, 

W. Germany, ed. by R. W. Hasse, I. Hofmann, D. Liese (GSI report GSI89-10, ISSN 0170-4546, 1989), p. 241. 

2. "Observation of Correlations in Finite, Strongly Coupled Ion Plasmas," in TN- 144 

Stronglv _- CouDled Plasma Physics, ed. by S. Ichimaru (Elsevier Science 

Publishers B.V. / Yamada Science Foundation, 1990) p. 177. 

3. "Microplasmas," J. J. Bollinger and D. J. Wineland, Sci. Am. 262, 124 TN- 155 

(1990). 

4. "Rotational Equilibria and Low-Order Modes of a Non-Neutral Ion TN- 162 

Plasma," D. J. Heinzen, J. J. Bollinger, F. L. Moore, W. M. Itano, and 

D. J. Wineland, Phys. Rev. Lett. 66, 2080 (1991). 

GENERAL ARTICLES 

1. "Cooling Methods in Ion Traps," W. M. Itano, J. C. Bergquist, J. J. 

Bollinger, and D. J. Wineland, chapter in Phvsics with Charged Particles 

in a Trap, ed. by G. Gabrielse and G. Werth, submitted January 1990. 

TN- 166 

2. "Recent Experiments on Trapped Ions at the National Institute of Standards TN- 182 

and Technology," D. J. Wineland, J. C. Bergquist, J. J. Bollinger, W. M. 

Itano, F. L. Moore, J. M. Gilligan, M. G. Raizen, D. J. Heinzen, C. S. 

Weimer, and C. H. Manney, Proc. Enrico Fermi Summer School on 

"Laser Manipulation of Atoms and Ions," July 1991, Varenna, Italy, 

submitted September, 1991. 

vii 
ADDITIONAL PUBLICATIONS 

Reports published or prepared during the period October 1988 to February 1992, 

but not included in this technical note. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

"Liquid and Solid Phases of Laser Cooled Ions," S.L. Gilbert, J.C. 

Bergquist, J.J. Bollinger, W. M. Itano, and D.J. Wineland, in Atomic 

Phvsics 11, ed. by S. Haroche, J. C. Gay, and G. Grynberg (World 

Scientific Press, Singapore, 1989), p. 261. 

"The Digitized Atom and Optical Pumping," D.J. Wineland, W.M. Itano, 

J.C. Bergquist and R.G. Hulet, in Atomic Phvsics 11, ed. by S. Haroche, 

J.C. Gay, G. Grynberg (World Scientific Press, Singapore, 1989), p. 741. 

"Progress at NIST Towards Absolute Frequency Standards Using Stored 

Ions," D. J. Wineland, J. C. Bergquist, J. J. Bollinger, W. M. Itano, D. 

J. Heinzen, S. L. Gilbert, C. H. Manney, and C. S. Weimer, Proc. 43rd 

Annual Symposium on Frequency Control, Denver, June 1989, IEEE 

Catalog no. 89CH2690-6. 

"Observation of Shell Structures with Ions Stored in Traps," J. J. 

Bollinger, S. L. Gilbert, and D. J. Wineland, Proc. Workshop on 

Crystalline Ion Beams, Wertheim, W. Germany, Ed. by R. W. Hasse, I. 

Hofmann, D. Liese (GSI report GSI-89-10, ISSN 0170-4546), p. 231. 

"Trapped Atoms and Laser Cooling," D. J. Wineland, "essay" for 

undergraduate text Physics, by Paul Tipler (Worth, New York, 1991). 

"Progress at NIST on Absolute Frequency Standards Using Stored Ions," 

D. J. Wineland, J. C. Bergquist, J. J. Bollinger, W. M. Itano, D. J. 

Heinzen, S. L. Gilbert, C. H. Manney, M. G. Raizen, and C. S. Weimer, 

Prac. 4th European Frequency and Time Forum, Neuchatel, March 1990, 

p. 267. 

"Liquid and Solid Plasmas," J. J. Bollinger, S. L. Gilbert, D. J. Heinzen, 

W. M. Itano, and D. J. Wineland, in Atomic Processes in Plasmas, ed. by 

Y. K. Kim and R. C. Elton, AIP Conference Proceedings 206 (American 

Institute of Physics, New York, 1990), p. 152. 

"Test of the Linearity of Quantum Mechanics by RF Spectroscopy of the 

'Be' Ground State," D. J. Heinzen, J. J. Bollinger, W. M. Itano, S. L. 

Gilbert, and D. J. Wineland, in Coherence and Ouantum Optics, ed. by J. 

H. Eberly, L. Mandel, and E. Wolf (Plenum, New York, 1990), p. 479. 

... 

Vlll 
9. "Trapped Ion Frequency Standards," D. J. Wineland, J. C. Bergquist, J. J. 

Bollinger, W. M. Itano, D. J. Heinzen, C. H. Manney, F. L. Moore, M. 

G. Raizen, and C. S. Weimer, Proc. 22nd Ann. Precise Time and Time 

Interval (P'ITI) Applications and Planning Meeting, ed. by R. L. Sydnor 

(NASA Conf. Publ. 3116, 1991), p. 53. 

10. "Atomic Ion Frequency Standards," W. M. Itano, Proc. IEEE 2, 936 

(1991). 

11. "High Resolution Atomic Spectroscopy of Laser-Cooled Ions," D. J. 

Wineland, J. C. Bergquist, J. J. Bollinger, W. M. Itano, F. L. Moore, J. 

M. Gilligan, M. G. Raizen, C. S. Weimer, and C. H. Manney, Proc. 

Enrico Fermi Summer School on "Laser Manipulation of Atoms and Ions," 

July 1991, Varenna, Italy, submitted. 

12. "Laser Cooling of Trapped Ions," W. M. Itano, J. C. Bergquist, J. J. 

Bollinger, and D. J. Wineland, ibid. 

13. "Ionic Crystals in a Linear Paul Trap," M. G. Raizen, J. M. Gilligan, J. 

C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. A, to be 

published. 

14. "Atomic Physics Tests of Nonlinear Quantum Mechanics," J. J. Bollinger, 

D. J. Heinzen, W. M. Itano, S. L. Gilbert, and D. J. Wineland, Santa Fe 

Conference on Quantum Measurements, July 1991, to be published. 

15. "Single Ion Spectroscopy," J. C. Bergquist, D. J. Wineland, W. M. Itano, 

F. Diedrich, M. G. Raizen, and F. Elmer, Proc. SOC. Photo-optical 

Instrumentation Engineers, to be published. 

16. "Low Order Modes of an Ion Cloud in a Penning Trap," J. J. Bollinger, 

D. J. Heinzen, F. L. Moore, W. M. Itano, and D. J. Wineland, 

Proceedings of the Workshop on Physics with Penning Traps, Lertorpet, 

Sweden, Physica Scripta, to be published. 

ix