OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 6, Iss. 11 — Nov. 1, 1989
  • pp: 2023–2045

Laser cooling below the Doppler limit by polarization gradients: simple theoretical models

J. Dalibard and C. Cohen-Tannoudji  »View Author Affiliations


JOSA B, Vol. 6, Issue 11, pp. 2023-2045 (1989)
http://dx.doi.org/10.1364/JOSAB.6.002023


View Full Text Article

Enhanced HTML    Acrobat PDF (2846 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+σ configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.

© 1989 Optical Society of America

History
Original Manuscript: April 3, 1989
Manuscript Accepted: June 29, 1989
Published: November 1, 1989

Citation
J. Dalibard and C. Cohen-Tannoudji, "Laser cooling below the Doppler limit by polarization gradients: simple theoretical models," J. Opt. Soc. Am. B 6, 2023-2045 (1989)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-6-11-2023


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. W. Hänsch, A. Schawlow, Opt. Commun. 13, 68 (1975). [CrossRef]
  2. D. Wineland, H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975).
  3. D. Wineland, W. Itano, Phys. Rev. A 20, 1521 (1979);V. S. Letokhov, V. G. Minogin, Phys. Rev. 73, 1 (1981). [CrossRef]
  4. S. Stenholm, Rev. Mod. Phys. 58, 699 (1986). [CrossRef]
  5. S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, A. Ashkin, Phys. Rev. Lett. 55, 48 (1985). [CrossRef] [PubMed]
  6. D. Sesko, C. G. Fan, C. E. Wieman, J. Opt. Soc. Am. B 5, 1225 (1988). [CrossRef]
  7. P. Lett, R. Watts, C. Westbrook, W. D. Phillips, P. Gould, H. Metcalf, Phys. Rev. Lett. 61, 169 (1988). [CrossRef] [PubMed]
  8. Y. Shevy, D. S. Weiss, S. Chu, in Proceedings of the Conference on Spin Polarized Quantum Systems, S. Stringari, ed. (World Scientific, Singapore, 1989);Y. Shevy, D. S. Weiss, P. J. Ungar, S. Chu, Phys. Rev. Lett. 62, 1118 (1989). [CrossRef] [PubMed]
  9. J. Dalibard, C. Salomon, A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, in Proceedings of the 11th Conference on Atomic Physics, S. Harsche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).
  10. S. Chu, D. S. Weiss, Y. Shevy, P. J. Ungar, in Proceedings of the 11th Conference on Atomic Physics, S. Harsche, J. C. Gay, G. Grynberg, eds. (World Scientific, Singapore, 1989).
  11. We restrict ourselves here to neutral atoms. Note that for trapped ions, mechanisms overcoming the Doppler limit were also proposed. They involve Raman two-photon processes:H. Dehmelt, G. Janik, W. Nagourney, Bull. Am. Phys. Soc. 30, 612 (1985);P. E. Toschek, Ann. Phys. (Paris) 10, 761 (1985);M. Lindberg, J. Javanainen, J. Opt. Soc. Am. B 3, 1008 (1986). [CrossRef]
  12. J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980). [CrossRef]
  13. J. Dalibard, C. Cohen-Tannoudji, J. Phys. B 18, 1661 (1985). [CrossRef]
  14. Other consequences of long atomic pumping times are described inW. Gawlik, J. Kowalski, F. Träger, M. Vollmer, J. Phys. B 20, 997 (1987). [CrossRef]
  15. J. Javanainen, S. Stenholm, Appl. Phys. 21, 35 (1980). [CrossRef]
  16. J. Dalibard, C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985). [CrossRef]
  17. A. Aspect, J. Dalibard, A. Heidmann, C. Salomon, C. Cohen-Tannoudji, Phys. Rev. Lett. 57, 1688 (1986). [CrossRef] [PubMed]
  18. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988);J. Opt. Soc. Am. B 6, 2112 (1989). [CrossRef] [PubMed]
  19. Y. Castin, H. Wallis, J. Dalibard, J. Opt. Soc. Am. B 6, 2046 (1989). [CrossRef]
  20. E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981). [CrossRef]
  21. J. Dalibard, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4577 (1984). [CrossRef]
  22. J.-C. Lehmann, C. Cohen-Tannoudji, C. R. Acad. Sci. 258, 4463 (1964).
  23. J. Dupont-Roc, S. Haroche, C. Cohen-Tannoudji, Phys. Lett. 28A, 638 (1969).
  24. M. Lombardi, C. R. Acad. Sci. 265, 191 (1967);J. Phys. 30, 631 (1969).
  25. C. Cohen-Tannoudji, J. Dupont-Roc, Opt. Commun. 1, 184 (1969). [CrossRef]
  26. C. Cohen-Tannoudji, in Frontiers in Laser Spectroscopy, R. Balian, S. Haroche, S. Liberman, eds. (North-Holland, Amsterdam, 1977).
  27. We also reincluded in the definition of the excited states the phase factors exp(±iπ/4) that appear when Eq. (2.7) is inserted into Eq. (4.1).
  28. J. Dalibard, A. Heidmann, C. Salomon, A. Aspect, H. Metcalf, C. Cohen-Tannoudji, in Fundamentals of Quantum Optics II, F. Ehlotzky, ed. (Springer-Verlag, Berlin1987), p. 196. [CrossRef]
  29. K. Mølmer, Y. Castin, J. Phys. B (to be published).
  30. D. S. Weiss, E. Riis, Y. Shevy, P. J. Ungar, S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989). [CrossRef]
  31. Y. Castin, K. Mølmer, J. Dalibard, C. Cohen-Tannoudji, in Proceedings of the Ninth International Conference on Laser Spectroscopy, M. Feld, A. Mooradian, J. Thomas, eds. (Springer-Verlag, Berlin, 1989).
  32. E. Arimondo, A. Aspect, R. Kaiser, C. Salomon, N. Vansteenkiste, Laboratoire de Spectroscopic Hertzienne Ecole Normale Supérieure, Université Paris VI, 24 Rue Lhomond, F-75231 Paris Cedex 05, France (personal communication).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited