Abstract

We analyze the light-induced atom–atom interactions in optically thick atomic clouds and show that, when the laser frequency is on-resonance with the atomic transition, they become attractive. On the basis of this analysis we propose and demonstrate a novel scheme to compress a cold and dense atomic cloud with a short on-resonance laser pulse. The compression force arises from attenuation of the laser light by the atomic cloud. The following free propagation of the atoms shows a lenslike behavior that yields a transient density increase at the focal time, where neither laser nor magnetic field perturbations exist. A cooling pulse, which is applied at the focal time of this lens, restores the initial temperature of atoms, and hence the phase space density is increased. Finally, we adopt our compression scheme to a quasi-steady-state mode by temporally chopping it with the cooling and trapping beams of a magnet-optical trap.

© 1999 Optical Society of America

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References

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  1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
    [CrossRef] [PubMed]
  2. See special issue on laser cooling and trapping of atoms, S. Chu and C. E. Wieman, eds., J. Opt. Soc. Am. B 6, 2020 (1989).
  3. D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946 (1991).
    [CrossRef]
  4. J. Dalibard, “Laser cooling of an optically thick gas: the simplest radiation pressure trap?” Opt. Commun. 68, 203 (1988).
    [CrossRef]
  5. A. P. Kazantsev, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, “Scattering, velocity bunching, and self-localization of atoms in a light field,” J. Opt. Soc. Am. B 6, 2130 (1989).
    [CrossRef]
  6. W. Petrich, M. H. Anderson, J. R. Ensher, and E. A. Cornell, “Behavior of atoms in a compressed magneto-optical trap,” J. Opt. Soc. Am. B 11, 1332 (1994).
    [CrossRef]
  7. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
    [CrossRef] [PubMed]
  8. C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
    [CrossRef] [PubMed]
  9. C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
    [CrossRef] [PubMed]
  10. These changes also affect the spring constant, as shown by A. Steane, M. Chowdhury, and C. Foot, “Radiation force in the magneto-optical trap,” J. Opt. Soc. Am. B 9, 2142 (1992).
    [CrossRef]
  11. See, for instance, evaporative cooling in N. Masuhara, J. M. Doyle, J. C. Sandberg, D. Kleppner, T. J. Greytak, H. F. Hess, and G. P. Kochanski, “Evaporative cooling of spin-polarized atomic hydrogen,” Phys. Rev. Lett. 61, 935 (1988), or Raman cooling in H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658 (1996).
    [CrossRef] [PubMed]
  12. B. R. Mollow, “Power spectrum of light scattered by two-level system,” Phys. Rev. 188, 1969 (1969).
    [CrossRef]
  13. B. R. Mollow, “Stimulated emission and absorption near resonance for driven system,” Phys. Rev. A 5, 2217 (1972).
    [CrossRef]
  14. After scattering of a few photons, optical pumping aligns each atom with respect to the linearly polarized laser light. For this situation the saturation intensity for rubidium is Isat=3 mW/cm2 instead of 1.65 mW/cm2 for a completely polarized atom. It is also nearly uniform among the three occupied m states. Throughout the paper we scale intensities to this Isat despite different experimental situations.
  15. We assume a uniform spatial distribution of the atoms over the period of the standing wave. This is applicable to the on-resonance case (δ=0), whereas at δ≠0 some localization of the atoms toward the nodes (δ>0) and the antinodes (δ<0) of the standing wave is expected owing to the dipole force. We neglect this localization here.
  16. A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
    [CrossRef]
  17. At low intensities the neglect of the repulsive inter-atomic forces by our simplified model is not justified anyway.
  18. To calculate Caverage, we extended the simulations to a two-dimensional Gaussian density distribution n(x, y, z=0), and the one-dimensional integrated density was defined as ∫n(x, y, z=0)dy, corresponding to our imaging fluorescence measurements that are described below.
  19. P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
    [CrossRef] [PubMed]
  20. We observed nearly identical dependence on laser detuning in one-beam and six-beam configurations.
  21. Note that for the pulsed compression the optimal compression was obtained for detuning of 1–2 MHz above resonance (see inset of Fig. 7). This frequency shift can be explained by the fact that when the atoms are accelerated during the ~100-μs compression pulses they acquire a negative Doppler shift of a few megahertz, so their average detuning is close to zero when their initial detuning is somewhat posi-tive. This does not apply for the quasi steady state of Fig. 9, as is confirmed by the exact zero location of the optimal detuning.
  22. D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
    [CrossRef]
  23. L. Khaykovich, N. Friedman, and N. Davidson, “Saturation of the weak probe amplification in a strongly driven cold and dense atomic cloud,” Europhys. J. (to be published).

