Abstract

Atoms in a thermal beam can be cooled, decelerated, and stopped using the radiation pressure from a nearly resonant laser beam. Several groups have already used this laser-cooling process on an atomic sodium beam. The techniques and results of the various experimental groups are reviewed, and applications of laser-cooled atoms, in particular the possibility of confining them in electromagnetic traps, are discussed.

© 1985 Optical Society of America

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    [CrossRef]

1985 (7)

J. Dalibard, C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
[CrossRef]

J. Javanainen, M. Kaivola, U. Nielsen, O. Poulsen, E. Riis, J. Opt. Soc. Am. B 2, 1768 (1985).
[CrossRef]

A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
[CrossRef] [PubMed]

J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
[CrossRef] [PubMed]

W. Ertmer, R. Blatt, J. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

J. Dalibard, W. D. Phillips, Bull. Am. Phys. Soc. 30, 748 (1985).

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985).
[CrossRef] [PubMed]

1984 (15)

R. Blatt, W. Ertmer, J. L. HallProg. Quantum Electron. 8, 237 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 142 (1983).
[CrossRef]

W. Ertmer, R. Blatt, J. Hall, Prog. Quantum Electron. 8, 249 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 154 (1983).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4577 (1984).
[CrossRef]

J. V. Prodan, W. D. Phillips, Prog. Quantum Electron. 8, 231 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 137 (1983).
[CrossRef]

W. D. Phillips, J. V. Prodan, H. J. Metcalf, Prog. Quantum Electron. 8, 119 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 1 (1983).
[CrossRef]

M. S. Lubell, K. Rubin, Prog. Quantum Electron. 8, 223 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed. Nat. Bur. Stand. (U.S.) Spec. Publ.653, 125 (1983).
[CrossRef]

V. I. Balykin, V. S. Letokhov, V. G. Minogin, T. V. Zueva, Appl. Phys. B 35, 149 (1984).
[CrossRef]

V. I. Balykin, V. S. Letokhov, A-I. Sidorov, Pis’ma Zh. Eksp. Teor. Fiz. 40, 251 (1984).

J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Opt. Commun. 49, 248 (1984).
[CrossRef]

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Zh. Eksp. Teor. Fiz. 86, 2019 (1984).

W. Stwalley, Prog. Quantum Electron. 8, 203 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 95 (1983).
[CrossRef]

A. Ashkin, Opt. Lett. 9, 454 (1984).
[CrossRef] [PubMed]

H. Metcalf, Prog. Quantum Electron. 8, 169 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 59 (1983).
[CrossRef]

L. Moi, Opt. Commun. 50, 349 (1984); J. Liang, L. Moi, C. Fabre, Opt. Commun. 52, 131 (1985).
[CrossRef]

1983 (7)

E. Giacombino et al., Phys. Rev. A 28, 2555 (1983); E. Giabobino, P. A. Berman, Prog. Quantum Electron. 8, 215 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 112 (1983).
[CrossRef]

D. E. Pritchard, Phys. Rev. Lett. 51, 1336 (1983); Prog. Quantum Electron. 8, 209 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 103 (1983).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 357 (1983).
[CrossRef]

P. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

S. Stenholm, Phys. Rev. A 27, 2513 (1983).
[CrossRef]

A. Ashkin, J. P. Gordon, Opt. Lett. 8, 511 (1983).
[CrossRef] [PubMed]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 395 (1983).
[CrossRef]

1982 (5)

R. Cook, R. Hill, Opt. Commun. 43, 258 (1982).
[CrossRef]

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982).
[CrossRef]

J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

V. G. Minogin, Kvantovaya Electron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].

V. G. Minogin, J. Javanainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

1981 (9)

R. Cook, Opt. Commun. 35, 347 (1981).
[CrossRef]

S. V. Andreev, V. I. Balykin, V. S. Letokhov, V. G. Minogin, Pis’ma Zh. Eksp. Teor. Fiz. 34, 463 (1981) [JETP Lett. 34, 442 (1981)].

