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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 9, Iss. 12 — Dec. 1, 1992
  • pp: 2142–2158

Radiation force in the magneto-optical trap

A. M. Steane, M. Chowdhury, and C. J. Foot  »View Author Affiliations

JOSA B, Vol. 9, Issue 12, pp. 2142-2158 (1992)

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An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.

© 1992 Optical Society of America

Original Manuscript: November 6, 1991
Revised Manuscript: June 1, 1992
Published: December 1, 1992

A. M. Steane, M. Chowdhury, and C. J. Foot, "Radiation force in the magneto-optical trap," J. Opt. Soc. Am. B 9, 2142-2158 (1992)

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  1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, D. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987). [CrossRef] [PubMed]
  2. S. Chu, C. Wieman, eds., feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B6, 2019–2278 (1989).
  3. A. Steane, C. Foot, “Laser Cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231 (1991). [CrossRef]
  4. D. Sesko, T. Walker, C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946 (1991). [CrossRef]
  5. K. Molmer, “Friction and diffusion coefficients for cooling of atoms in laser fields with multidimensional periodicity,” Phys. Rev. A 44, 5820 (1991). [CrossRef] [PubMed]
  6. N. Wax, Selected Papers on Noise and Stochastic Processes (Dover, New York, 1954), Eq. (297), p. 40.
  7. J. Nellessen, J. Werner, W. Ertmer, “Magneto-optical compression of a monoenergetic sodium atomic beam,” Opt. Commun. 78, 300 (1990). [CrossRef]
  8. D. Sesko, T. Walker, C. Monroe, A. Gallagher, C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961 (1989). [CrossRef] [PubMed]
  9. C. Monroe, W. Swann, H. Robinson, C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571 (1990). [CrossRef] [PubMed]
  10. H. Metcalf, “Magneto-optical trapping and its application to helium metastables,” J. Opt. Soc. Am. B 6, 2206 (1989). [CrossRef]
  11. E. A. Power, Introductory Quantum Electronics (American Elsevier, New York, 1965).
  12. M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, D. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452 (1988). [CrossRef] [PubMed]
  13. A. Cable, M. Prentiss, N. P. Bigelow, “Observations of sodium atoms in a magnetic molasses trap loaded by a continuous uncooled source,” Opt. Lett. 15, 507 (1990). [CrossRef] [PubMed]
  14. E. L. Raab, “Trapping sodium with light,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1988).
  15. P. Julienne, F. Mies, “Collisions of ultracold trapped atoms,” J. Opt. Soc. Am. B 6, 2257 (1989). [CrossRef]
  16. H. S. W. Massey, Electronic and Ionic Impact Phenomena (Oxford U. Press, London, 1971), Vol. 3.
  17. A. Corney, Atomic and Laser Spectroscopy (Oxford U. Press, London, 1977), Chap. 8.
  18. T. Walker, D. Sesko, C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408 (1990). [CrossRef] [PubMed]
  19. J. Dalibard, “Laser cooling of an optically thick gas: the simplest radiation pressure trap?” Opt. Commun. 68, 203 (1988). [CrossRef]
  20. R. Loudon, The Quantum Theory of Light (Oxford U. Press, London, 1983), Chap. 8.
  21. B. Mollow, “Power spectrum of light scattered by two-level systems,” Phys. Rev. 188, 1969 (1969). [CrossRef]
  22. B. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217 (1972). [CrossRef]
  23. W. Phillips, H. Metcalf, “Laser deceleration of an atomic beam,” Phys. Rev. Lett. 48, 596 (1982). [CrossRef]
  24. P. Lett, W. Phillips, S. Rolston, C. Tanner, R. Watts, C. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084 (1989). [CrossRef]
  25. E. Riis, D. Weiss, K. Moler, S. Chu, “Atom funnel for the production of a slow, high-density atomic beam,” Phys. Rev. Lett. 64, 1658 (1990). [CrossRef] [PubMed]
  26. J. Dalibard, C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients: simple theoretical models,” J. Opt. Soc. Am. B 6, 2023 (1989). [CrossRef]
  27. B. Sheehy, S.-Q. Shang, P. van der Straten, S. Hatamian, H. Metcalf, “Magnetic-field induced laser cooling below the Doppler limit,” Phys. Rev. Lett. 64, 858 (1990). [CrossRef] [PubMed]
  28. S.-Q. Shang, B. Sheehy, P. van der Straten, H. Metcalf, “Velocity-selective magnetic resonance laser cooling,” Phys. Rev. Lett. 65, 317 (1990). [CrossRef] [PubMed]
  29. S.-Q. Shang, B. Sheehy, H. Metcalf, “Velocity-selective resonances and sub-Doppler laser cooling,” Phys. Rev. Lett. 67, 1094 (1991). [CrossRef] [PubMed]
  30. We use this expression following Refs. 28 and 29, although the name is slightly misleading, since there is no oscillating magnetic field: The mathematical description is merely analagous to a magnetic resonance.
  31. A. Hemmerich, D. Schropp, T. Hänsch, “Light forces in two crossed standing waves with controlled time phase difference,” Phys. Rev. A 44, 1910 (1991). [CrossRef] [PubMed]
  32. N. Bigelow, M. Prentiss, “Observation of channeling of atoms in the three-dimensional interference pattern of optical standing waves,” Phys. Rev. Lett. 65, 29 (1990). [CrossRef] [PubMed]
  33. N. Bigelow, M. Prentiss, “Decreased damping of ultracold atoms in optical molasses: predictions and a possible solution,” Opt. Lett. 15, 1479 (1990). [CrossRef] [PubMed]
  34. G. Nienhuis, P. van der Straten, S.-Q. Shang, “Operator description of laser cooling below the Doppler limit,” Phys. Rev. A 44, 462 (1991);A. Steane, G. Hillenbrand, C. Foot, “Polarization gradient cooling in a one-dimensional σ+–σ− configuration for any atomic transition,” J. Phys. B (to be published). [CrossRef] [PubMed]
  35. T. Bergman, G. Erez, H. Metcalf, “Magnetostatic trapping fields for neutral atoms,” Phys. Rev. A 35, 1535 (1987).N. B.: There is an error in Table II. Bρ for n= 3 is missing a z and should read −3ρz2/2 + 3ρ2z/8. [CrossRef]
  36. C. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1 (1991). [CrossRef]
  37. “Pressure measurement and electron beam guns,” in Vacuum Generators Product Manual (Vacuum Generators Ltd., Hastings, UK, 1991), Sec. 07;S. Dushman, Scientific Foundations of Vacuum Technique (Wiley, New York, 1949).
  38. C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683 (1990). [CrossRef]

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