1998 (2)

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

1996 (1)

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

1995 (1)

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

1992 (1)

1991 (1)

1989 (2)

1988 (2)

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

J. Dalibard, “Laser cooling of an optically thick gas: the simplest radiation pressure trap?” Opt. Commun. 68, 203 (1988).
[CrossRef]

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

1972 (1)

B. R. Mollow, “Stimulated emission and absorption near resonance for driven system,” Phys. Rev. A 5, 2217 (1972).
[CrossRef]

1969 (1)

B. R. Mollow, “Power spectrum of light scattered by two-level system,” Phys. Rev. 188, 1969 (1969).
[CrossRef]

Allegrini, M.

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

Anderson, M. H.

Boiron, D.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Chowdhury, M.

Chu, S.

See special issue on laser cooling and trapping of atoms, S. Chu and C. E. Wieman, eds., J. Opt. Soc. Am. B 6, 2020 (1989).

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Chudesnikov, D. O.

Cooper, C. G.

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Cooper, C. J.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

Cornell, E. A.

Dalibard, J.

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

J. Dalibard, “Laser cooling of an optically thick gas: the simplest radiation pressure trap?” Opt. Commun. 68, 203 (1988).
[CrossRef]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Edwards, N. H.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Ensher, J. R.

Fioretti, A.

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

Foot, C.

Foot, C. J.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Fournier, J. M.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Gould, P. L.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Grinberg, G.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Joffe, M. A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Kazantsev, A. P.

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Lett, P. D.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Martin, A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

Metcalf, H. J.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Michaud, A.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Molisch, A. F.

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

Mollow, B. R.

B. R. Mollow, “Stimulated emission and absorption near resonance for driven system,” Phys. Rev. A 5, 2217 (1972).
[CrossRef]

B. R. Mollow, “Power spectrum of light scattered by two-level system,” Phys. Rev. 188, 1969 (1969).
[CrossRef]

Müller, J. H.

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

Perrin, H.

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Petrich, W.

Phillips, W. D.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Pritchard, D. E.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Rink, J.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

Salomon, C.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Sesko, D.

Simard, L.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Sprenger, M.

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Steane, A.

Steane, A. M.

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Surdutovich, G. I.

Szriftgiser, P.

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Townsend, C. G.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

Verkerk, P.

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

Walker, T.

Watts, R. N.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Westbrook, C. I.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Wieman, C.

Wieman, C. E.

Yakovlev, V. P.

Zetie, K. P.

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (5)

Opt. Commun. (2)

A. Fioretti, A. F. Molisch, J. H. Müller, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415 (1998).
[CrossRef]

J. Dalibard, “Laser cooling of an optically thick gas: the simplest radiation pressure trap?” Opt. Commun. 68, 203 (1988).
[CrossRef]

Phys. Rev. (1)

B. R. Mollow, “Power spectrum of light scattered by two-level system,” Phys. Rev. 188, 1969 (1969).
[CrossRef]

Phys. Rev. A (4)

B. R. Mollow, “Stimulated emission and absorption near resonance for driven system,” Phys. Rev. A 5, 2217 (1972).
[CrossRef]

C. G. Townsend, N. H. Edwards, K. P. Zetie, C. J. Cooper, J. Rink, and C. J. Foot, “High-density trapping of cesium atoms in a dark magneto-optical trap,” Phys. Rev. A 53, 1702 (1996).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. G. Cooper, K. P. Zetie, C. J. Foot, A. M. Steane, P. Szriftgiser, H. Perrin, and J. Dalibard, “Phase-space density in the magneto-optical trap,” Phys. Rev. A 52, 1423 (1995).
[CrossRef] [PubMed]

D. Boiron, A. Michaud, J. M. Fournier, L. Simard, M. Sprenger, G. Grinberg, and C. Salomon, “Cold and dense cesium clouds in far-detuned dipole traps,” Phys. Rev. A 57, R4106 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High density of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253 (1993).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Other (8)

We observed nearly identical dependence on laser detuning in one-beam and six-beam configurations.

Note that for the pulsed compression the optimal compression was obtained for detuning of 1–2 MHz above resonance (see inset of Fig. 7). This frequency shift can be explained by the fact that when the atoms are accelerated during the ~100-μs compression pulses they acquire a negative Doppler shift of a few megahertz, so their average detuning is close to zero when their initial detuning is somewhat posi-tive. This does not apply for the quasi steady state of Fig. 9, as is confirmed by the exact zero location of the optimal detuning.

At low intensities the neglect of the repulsive inter-atomic forces by our simplified model is not justified anyway.

To calculate Caverage, we extended the simulations to a two-dimensional Gaussian density distribution n(x, y, z=0), and the one-dimensional integrated density was defined as ∫n(x, y, z=0)dy, corresponding to our imaging fluorescence measurements that are described below.

See, for instance, evaporative cooling in N. Masuhara, J. M. Doyle, J. C. Sandberg, D. Kleppner, T. J. Greytak, H. F. Hess, and G. P. Kochanski, “Evaporative cooling of spin-polarized atomic hydrogen,” Phys. Rev. Lett. 61, 935 (1988), or Raman cooling in H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Raman cooling of atoms in an optical dipole trap,” Phys. Rev. Lett. 76, 2658 (1996).
[CrossRef] [PubMed]

After scattering of a few photons, optical pumping aligns each atom with respect to the linearly polarized laser light. For this situation the saturation intensity for rubidium is Isat=3 mW/cm2 instead of 1.65 mW/cm2 for a completely polarized atom. It is also nearly uniform among the three occupied m states. Throughout the paper we scale intensities to this Isat despite different experimental situations.

We assume a uniform spatial distribution of the atoms over the period of the standing wave. This is applicable to the on-resonance case (δ=0), whereas at δ≠0 some localization of the atoms toward the nodes (δ>0) and the antinodes (δ<0) of the standing wave is expected owing to the dipole force. We neglect this localization here.

L. Khaykovich, N. Friedman, and N. Davidson, “Saturation of the weak probe amplification in a strongly driven cold and dense atomic cloud,” Europhys. J. (to be published).

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Figures (9)

Fig. 1
Fig. 1

Average absorption cross sections of rescattered photons (σR) and laser photons (σL) calculated for a two-level atom in a plane wave (solid curves) and a standing wave (dashed curves) as a function of average laser intensity for three different laser detunings. Above σR/σL-1=0 there is a repulsive regime, which applies for typical MOT parameters, and below it there is an attractive regime where our experiments were performed.

Fig. 2
Fig. 2

Distribution of calculated velocities of atoms as a function of position inside a 1-D atomic cloud [an initial 1/e diameter of 0.27 cm and optical thickness of exp(-11)] immediately after a 100-µs compression pulse for three incoming laser intensities. Spherical aberration is manifested by the amount of distortion from the general linear slope to the velocity curves, and heating is manifested by the noiselike fluctuations.

Fig. 3
Fig. 3

Atomic trajectories as a function of time are shown, after a 100-µs compression pulse with optimal intensity was applied to an atomic cloud with a Gaussian initial distribution. A maximal compression is observed at Tfocus600 µs.

Fig. 4
Fig. 4

Calculated dependence of the average compression ratio for a 3-D atomic cloud18 on incoming laser intensity. The cloud 1/e diameter is 0.27 cm, the maximal optical thickness is exp(-11), and the compression-pulse duration is 100 µs. The scatter graph shows experimental measurements in the one-beam configuration. Each data point is taken at Tfocus, which is different for each intensity.

Fig. 5
Fig. 5

Schematic diagram of our experimental setup.

Fig. 6
Fig. 6

Time developments of the 1-D integrated density profile (the central line scan of the CCD fluorescence image) of the atomic cloud after the compression pulse is switched off. At Tfocus=700 µs the peak reaches its maximum and then decreases, while the width of the atomic cloud minimizes at Tfocus.

Fig. 7
Fig. 7

Peak density compression ratio in the six-beam configuration with δ=0 as a function of average laser intensity. The symbols are our experimental data, and the connecting lines are only to guide the eye. The inset shows the dependence of the compression ratio on detuning of the laser frequency from resonance at I/Isat=4.

Fig. 8
Fig. 8

Time dependence of size of the atomic cloud after the compression pulse is switched off without (■) and with (▲) cooling pulse that is applied at Tfocus.

Fig. 9
Fig. 9

Dependence of the two-beam compression ratio in quasi-steady-state realization on detuning of the compressed laser frequency from resonance. The symbols are our experimental data, and the connecting lines are only to guide the eye.

Equations (4)

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σR= σ(ν)F(ν)dν,
F(x, t)=1/2kγs(x, t)s(x, t)+1,
s(x, t)=I(x, t)/Isat1+4(kν(x, t)/γ)2
1I(x, t)dI(x, t)dx=2σL0-xn(x, t)dx1+I(x, t)/Isat+4[kν(x, t)/γ]2,

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