Abstract

We derive expressions for the damping rate for a two-level atom trapped in the antinodes of an optical interference pattern. We find that the decay rate is much slower than the rate for untrapped atoms in optical molasses. Although the velocity of untrapped atoms decays exponentially in time, the velocity of trapped atoms decays only as t−1/2. We show that the slow damping rate can be circumvented by the addition of a traveling-wave component to the molasses standing wave and discuss how these results can be extended to multilevel atoms.

© 1990 Optical Society of America

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  1. N. P. Bigelow, M. G. Prentiss, Phys. Rev. Lett. 65, 29 (1990).
    [CrossRef] [PubMed]
  2. C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
    [CrossRef] [PubMed]
  3. S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).
  4. E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
    [CrossRef] [PubMed]
  5. J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).
  6. B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
    [CrossRef]
  7. S.-Q. Shang, B. Sheehy, P. van der Straten, H. Metcalf, Phys. Rev. Lett. 65, 317 (1990).
    [CrossRef] [PubMed]
  8. C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
    [CrossRef]
  9. J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
    [CrossRef]
  10. A. Ashkin, Phys. Rev. Lett. 40, 729 (1978).
    [CrossRef]
  11. C. Salomon, Laboratoire de Physique, ENS, Paris, France (personal communication).
  12. Y. Castin, J. Dalibard, C. Cohen-Tannoudji, Laboratoire de Physique, ENS, Paris, France (communication regarding the limits of sisyphus cooling).
  13. R. J. Cook, Phys. Rev. A 20, 224 (1979).
    [CrossRef]
  14. For a system with several ground- and excited-state levels, processes that transfer kinetic energy to the light field by means of a change of internal state can further enhance the low-velocity damping behavior, ultimately leading to a lower average ratio 〈EK/U〉.5–8 We note, however, that such mechanisms can become less important once 〈EK/U〉 < 1 and the atom is trapped.12
  15. J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4577 (1984).
    [CrossRef]

1990 (5)

N. P. Bigelow, M. G. Prentiss, Phys. Rev. Lett. 65, 29 (1990).
[CrossRef] [PubMed]

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

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

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

1984 (1)

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

1980 (1)

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

1979 (1)

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

1978 (1)

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

1900 (1)

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Arimondo, E.

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Ashkin, A.

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

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

Aspect, A.

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Bigelow, N. P.

N. P. Bigelow, M. G. Prentiss, Phys. Rev. Lett. 65, 29 (1990).
[CrossRef] [PubMed]

Bjorkholm, J. E.

S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).

Cable, A. E.

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).

Castin, Y.

Y. Castin, J. Dalibard, C. Cohen-Tannoudji, Laboratoire de Physique, ENS, Paris, France (communication regarding the limits of sisyphus cooling).

Chu, S.

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).

Clairon, A.

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

Cohen-Tannoudji, C.

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

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Y. Castin, J. Dalibard, C. Cohen-Tannoudji, Laboratoire de Physique, ENS, Paris, France (communication regarding the limits of sisyphus cooling).

Cook, R. J.

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

Dalibard, J.

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

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

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Y. Castin, J. Dalibard, C. Cohen-Tannoudji, Laboratoire de Physique, ENS, Paris, France (communication regarding the limits of sisyphus cooling).

Gordon, J. P.

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

Gould, P. L.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

Guellati, S.

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

Hatamian, S.

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Kaiser, R.

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Lett, P. D.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

Metcalf, H.

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

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Phillips, W. D.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

Prentiss, M. G.

N. P. Bigelow, M. G. Prentiss, Phys. Rev. Lett. 65, 29 (1990).
[CrossRef] [PubMed]

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).

Pritchard, D. E.

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

Ralston, S. L.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

Reynaud, S.

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

Salomon, C.

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

C. Salomon, Laboratoire de Physique, ENS, Paris, France (personal communication).

Shang, S.-Q.

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

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Sheehy, B.

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

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Tanner, C. E.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

van der Straten, P.

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

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

Vansteenkiste, N.

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

Watts, R. N.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

Westbrook, C.