V. S. Letokhov, V. G. Minogin, J. Phys. 42, C8-374 (1981).

W. D. Phillips, Appl. Opt. 20, 3826 (1981).
[CrossRef] [PubMed]

V. S. Letokhov, V. G. Minogin, Phys. Rep. 73, 1 (1981). Much of the early work on laser trapping and cooling is reviewed in this paper.
[CrossRef]

N. Djeu, W. T. Whitney, Phys. Rev. Lett. 46, 236 (1981).
[CrossRef]

T. Breeden, H. Metcalf, Phys. Rev. Lett. 47, 1726 (1981).
[CrossRef]

T. V. Zueva, V. G. Minogin, Pis’ma Zh. Tekh. Fiz. 7, 953 (1981) [Sov. Tech. Phys. Lett. 7, 411 (1981)].

T. V. Zueva, V. S. Ketokhov, V. G. Minogin, Zh. Eksp. Teor. Fiz. 81, 84 (1981) [Sov. Phys. JETP 54, 38 (1981)].

1980 (9)

V. G. Minogin, Opt. Commun. 34, 265 (1980).
[CrossRef]

A. Ashkin, Science 210, 1081 (1980). This contains references to early work on both atom trapping and trapping of macroscopic particles.
[CrossRef] [PubMed]

W. Wing, Phys. Rev. Lett. 45, 631 (1980); Prog. Quantum Electron. 8, 181 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 74 (1983).
[CrossRef]

R. J. Cook, Phys. Rev. Lett. 44, 976 (1980).
[CrossRef]

R. J. Cook, Phys. Rev. A 22, 1078 (1980).
[CrossRef]

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Zh. Eksp. Teor. Fiz. 78, 1376 (1980) [Sov. Phys. JETP 51, 692 (1980)].

V. I. Balykin, Opt. Commun. 33, 31 (1980).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, H. Dehmelt, Phys. Rev. A 22, 1137 (1980).
[CrossRef]

1979 (3)

A. Ashkin, J. P. Gordon, Opt. Lett. 4, 161 (1979).
[CrossRef] [PubMed]

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Pis’ma Zh. Eksp. Teor. Fiz. 29, 614 (1979) [JETP Lett. 29, 560 (1979)].

D. Wineland, W. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

1978 (9)

P. R. Berman, S. Stenholm, Opt. Commun. 24, 155 (1978).
[CrossRef]

D. Wineland, R. Drullinger, F. Walls, Phys. Rev. Lett. 40, 1639 (1978).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978).
[CrossRef]

A. P. Kazantsev, Usp. Fiz. Nauk 124, 113 (1978) Sov. Phys. Usp. 21, 58 (1978)].

S. Stenholm, Phys. Rep. 43, 151 (1978). Section 6 contains an early review of mechanical effects of light.
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
[CrossRef]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

K. J. Kugler, W. Paul, U. Trinks, Phys. Lett. 72B, 422 (1978).

W. Paul, U. Trinks, Inst. Phys. Conf. Ser. No. 42, p. 18 (1978).

1976 (1)

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Opt. Commun. 19, 72 (1976). This proposal was made in connection with cooling of trapped atoms.
[CrossRef]

1975 (3)

T. Hänsch, A. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

D. Wineland, H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975).

W. Fairbank, T. Hänsch, A. Schawlow, J. Opt. Soc. Am. 65, 199 (1975).
[CrossRef]

1970 (2)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970); Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

I. V. Krasnov, N. Ya. Shaparev, Zh. Eksp. Teor. Fiz. 77, 899 (1970) [Sov. Phys. JETP 50, 453 (1979)].

1968 (1)

V. S. Letokhov, Pisma Zh. Eksp. Teor. Fiz. 7, 348 (1968) [JETP Lett. 7, 272 (1968)].

1967 (1)

H. Dehmelt, Adv. At. Mol. Phys. 3, 53 (1967).
[CrossRef]

1963 (1)

C. V. Heer, Rev. Sci. Instrum. 34, 532 (1963).
[CrossRef]

1960 (1)

V. V. Vladimirskii, Zh. Eksp. Teor. Fiz. 39, 1062 (1960) [Sov. Phys. JETP 12, 740 (1961)].

1959 (1)

E. Fischer, Z. Phys. 156, 1 (1959); R. Wuenker, H. Shelton, R. V. Langmuir, J. Appl. Phys. 30, 342 (1958).
[CrossRef]

1951 (1)

H. Friedburg, W. Paul, Naturwissenschaften 38, 159 (1951); Z. Phys. 130, 493 (1951).
[CrossRef]

1950 (1)

A. Kastler, J. Phys. Rad. 11, 255 (1950).
[CrossRef]

1933 (1)

R. Frisch, Z. Phys. 86, 42 (1933).
[CrossRef]

1921 (1)

O. Stern, Z. Phys. 7, 249 (1921); W. Gerlach, O. Stern, Ann. Phy. 74, 673 (1924); Ann. Phy. 76, 163 (1925).
[CrossRef]

Aminoff, C. G.

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A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
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S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985).
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W. Ertmer, R. Blatt, J. Hall, Prog. Quantum Electron. 8, 249 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 154 (1983).
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J. Dalibard, W. D. Phillips, Bull. Am. Phys. Soc. 30, 748 (1985).

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[CrossRef]

J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

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W. Ertmer, R. Blatt, J. Hall, Prog. Quantum Electron. 8, 249 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 154 (1983).
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W. Ertmer, R. Blatt, C. G. Aminoff, M. Zhu, C. Salamon, J. Hall, J. Opt. Soc. Am. B (to be published).

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J. C. Berquist, R. L. Barger, D. J. Glaze, in Laser Spectroscopy IV, H. Walther, K. Rothe, eds. (Springer-Verlag, Berlin, 1979), p. 120; R. L. Barger, Opt. Lett. 6, 145 (1981).
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P. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
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W. Ertmer, R. Blatt, J. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

W. Ertmer, R. Blatt, J. Hall, Prog. Quantum Electron. 8, 249 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 154 (1983).
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W. Ertmer, R. Blatt, C. G. Aminoff, M. Zhu, C. Salamon, J. Hall, J. Opt. Soc. Am. B (to be published).

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R. Blatt, W. Ertmer, J. L. HallProg. Quantum Electron. 8, 237 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 142 (1983).
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F. C. Hansen, K. Harvey, University of Michigan (personal communication, 1984).

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F. C. Hansen, K. Harvey, University of Michigan (personal communication, 1984).

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R. Cook, R. Hill, Opt. Commun. 43, 258 (1982).
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W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978).
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S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985).
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T. V. Zueva, V. S. Ketokhov, V. G. Minogin, Zh. Eksp. Teor. Fiz. 81, 84 (1981) [Sov. Phys. JETP 54, 38 (1981)].

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K. J. Kugler, W. Paul, U. Trinks, Phys. Lett. 72B, 422 (1978).

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V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Opt. Commun. 49, 248 (1984).
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S. V. Andreev, V. I. Balykin, V. S. Letokhov, V. G. Minogin, Pis’ma Zh. Eksp. Teor. Fiz. 34, 463 (1981) [JETP Lett. 34, 442 (1981)].

V. S. Letokhov, V. G. Minogin, Phys. Rep. 73, 1 (1981). Much of the early work on laser trapping and cooling is reviewed in this paper.
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V. S. Letokhov, V. G. Minogin, J. Phys. 42, C8-374 (1981).

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Zh. Eksp. Teor. Fiz. 78, 1376 (1980) [Sov. Phys. JETP 51, 692 (1980)].

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Pis’ma Zh. Eksp. Teor. Fiz. 29, 614 (1979) [JETP Lett. 29, 560 (1979)].

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Opt. Commun. 19, 72 (1976). This proposal was made in connection with cooling of trapped atoms.
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M. S. Lubell, K. Rubin, Prog. Quantum Electron. 8, 223 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed. Nat. Bur. Stand. (U.S.) Spec. Publ.653, 125 (1983).
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A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
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J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
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J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

H. Metcalf, Prog. Quantum Electron. 8, 169 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 59 (1983).
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W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982).
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J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
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T. Breeden, H. Metcalf, Phys. Rev. Lett. 47, 1726 (1981).
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H. Metcalf, W. Phillips, J. Prodan, Bull. Am. Phys. Soc. 29(795) 1984.

T. Bergeman, H. Metcalf, presented at the Ninth Interntional Conference on Atomic Physics, Seattle, Wash., July 23–27, 1984 (preprint, R. S. VanDyck, E. N. Fortson, eds.)

Metcalf, H. J.

W. D. Phillips, J. V. Prodan, H. J. Metcalf, Prog. Quantum Electron. 8, 119 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 1 (1983).
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J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
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A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
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A. Migdall, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1983).

A. Migdall, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1985).

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V. I. Balykin, V. S. Letokhov, V. G. Minogin, T. V. Zueva, Appl. Phys. B 35, 149 (1984).
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V. S. Letokhov, V. G. Minogin, J. Phys. 42, C8-374 (1981).

S. V. Andreev, V. I. Balykin, V. S. Letokhov, V. G. Minogin, Pis’ma Zh. Eksp. Teor. Fiz. 34, 463 (1981) [JETP Lett. 34, 442 (1981)].

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T. V. Zueva, V. G. Minogin, Pis’ma Zh. Tekh. Fiz. 7, 953 (1981) [Sov. Tech. Phys. Lett. 7, 411 (1981)].

