Abstract

Cooling that results from optical dipole forces is considered for a bound atom. Through optical pumping, the atom can be made to feel decelerating optical dipole forces more strongly than accelerating optical dipole forces. This effect, which has previously been realized for free atoms, is called Sisyphus cooling. A simple model for a bound atom is examined in order to reveal the basic aspects of cooling and heating when the atom is confined in the Lamb–Dicke regime. Results of semiclassical and quantum treatments show that the minimum energy achieved is near the zero-point energy and can be much lower than the Doppler cooling limit. Two practical examples that approximate the model are briefly examined.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. For a review of early experiments and theory see W. D. Phillips, ed., Laser Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics (Pergamon, Oxford, 1984); P. Meystre and S. Stenholm, eds. feature on the mechanical effects of light, J. Opt. Soc. Am. 2, 1705 (1985); S. Stenholm, Rev. Mod. Phys.,  58, 699 (1986); D. J. Wineland and W. M. Itano, Phys. Today 40(6), 34 (1987).
    [CrossRef]
  2. P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
    [CrossRef] [PubMed]
  3. J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
    [CrossRef]
  4. S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
    [CrossRef]
  5. P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, J. Opt. Soc. Am. B 6, 2084 (1989).
    [CrossRef]
  6. B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
    [CrossRef] [PubMed]
  7. See S. Chu and C. Wieman, eds., feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2109 (1990); L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and F. Strumia, eds., Light Induced Kinetic Effects on Atoms, Ions, and Molecules (ETS Editrice, Pisa, 1991).
  8. C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43(10), 33 (1990).
    [CrossRef]
  9. J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
    [CrossRef]
  10. A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974) [Sov. Phys. JETP 39, 784 (1974)]; A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovitch, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
    [CrossRef]
  11. V. G. Minogin and O. T. Serimaa, Opt. Commun. 30, 123 (1977).
  12. T. Breeden and H. Metcalf, Phys. Rev. Lett. 47, 1726 (1981).
    [CrossRef]
  13. D. Pritchard, Phys. Rev. Lett. 51, 1336 (1983).
    [CrossRef]
  14. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
    [CrossRef] [PubMed]
  15. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
    [CrossRef] [PubMed]
  16. Sideband cooling in the resolved sideband limit could also be obtained by using stimulated Raman scattering. See, for example, M. Lindberg and J. Javanainen, J. Opt. Soc. Am. B 3, 1008 (1986); H. Dehmelt, G. Janik, and W. Nagourney, Bull. Am. Phys. Soc. 30, 111 (1988); P. E. Toschek and W. Neuhauser, J. Opt. Soc. Am B 6, 2220 (1989); D. J. Heinzen and D. J. Wineland, Phys. Rev. A 42, 2977 (1990).
    [CrossRef] [PubMed]
  17. T. V. Zueva and V. G. Minogin, Sov. Tech. Phys. Lett. 7, 411 (1981); L. Moi, Opt. Commun. 50, 349 (1984); J. Liang and C. Fabre, Opt. Commun. 59, 131 (1986); D. E. Pritchard, K. Helmerson, V. S. Bagnato, G. P. Lafayatis, and A. G. Martin, in Laser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Berlin, 1987), p. 68; J. Hoffnagle, Opt. Lett. 13, 102 (1988); H. Wallis and W. Ertmer, J. Opt. Soc. Am. B 6, 2211 (1989).
    [CrossRef]
  18. Y. Castin and J. Dalibard, Europhys. Lett. 16, 761 (1991).
    [CrossRef]
  19. D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
    [CrossRef]
  20. S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).
  21. These results may be derived from more-general density matrix treatments. See, for example, Ref. 20 and V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).
    [CrossRef]
  22. W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
    [CrossRef]

1991 (1)

Y. Castin and J. Dalibard, Europhys. Lett. 16, 761 (1991).
[CrossRef]

1990 (3)

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

See S. Chu and C. Wieman, eds., feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2109 (1990); L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and F. Strumia, eds., Light Induced Kinetic Effects on Atoms, Ions, and Molecules (ETS Editrice, Pisa, 1991).

C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43(10), 33 (1990).
[CrossRef]

1989 (2)

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, J. Opt. Soc. Am. B 6, 2084 (1989).
[CrossRef]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

1988 (2)

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

1986 (1)

1985 (1)

1983 (1)

D. Pritchard, Phys. Rev. Lett. 51, 1336 (1983).
[CrossRef]

1982 (1)

W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
[CrossRef]

1981 (2)

T. V. Zueva and V. G. Minogin, Sov. Tech. Phys. Lett. 7, 411 (1981); L. Moi, Opt. Commun. 50, 349 (1984); J. Liang and C. Fabre, Opt. Commun. 59, 131 (1986); D. E. Pritchard, K. Helmerson, V. S. Bagnato, G. P. Lafayatis, and A. G. Martin, in Laser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Berlin, 1987), p. 68; J. Hoffnagle, Opt. Lett. 13, 102 (1988); H. Wallis and W. Ertmer, J. Opt. Soc. Am. B 6, 2211 (1989).
[CrossRef]

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

1979 (1)

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

1977 (1)

V. G. Minogin and O. T. Serimaa, Opt. Commun. 30, 123 (1977).

1974 (1)

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974) [Sov. Phys. JETP 39, 784 (1974)]; A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovitch, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

Arimondo, E.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Bergquist, J. C.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

Breeden, T.

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

Castin, Y.

Y. Castin and J. Dalibard, Europhys. Lett. 16, 761 (1991).
[CrossRef]

Chebotayev, V. P.

These results may be derived from more-general density matrix treatments. See, for example, Ref. 20 and V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).
[CrossRef]

Chu, S.

S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43(10), 33 (1990).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

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

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Dalibard, J.

Y. Castin and J. Dalibard, Europhys. Lett. 16, 761 (1991).
[CrossRef]

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

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Diedrich, F.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

Gould, P.

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Hatamian, S.

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

Itano, W. M.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
[CrossRef]

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

Javanainen, J.

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Kazantsev, A. P.

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974) [Sov. Phys. JETP 39, 784 (1974)]; A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovitch, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

Letokhov, V. S.

These results may be derived from more-general density matrix treatments. See, for example, Ref. 20 and V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).
[CrossRef]

Lett, P.

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Lett, P. D.

Lindberg, M.

Metcalf, H.

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

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

Minogin, V. G.

T. V. Zueva and V. G. Minogin, Sov. Tech. Phys. Lett. 7, 411 (1981); L. Moi, Opt. Commun. 50, 349 (1984); J. Liang and C. Fabre, Opt. Commun. 59, 131 (1986); D. E. Pritchard, K. Helmerson, V. S. Bagnato, G. P. Lafayatis, and A. G. Martin, in Laser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Berlin, 1987), p. 68; J. Hoffnagle, Opt. Lett. 13, 102 (1988); H. Wallis and W. Ertmer, J. Opt. Soc. Am. B 6, 2211 (1989).
[CrossRef]

V. G. Minogin and O. T. Serimaa, Opt. Commun. 30, 123 (1977).

Phillips, W. D.

C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43(10), 33 (1990).
[CrossRef]

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, J. Opt. Soc. Am. B 6, 2084 (1989).
[CrossRef]

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Pritchard, D.

D. Pritchard, Phys. Rev. Lett. 51, 1336 (1983).
[CrossRef]

Rolston, S. L.

Salomon, C.

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Serimaa, O. T.

V. G. Minogin and O. T. Serimaa, Opt. Commun. 30, 123 (1977).

Shang, S-Q.

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

Sheehy, B.

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

Shevy, Y.

S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

Stenholm, S.

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

Tanner, C. E.

Ungar, P. J.

S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

van der Straten, P.

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

Vansteenkiste, N.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Watts, R.

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Watts, R. N.

Weiss, D. S.

S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

Westbrook, C.

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Westbrook, C. I.

Wineland, D. J.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
[CrossRef]

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

Zueva, T. V.

T. V. Zueva and V. G. Minogin, Sov. Tech. Phys. Lett. 7, 411 (1981); L. Moi, Opt. Commun. 50, 349 (1984); J. Liang and C. Fabre, Opt. Commun. 59, 131 (1986); D. E. Pritchard, K. Helmerson, V. S. Bagnato, G. P. Lafayatis, and A. G. Martin, in Laser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Berlin, 1987), p. 68; J. Hoffnagle, Opt. Lett. 13, 102 (1988); H. Wallis and W. Ertmer, J. Opt. Soc. Am. B 6, 2211 (1989).
[CrossRef]

Europhys. Lett. (1)

Y. Castin and J. Dalibard, Europhys. Lett. 16, 761 (1991).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

V. G. Minogin and O. T. Serimaa, Opt. Commun. 30, 123 (1977).

Phys. Rev. A (2)

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

W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
[CrossRef]

Phys. Rev. Lett. (6)

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

D. Pritchard, Phys. Rev. Lett. 51, 1336 (1983).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Opt. Soc. Am. B 6, 2112 (1989).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 62, 403 (1989); W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, Phys. Rev. Lett. 41, 233 (1978); D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987).
[CrossRef] [PubMed]

B. Sheehy, S-Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, Phys. Rev. Lett. 64, 858 (1990); S-Q. Shang, B. Sheehy, P. van der Straten, and H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
[CrossRef] [PubMed]

P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, and H. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Phys. Today (1)

C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43(10), 33 (1990).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

T. V. Zueva and V. G. Minogin, Sov. Tech. Phys. Lett. 7, 411 (1981); L. Moi, Opt. Commun. 50, 349 (1984); J. Liang and C. Fabre, Opt. Commun. 59, 131 (1986); D. E. Pritchard, K. Helmerson, V. S. Bagnato, G. P. Lafayatis, and A. G. Martin, in Laser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Berlin, 1987), p. 68; J. Hoffnagle, Opt. Lett. 13, 102 (1988); H. Wallis and W. Ertmer, J. Opt. Soc. Am. B 6, 2211 (1989).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

A. P. Kazantsev, Zh. Eksp. Teor. Fiz. 66, 1599 (1974) [Sov. Phys. JETP 39, 784 (1974)]; A. P. Kazantsev, V. S. Smirnov, G. I. Surdutovitch, D. O. Chudesnikov, and V. P. Yakovlev, J. Opt. Soc. Am. B 2, 1731 (1985).
[CrossRef]

Other (5)

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 199; J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

S. Chu, D. S. Weiss, Y. Shevy, and P. J. Ungar, in Atomic Physics 11, S. Haroche, J. C. Gay, and G. Grynberg, eds. (World Scientific, Singapore, 1989), p. 636; P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989); D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

These results may be derived from more-general density matrix treatments. See, for example, Ref. 20 and V. S. Letokhov and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).
[CrossRef]

For a review of early experiments and theory see W. D. Phillips, ed., Laser Cooled and Trapped Atoms, Vol. 8 of Progress in Quantum Electronics (Pergamon, Oxford, 1984); P. Meystre and S. Stenholm, eds. feature on the mechanical effects of light, J. Opt. Soc. Am. 2, 1705 (1985); S. Stenholm, Rev. Mod. Phys.,  58, 699 (1986); D. J. Wineland and W. M. Itano, Phys. Today 40(6), 34 (1987).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Model system. (a) The atom has three internal energy levels: g, e, and r. A standing-wave laser beam drives ge above its resonance frequency. Level e decays with branching fraction β to level r and with branching fraction 1 − β to level g. Transfer from level r to g occurs at a rate Rrg. (b) The atom is assumed to be confined by a harmonic well in the x direction. The maximum extent of the atom’s motion is assumed to be less than λ/2π (Lamb–Dicke regime).

Fig. 2
Fig. 2

Qualitative explanation of the cooling. When the atom is in state r, it experiences the confining potential Ur(x), which is unperturbed by the laser fields. When the atom is in level g, the potential well is shifted in the +x direction by the dipole force of the laser. This shifted potential is represented by Ug(x). The laser excitation is assumed to be weak enough that the atom spends a negligible amount of time in level e. Therefore the spontaneous Raman transitions ger can be represented by transitions between g and r such as those indicated by (I) and (II) in the figure. Process (I) is favored more than process (II) because, when the atom is on the left-hand side of the well Ug, the chance of ge excitation is higher since the laser intensity is higher [see Fig. 1(b)]. Process (I) leads to cooling because the atom drops to a lower part of the well Ur. Process (II) causes heating and, along with the heating resulting from recoil, eventually balances the cooling, resulting in a minimum energy.

Fig. 3
Fig. 3

Diagram for the cooling when the motion is quantized. Each electronic state has a sublevel structure of harmonic-oscillator levels labeled by the quantum numbers nj, where j = g, e, or r. Cooling is represented by scattering processes of the form ngnenr, where nr < ng. This may be viewed as due to spontaneous Raman scattering off states |g, ng〉′ and |e, ne〉″, which are dressed by the laser.

Fig. 4
Fig. 4

The cooling described in the text could be approximately realized by a trapped 24Mg+ ion in a magnetic field. A specific case is illustrated for the levels labeled g, e, and r in (a). Transfer from level r to level g could be realized with microwave radiation tuned to the rg transition. This transfer could also be accomplished by spontaneous Raman transitions re′ → g by using a traveling-wave laser beam (laser 2 in the figure) tuned to the re′ transition. In this case additional recoil heating must be accounted for (see the text). Another case that would apply to an ion or an atom with an outer unpaired electron and a spin 1/2 nucleus (and no intermediate electronic states) is shown in (b). Here the magnetic field is assumed to be small enough that the Zeeman structure is unresolved. Transfer from r to g through spontaneous Raman transitions (laser 2) is indicated in the figure.

Equations (72)

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

E = ( E max / 2 ) [ cos ( k x - ω t ) + cos ( k x + ω t ) ] = E max cos ω t cos k x ,
R g r , R r g ω v Γ δ ,
s 2 ω 1 2 4 δ 2 + Γ 2 1.
R g r E max 2 2 cos 2 ( k x ) I ( x = π 4 k ) [ 1 - 2 k ( x - π 4 k ) ] .
π ˙ g = - R g e ( x ) ( π g - π e ) + R r g π r + ( 1 - β ) Γ π e ,
π ˙ e = R g e ( x ) ( π g - π e ) - Γ π e ,
π ˙ r = - R r g π r + β Γ π e ,
R g e ( x ) = ( Γ s / 2 ) cos 2 ( k x ) .
π e = π g ( s / 2 ) cos 2 ( k x ) ,
π ˙ g = - R g r ( x ) π g + R r g π r ,
π ˙ r = - π ˙ g ,
R g r ( x ) = β R g e ( x ) = β ( Γ s / 2 ) cos 2 ( k x ) .
π g st = R r g R g r + R r g ,
π r st = R g r R g r + R r g ,
1 / τ int = R g r + R r g .
U r ( x ) = U 0 ( x ) = ½ m ω v 2 ( x - x r 0 ) 2 .
U L ( x ) = 2 [ ω 1 2 cos 2 ( k x ) + δ 2 ] 1 / 2 - 2 δ U L 0 cos 2 ( k x ) ,
U L 0 = ω 1 2 / 4 δ
U g ( x ) = U r ( x ) + U L ( x ) .
U L ( x ) U L 0 / 2 - k U L 0 ( x - x r 0 ) .
Δ x 0 = x g 0 - x r 0 = 2 ξ ( k x 0 ) x 0 ,
ξ = U L 0 / ω v
E ˙ x = π g R g r ( x ) [ U r ( x ) - U g ( x ) ] + π r R r g U g ( x ) - U r ( x ) + π g R g e ( x ) 2 R .
R g r ( x ) β ( Γ s / 4 ) [ 1 - 2 k ( x - x r 0 ) ] ,
E x = 2 1 2 m ω v 2 ( x - x g 0 ) 2 .
E ˙ x = - ( 1 / τ s ) ( E x - E x 0 ) ,