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

Europhys. Lett. (1)

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, Europhys. Lett. 12, 683 (1990).
[CrossRef]

J. Phys. B (1)

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

Phys. Rev. A (2)

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

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

Phys. Rev. Lett. (6)

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

N. P. Bigelow, M. G. Prentiss, Phys. Rev. Lett. 65, 29 (1990).
[CrossRef] [PubMed]

C. Westbrook, R. N. Watts, C. E. Tanner, S. L. Ralston, W. D. Phillips, P. D. Lett, P. L. Gould, Phys. Rev. Lett. 65, 33 (1990).
[CrossRef] [PubMed]

E. L. Raab, M. G. Prentiss, A. E. Cable, S. Chu, D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1990); C. Monroe, W. Swann, H. Robinson, C. Wieman, Phys. Rev. Lett. 65, 1571 (1990). In one experiment on well-aligned optical molasses [P. L. Gould, P. D. Lett, and W. D. Phillips, inLaser Spectroscopy VIII, W. Persson and S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987)], workers observed a decrease in the lifetime for beam imbalances >15%, which was attributed to the pushing of atoms out of the molasses by the TW. However, the observed decrease in lifetime was found to be at least a factor of 10 less than predicted by a theory that did not include the effects of the SW potentials. We are not aware of any experimental results that uniquely either confirm or refute the beneficial effects of the TW on the velocity damping in optical molasses discussed in this Letter.
[CrossRef] [PubMed]

B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, Phys. Rev. Lett. 64, 858 (1900).
[CrossRef]

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

Other (5)

For a system with several ground- and excited-state levels, processes that transfer kinetic energy to the light field by means of a change of internal state can further enhance the low-velocity damping behavior, ultimately leading to a lower average ratio 〈EK/U〉.5–8 We note, however, that such mechanisms can become less important once 〈EK/U〉 < 1 and the atom is trapped.12

J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989); S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th International Conference on Atomic Physics, S. Harosche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).

S. Chu, M. G. Prentiss, A. E. Cable, J. E. Bjorkholm, in Laser Spectroscopy VIII, W. Persson, S. Svanberg, eds. (Springer-Verlag, Heidelberg, 1987).

C. Salomon, Laboratoire de Physique, ENS, Paris, France (personal communication).

Y. Castin, J. Dalibard, C. Cohen-Tannoudji, Laboratoire de Physique, ENS, Paris, France (communication regarding the limits of sisyphus cooling).

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Figures (2)

Fig. 1
Fig. 1

Velocity and position versus time for an atom in a molasses SW. Here υ(0) = 3 m/sec, Δ = −5 MHz, and ΩR2 = 0.1 (Γ/2)2. Inset: damping envelopes for a trapped atom in a combination of SW + TW fields as calculated from Eq. (4). In descending order the envelopes correspond to = 0.5, 0.35, 0.2, 0.1. Here ΩR = 0.1(Γ/2)2 and Δ = −Γ/2.

Fig. 2
Fig. 2

Left, Effective potential U(z) for a TLA in a combination of SW + TW fields. Here = 0.5, Δ = 5 MHz, and ΩR2 = 0.1(Γ/2)2. Right, Effective potential for a three-level atom in a combination of SW + TW under the same conditions as for the figure below. The dashed curve corresponds to the σ+ transition, the dashed–dotted curve to the σ transition, and the solid curve to the net effective potential.

Equations (4)

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F l t = 2 ћk Ω R 2 { Δ γ 2 + Δ 2 sin ( 2 kz ) + γ 2 υ k Δ ( γ 2 + Δ 2 ) 2 [ 1 cos ( 2 kz ) ] } ,
υ max ( t ) = { [ 8 / ( 3 π ) k 2 γ γ 2 + Δ 2 ] t + υ max 2 ( 0 ) } 1 / 2
F l t = ћk Ω R 2 ( 1 γ 2 + Δ 2 { 2 Δ ( 1 + ) sin ( 2 kz ) γ [ 1 ( 1 + ) 2 ] } + 2 γυ k Δ ( γ 2 + Δ 2 ) 2 × { [ 1 + ( 1 + ) 2 ] 2 ( 1 + ) cos ( 2 kz ) } ) .
υ max ( t ) { [ 4 3 ( 1 + ) 2 k Ω + υ max 2 ( 0 ) ] × exp ( 2 π 2 θt ) 1 } 1 / 2 .

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