V. S. Letokhov, V. G. Minogin, Phys. Rep. 73, 1 (1981). Much of the early work on laser trapping and cooling is reviewed in this paper.
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V. G. Minogin, Opt. Commun. 34, 265 (1980).
[CrossRef]

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Opt. Commun. 19, 72 (1976). This proposal was made in connection with cooling of trapped atoms.
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L. Moi, Opt. Commun. 50, 349 (1984); J. Liang, L. Moi, C. Fabre, Opt. Commun. 52, 131 (1985).
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P. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
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V. I. Balykin, V. S. Letokhov, V. I. Mushin, Zh. Eksp. Teor. Fiz. 78, 1376 (1980) [Sov. Phys. JETP 51, 692 (1980)].

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Pis’ma Zh. Eksp. Teor. Fiz. 29, 614 (1979) [JETP Lett. 29, 560 (1979)].

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W. Neuhauser, M. Hohenstatt, P. E. Toschek, H. Dehmelt, Phys. Rev. A 22, 1137 (1980).
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N. Niehues, thesis, Universität Bonn (Bonn-IR-76-35) (1976), unpublished; B. Martin, thesis, Universität Bonn (Bonn-IR-75-8) (1975), unpublished. Martin saw some indications of magnetic trapping.

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K. J. Kugler, W. Paul, U. Trinks, Phys. Lett. 72B, 422 (1978).

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V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Opt. Commun. 19, 72 (1976). This proposal was made in connection with cooling of trapped atoms.
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J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
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A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
[CrossRef] [PubMed]

H. Metcalf, W. Phillips, J. Prodan, Bull. Am. Phys. Soc. 29(795) 1984.

Phillips, W. D.

J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
[CrossRef] [PubMed]

J. Dalibard, W. D. Phillips, Bull. Am. Phys. Soc. 30, 748 (1985).

J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

J. V. Prodan, W. D. Phillips, Prog. Quantum Electron. 8, 231 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 137 (1983).
[CrossRef]

W. D. Phillips, J. V. Prodan, H. J. Metcalf, Prog. Quantum Electron. 8, 119 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 1 (1983).
[CrossRef]

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982).
[CrossRef]

J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

W. D. Phillips, Appl. Opt. 20, 3826 (1981).
[CrossRef] [PubMed]

W. D. Phillips, J. V. Prodan in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984), p. 15; W. D. Phillips, J. V. Prodan, H. J. Metcalf, in Laser Spectroscopy VI, H. P. Weber, W. Luthy, eds. (Springer-Verlag, Berlin, 1983), p. 162.
[CrossRef]

Poulsen, O.

Pritchard, D. E.

P. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
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D. E. Pritchard, Phys. Rev. Lett. 51, 1336 (1983); Prog. Quantum Electron. 8, 209 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 103 (1983).
[CrossRef]

Prodan, J.

A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
[CrossRef] [PubMed]

J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

H. Metcalf, W. Phillips, J. Prodan, Bull. Am. Phys. Soc. 29(795) 1984.

Prodan, J. V.

J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
[CrossRef] [PubMed]

J. V. Prodan, W. D. Phillips, Prog. Quantum Electron. 8, 231 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 137 (1983).
[CrossRef]

W. D. Phillips, J. V. Prodan, H. J. Metcalf, Prog. Quantum Electron. 8, 119 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 1 (1983).
[CrossRef]

J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

W. D. Phillips, J. V. Prodan in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984), p. 15; W. D. Phillips, J. V. Prodan, H. J. Metcalf, in Laser Spectroscopy VI, H. P. Weber, W. Luthy, eds. (Springer-Verlag, Berlin, 1983), p. 162.
[CrossRef]

Reynaud, S.

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4577 (1984).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 395 (1983).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 357 (1983).
[CrossRef]

Riis, E.

Rubin, K.

M. S. Lubell, K. Rubin, Prog. Quantum Electron. 8, 223 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed. Nat. Bur. Stand. (U.S.) Spec. Publ.653, 125 (1983).
[CrossRef]

Salamon, C.

W. Ertmer, R. Blatt, C. G. Aminoff, M. Zhu, C. Salamon, J. Hall, J. Opt. Soc. Am. B (to be published).

Schawlow, A.

Shaparev, N. Ya.

I. V. Krasnov, N. Ya. Shaparev, Zh. Eksp. Teor. Fiz. 77, 899 (1970) [Sov. Phys. JETP 50, 453 (1979)].

Sidorov, A. I.

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Zh. Eksp. Teor. Fiz. 86, 2019 (1984).

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Opt. Commun. 49, 248 (1984).
[CrossRef]

Sidorov, A-I.