E x 0 = m ω v 2 ( Δ x 0 ) 2 k + R k β ( Δ x 0 ) = U L 0 2 ( 1 + 1 ξ 2 β ) = ω v 2 ( ξ + 1 ξ β )
1 τ s = 4 R g r R r g R g r + R r g ( R ω ν ) ξ .
E x 0 min = ω v / β = U L 0 .
Γ g , n g r , n r = C | n e n r exp ( - i k s · X n e { n e } f ( X ) n g δ - ( E n e - E n g ) / + i Γ / 2 | 2 ,
Γ g , n g r , n r = β ( C / δ 2 ) n r exp ( - i k s · X ) f ( X ) n g 2 .
Γ g , n g g , n g * = ( 1 - β ) ( C / δ 2 ) { n g * } exp ( - i k s · X ) f ( X ) n g 2 ,
Γ r , n r g , n g = C { n g } 1 n r 2 ,
n g = exp ( - i Δ x 0 P x / ) n g ,
X = x 0 ( a + a ) ,
P x = i x 0 m ω v ( a - a ) .
Γ g , n g r , n r = β ( C / δ 2 ) n r A 1 n g 2 ,
Γ g , n g g , n g * = ( 1 - β ) ( C / δ 2 ) n g * A 2 n g 2 ,
Γ r , n r g , n g = C n g A 3 n r 2 ,
A 1 = exp ( - i k s X ) f ( X ) exp ( - i Δ x 0 P x / ) ,
A 2 = exp ( i Δ x 0 P x / ) exp ( - i k s X ) f ( X ) exp ( - i Δ x 0 P x / ) ,
A 3 = exp ( - i Δ x 0 P x / )
A 1 1 - k x 0 [ a ( 1 - ξ + i k s / k ) + a ( 1 + ξ + i k s / k ) ] ,
A 2 1 - k x 0 ( a + a ) ( 1 + i k s / k ) ,
A 3 1 + ξ k x 0 ( a - a ) .
Γ g , n r , n = β C δ 2 R g r ,
Γ g , n r , n + 1 = R g r ( k x 0 ) 2 ( n + 1 ) [ 1 + ( 1 - ξ ) 2 ] ,
Γ g , n r , n - 1 = R g r ( k x 0 ) 2 n [ 1 + ( 1 + ξ ) 2 ] ,
Γ r , n g , n = C R r g ,
Γ r , n g , n + 1 = R r g ( k x 0 ) 2 ( n + 1 ) ξ 2 = ( n + 1 n ) Γ r , n g , n - 1 ,
Γ g , n g , n + 1 = 1 - β β R g r 2 ( k x 0 ) 2 ( n + 1 ) = ( n + 1 n ) Γ g , n g , n - 1 .
π ˙ g , n = n = n - 1 n + 1 i = g , r ( - Γ g , n i , n π g , n + Γ i , n g , n π i , n ) ,
π ˙ r , n = n = n - 1 n + 1 ( - Γ r , n g , n π r , n + Γ g , n r , n π g , n ) ,
( Γ g , n r , n + 1 + Γ g , n g , n + 1 ) π g , n + Γ r , n g , n + 1 π r , n = ( Γ g , n + 1 r , n + Γ g , n + 1 g , n ) π g , n + 1 + Γ r , n + 1 g , n π r , n + 1 .
π g n Γ r , n g , n Γ g , n r , n + Γ r , n g , n π n ,
π r n Γ g , n r , n Γ g , n r , n + Γ r , n g , n π n .
π n + 1 π n = 1 + β ξ ( ξ - 1 ) 1 + β ξ ( ξ + 1 ) ,
( π n + 1 π n ) min = 2 - β 2 + β .
π n + 1 π n = exp ( - ω v k B T ) ,
n v = [ 1 + β ξ ( ξ - 1 ) ] / 2 β ξ .
n v = β - 1 / 2 - 1 / 2.
E x 0 min = ω v ( n v + 1 / 2 ) = ω v β - 1 / 2 ,
τ D - 1 = - 2 R S D k 2 δ D { m [ ( Γ / 2 ) 2 + δ D 2 ] } - 1 ,
τ D - 1 = 4 R S D R / Γ .
τ s - 1 τ D - 1 = ( Γ ω v ) ( R g r R S D ) ξ .
τ D - 1 = ( 4 π g R g r β ) R δ = ( 4 β ) ( R g r R r g R g r + R r g ) ( R δ ) .
τ D - 1 τ S - 1 = ( 1 β ξ ) ω v δ 1.
E ˙ x = E ˙ x + π r R r e ( 2 R ) ,
T = ω v / [ k B ln ( 1 + n v - 1 ) ] .
ζ = 1 k | [ d I / d x i ] x i ( 0 ) 2 I [ x i ( 0 ) ] | ,
E x 0 = U L 0 1 + 1 / ξ 2 ζ 2 β 2 .
E x 0 min = ω v / ζ β .

Metrics