V. I. Balykin, V. S. Letokhov, A-I. Sidorov, Pis’ma Zh. Eksp. Teor. Fiz. 40, 251 (1984).

Snyder, J. J.

J. J. Snyder, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1981).

So, I.

J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
[CrossRef] [PubMed]

Stenholm, S.

S. Stenholm, Phys. Rev. A 27, 2513 (1983).
[CrossRef]

S. Stenholm, Phys. Rep. 43, 151 (1978). Section 6 contains an early review of mechanical effects of light.
[CrossRef]

P. R. Berman, S. Stenholm, Opt. Commun. 24, 155 (1978).
[CrossRef]

Stern, O.

O. Stern, Z. Phys. 7, 249 (1921); W. Gerlach, O. Stern, Ann. Phy. 74, 673 (1924); Ann. Phy. 76, 163 (1925).
[CrossRef]

Stwalley, W.

W. Stwalley, Prog. Quantum Electron. 8, 203 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 95 (1983).
[CrossRef]

Toschek, P.

W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978).
[CrossRef]

Toschek, P. E.

W. Neuhauser, M. Hohenstatt, P. E. Toschek, H. Dehmelt, Phys. Rev. A 22, 1137 (1980).
[CrossRef]

Trinks, U.

W. Paul, U. Trinks, Inst. Phys. Conf. Ser. No. 42, p. 18 (1978).

K. J. Kugler, W. Paul, U. Trinks, Phys. Lett. 72B, 422 (1978).

Vladimirskii, V. V.

V. V. Vladimirskii, Zh. Eksp. Teor. Fiz. 39, 1062 (1960) [Sov. Phys. JETP 12, 740 (1961)].

Walls, F.

D. Wineland, R. Drullinger, F. Walls, Phys. Rev. Lett. 40, 1639 (1978).
[CrossRef]

Whitney, W. T.

N. Djeu, W. T. Whitney, Phys. Rev. Lett. 46, 236 (1981).
[CrossRef]

Wineland, D.

D. Wineland, W. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

D. Wineland, R. Drullinger, F. Walls, Phys. Rev. Lett. 40, 1639 (1978).
[CrossRef]

D. Wineland, H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975).

Wing, W.

W. Wing, Phys. Rev. Lett. 45, 631 (1980); Prog. Quantum Electron. 8, 181 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 74 (1983).
[CrossRef]

Zhu, M.

W. Ertmer, R. Blatt, J. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

W. Ertmer, R. Blatt, C. G. Aminoff, M. Zhu, C. Salamon, J. Hall, J. Opt. Soc. Am. B (to be published).

Zorn, J.

J. Zorn, presented at Ninth International Conference on Atomic Physics, Seattle, Wash., July 23–27, 1984 (preprint, R. S. Van-Dyck, E. N. Fortson, eds., p. B22).

Zueva, T. V.

V. I. Balykin, V. S. Letokhov, V. G. Minogin, T. V. Zueva, Appl. Phys. B 35, 149 (1984).
[CrossRef]

T. V. Zueva, V. G. Minogin, Pis’ma Zh. Tekh. Fiz. 7, 953 (1981) [Sov. Tech. Phys. Lett. 7, 411 (1981)].

T. V. Zueva, V. S. Ketokhov, V. G. Minogin, Zh. Eksp. Teor. Fiz. 81, 84 (1981) [Sov. Phys. JETP 54, 38 (1981)].

Adv. At. Mol. Phys. (1)

H. Dehmelt, Adv. At. Mol. Phys. 3, 53 (1967).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

V. I. Balykin, V. S. Letokhov, V. G. Minogin, T. V. Zueva, Appl. Phys. B 35, 149 (1984).
[CrossRef]

Bull. Am. Phys. Soc. (4)

J. Prodan, W. D. Phillips, J. Dalibard, H. Metcalf, Bull. Am. Phys. Soc. 29(822) 1984.

H. Metcalf, W. Phillips, J. Prodan, Bull. Am. Phys. Soc. 29(795) 1984.

D. Wineland, H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975).

J. Dalibard, W. D. Phillips, Bull. Am. Phys. Soc. 30, 748 (1985).

Inst. Phys. Conf. Ser. No. 42 (1)

W. Paul, U. Trinks, Inst. Phys. Conf. Ser. No. 42, p. 18 (1978).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Phys. (1)

V. S. Letokhov, V. G. Minogin, J. Phys. 42, C8-374 (1981).

J. Phys. B (1)

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4577 (1984).
[CrossRef]

J. Phys. Rad. (1)

A. Kastler, J. Phys. Rad. 11, 255 (1950).
[CrossRef]

Kvantovaya Electron. (Moscow) (1)

V. G. Minogin, Kvantovaya Electron. (Moscow) 9, 505 (1982) [Sov. J. Quantum Electron. 12, 299 (1982)].

Naturwissenschaften (1)

H. Friedburg, W. Paul, Naturwissenschaften 38, 159 (1951); Z. Phys. 130, 493 (1951).
[CrossRef]

Opt. Commun. (12)

R. Cook, Opt. Commun. 35, 347 (1981).
[CrossRef]

L. Moi, Opt. Commun. 50, 349 (1984); J. Liang, L. Moi, C. Fabre, Opt. Commun. 52, 131 (1985).
[CrossRef]

V. I. Balykin, Opt. Commun. 33, 31 (1980).
[CrossRef]

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Opt. Commun. 49, 248 (1984).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 357 (1983).
[CrossRef]

T. Hänsch, A. Schawlow, Opt. Commun. 13, 68 (1975).
[CrossRef]

P. R. Berman, S. Stenholm, Opt. Commun. 24, 155 (1978).
[CrossRef]

V. S. Letokhov, V. G. Minogin, B. D. Pavlik, Opt. Commun. 19, 72 (1976). This proposal was made in connection with cooling of trapped atoms.
[CrossRef]

V. G. Minogin, Opt. Commun. 34, 265 (1980).
[CrossRef]

V. G. Minogin, J. Javanainen, Opt. Commun. 43, 119 (1982).
[CrossRef]

J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, Opt. Commun. 47, 395 (1983).
[CrossRef]

R. Cook, R. Hill, Opt. Commun. 43, 258 (1982).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. (1)

K. J. Kugler, W. Paul, U. Trinks, Phys. Lett. 72B, 422 (1978).

Phys. Rep. (2)

S. Stenholm, Phys. Rep. 43, 151 (1978). Section 6 contains an early review of mechanical effects of light.
[CrossRef]

V. S. Letokhov, V. G. Minogin, Phys. Rep. 73, 1 (1981). Much of the early work on laser trapping and cooling is reviewed in this paper.
[CrossRef]

Phys. Rev. A (6)

D. Wineland, W. Itano, Phys. Rev. A 20, 1521 (1979).
[CrossRef]

S. Stenholm, Phys. Rev. A 27, 2513 (1983).
[CrossRef]

R. J. Cook, Phys. Rev. A 22, 1078 (1980).
[CrossRef]

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

E. Giacombino et al., Phys. Rev. A 28, 2555 (1983); E. Giabobino, P. A. Berman, Prog. Quantum Electron. 8, 215 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 112 (1983).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. E. Toschek, H. Dehmelt, Phys. Rev. A 22, 1137 (1980).
[CrossRef]

Phys. Rev. Lett. (17)

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985).
[CrossRef] [PubMed]

T. Breeden, H. Metcalf, Phys. Rev. Lett. 47, 1726 (1981).
[CrossRef]

N. Djeu, W. T. Whitney, Phys. Rev. Lett. 46, 236 (1981).
[CrossRef]

D. E. Pritchard, Phys. Rev. Lett. 51, 1336 (1983); Prog. Quantum Electron. 8, 209 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 103 (1983).
[CrossRef]

W. Wing, Phys. Rev. Lett. 45, 631 (1980); Prog. Quantum Electron. 8, 181 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 74 (1983).
[CrossRef]

D. Wineland, R. Drullinger, F. Walls, Phys. Rev. Lett. 40, 1639 (1978).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970); Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

R. J. Cook, Phys. Rev. Lett. 44, 976 (1980).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
[CrossRef]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

P. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

A. Migdall, J. Prodan, W. Phillips, T. Bergeman, H. Metcalf, Phys. Rev. Lett. 54, 2596 (1985).
[CrossRef] [PubMed]

W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 48, 596 (1982).
[CrossRef]

J. V. Prodan, W. D. Phillips, H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

W. Ertmer, R. Blatt, J. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

J. V. Prodan, A. Migdall, W. D. Phillips, I. So, H. Metcalf, J. Dalibard, Phys. Rev. Lett. 54, 992 (1985).
[CrossRef] [PubMed]

Pis’ma Zh. Eksp. Teor. Fiz. (3)

V. I. Balykin, V. S. Letokhov, A-I. Sidorov, Pis’ma Zh. Eksp. Teor. Fiz. 40, 251 (1984).

S. V. Andreev, V. I. Balykin, V. S. Letokhov, V. G. Minogin, Pis’ma Zh. Eksp. Teor. Fiz. 34, 463 (1981) [JETP Lett. 34, 442 (1981)].

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Pis’ma Zh. Eksp. Teor. Fiz. 29, 614 (1979) [JETP Lett. 29, 560 (1979)].

Pis’ma Zh. Tekh. Fiz. (1)

T. V. Zueva, V. G. Minogin, Pis’ma Zh. Tekh. Fiz. 7, 953 (1981) [Sov. Tech. Phys. Lett. 7, 411 (1981)].

Pisma Zh. Eksp. Teor. Fiz. (1)

V. S. Letokhov, Pisma Zh. Eksp. Teor. Fiz. 7, 348 (1968) [JETP Lett. 7, 272 (1968)].

Prog. Quantum Electron. (7)

W. Stwalley, Prog. Quantum Electron. 8, 203 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 95 (1983).
[CrossRef]

H. Metcalf, Prog. Quantum Electron. 8, 169 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 59 (1983).
[CrossRef]

W. D. Phillips, J. V. Prodan, H. J. Metcalf, Prog. Quantum Electron. 8, 119 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 1 (1983).
[CrossRef]

M. S. Lubell, K. Rubin, Prog. Quantum Electron. 8, 223 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed. Nat. Bur. Stand. (U.S.) Spec. Publ.653, 125 (1983).
[CrossRef]

R. Blatt, W. Ertmer, J. L. HallProg. Quantum Electron. 8, 237 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 142 (1983).
[CrossRef]

J. V. Prodan, W. D. Phillips, Prog. Quantum Electron. 8, 231 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ.653, 137 (1983).
[CrossRef]

W. Ertmer, R. Blatt, J. Hall, Prog. Quantum Electron. 8, 249 (1984); in Laser-Cooled and Trapped Atoms, W. D. Phillips, ed., Nat. Bur. Stand. (U.S.) Spec. Publ. 653, 154 (1983).
[CrossRef]

Rev. Sci. Instrum. (1)

C. V. Heer, Rev. Sci. Instrum. 34, 532 (1963).
[CrossRef]

Science (1)

A. Ashkin, Science 210, 1081 (1980). This contains references to early work on both atom trapping and trapping of macroscopic particles.
[CrossRef] [PubMed]

Usp. Fiz. Nauk (1)

A. P. Kazantsev, Usp. Fiz. Nauk 124, 113 (1978) Sov. Phys. Usp. 21, 58 (1978)].

Z. Phys. (3)

R. Frisch, Z. Phys. 86, 42 (1933).
[CrossRef]

O. Stern, Z. Phys. 7, 249 (1921); W. Gerlach, O. Stern, Ann. Phy. 74, 673 (1924); Ann. Phy. 76, 163 (1925).
[CrossRef]

E. Fischer, Z. Phys. 156, 1 (1959); R. Wuenker, H. Shelton, R. V. Langmuir, J. Appl. Phys. 30, 342 (1958).
[CrossRef]

Zh. Eksp. Teor. Fiz. (5)

V. V. Vladimirskii, Zh. Eksp. Teor. Fiz. 39, 1062 (1960) [Sov. Phys. JETP 12, 740 (1961)].

V. I. Balykin, V. S. Letokhov, A. I. Sidorov, Zh. Eksp. Teor. Fiz. 86, 2019 (1984).

V. I. Balykin, V. S. Letokhov, V. I. Mushin, Zh. Eksp. Teor. Fiz. 78, 1376 (1980) [Sov. Phys. JETP 51, 692 (1980)].

T. V. Zueva, V. S. Ketokhov, V. G. Minogin, Zh. Eksp. Teor. Fiz. 81, 84 (1981) [Sov. Phys. JETP 54, 38 (1981)].

I. V. Krasnov, N. Ya. Shaparev, Zh. Eksp. Teor. Fiz. 77, 899 (1970) [Sov. Phys. JETP 50, 453 (1979)].

Other (14)

F. C. Hansen, K. Harvey, University of Michigan (personal communication, 1984).

J. Zorn, presented at Ninth International Conference on Atomic Physics, Seattle, Wash., July 23–27, 1984 (preprint, R. S. Van-Dyck, E. N. Fortson, eds., p. B22).

N. Niehues, thesis, Universität Bonn (Bonn-IR-76-35) (1976), unpublished; B. Martin, thesis, Universität Bonn (Bonn-IR-75-8) (1975), unpublished. Martin saw some indications of magnetic trapping.

A. Migdall, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1983).

J. J. Snyder, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1981).

W. Ertmer, R. Blatt, C. G. Aminoff, M. Zhu, C. Salamon, J. Hall, J. Opt. Soc. Am. B (to be published).

J. C. Berquist, R. L. Barger, D. J. Glaze, in Laser Spectroscopy IV, H. Walther, K. Rothe, eds. (Springer-Verlag, Berlin, 1979), p. 120; R. L. Barger, Opt. Lett. 6, 145 (1981).
[CrossRef] [PubMed]

W. D. Phillips, J. V. Prodan in Coherence and Quantum Optics V, L. Mandel, E. Wolf, eds. (Plenum, New York, 1984), p. 15; W. D. Phillips, J. V. Prodan, H. J. Metcalf, in Laser Spectroscopy VI, H. P. Weber, W. Luthy, eds. (Springer-Verlag, Berlin, 1983), p. 162.
[CrossRef]

A. Migdall, National Bureau of Standards, Gaithersburg, Md. (personal communication, 1985).

J. Dalibard, École Normale Supérieure, Paris (personal communication, 1984).

The placement of the coils at 30-deg latitudes, as indicated in some papers, does not produce zero field at the origin unless the currents are unequal. It is a simple exercise to determine the optimal placements and currents for particular application.

W. Paul, Universität Bonn (personal communication, 1985).

T. Bergeman, H. Metcalf, presented at the Ninth Interntional Conference on Atomic Physics, Seattle, Wash., July 23–27, 1984 (preprint, R. S. VanDyck, E. N. Fortson, eds.)

C. Edge, University of Virginia (personal communication, 1985).

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Figures (16)

Fig. 1
Fig. 1

Na energy-level diagram (not to scale).

Fig. 2
Fig. 2

Na energy levels in a magnetic field (not to scale). The nuclear quantum number mI = mFmJ.

Fig. 3
Fig. 3

Simplified schematic of Balykin et al. apparatus.36 The reference beam crosses the laser at right angles and provides a calibration marker for the laser scan.

Fig. 4
Fig. 4

Apparatus of Andreev et al.38

Fig. 5
Fig. 5

Deceleration and cooling similar to that observed by Andreev et al. using the nonresonant technique. Dashed curve is the atomic velocity distribution before cooling; solid curve is after cooling.

Fig. 6
Fig. 6

The apparatus of the present authors.

Fig. 7
Fig. 7

Timing diagrams for prompt observation of (a) cooled atoms, (b) delayed observation, and (c) postcooling.

Fig. 8
Fig. 8

Results of Zeeman-tuned cooling. Arrow indicates the highest velocity resonant with the cooling laser. The velocity scale refers only to F = 2 atoms.

Fig. 9
Fig. 9

Laser-cooled velocity distributions for different laser tunings. The highest velocity resonant with the laser in each case is indicated by the arrows. Trace (g) is the uncooled velocity distribution.

Fig. 10
Fig. 10

Velocity distributions obtained with Zeeman-tuned cooling and delayed observation. The delay times are indicated for each curve.

Fig. 11
Fig. 11

Effect of postcooling after a 10-msec delay. The sloping baseline is from the uncooled thermal distribution, Zeeman shifted into resonance with the probe.

Fig. 12
Fig. 12

Velocity changes versus laser tuning for postcooling after a 6-msec delay. The arrow indicates the frequency that is resonant with the atomic velocity before postcooling.

Fig. 13
Fig. 13

Chirp-cooled velocity distribution (solid line) compared with the uncooled thermal distribution (dashed line).

Fig. 14
Fig. 14

Apparatus of the NBS—JILA group.56

Fig. 15
Fig. 15

Chirped-cooling results of the NBS–JILA group.56 The velocity scale is for the F = 2 atoms only.

Fig. 16
Fig. 16

Optical trap formed from two opposed, diverging laser beams with Gaussian intensity profiles. When tuned below resonance the trap provides transverse confinement by the dipole force. Longitudinal confinement is from radiation pressure.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

a max = Δ v / 2 τ = h ν / 2 M c τ 10 6 m / sec 2 .
v ( z ) = ( v 0 2 - 2 a z ) 1 / 2 .
B ( z ) = B 0 ( 1 - x ) 1 / 2 ,             x = 2 a z / v 0 2 ,
d ν d B d B d z · v a max / λ ,
μ r c ( d B / d r ) v 0 r c , r c 2 v 0 μ ( d B / d r ) ,
r 3 2 μ ( d B / d r ) M ,
n v A 4 = n V τ dif
n n = v A τ dif 4 V = 3 v r 4 v c 2 τ cool ,

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