Abstract

We apply a three-dimensional Doppler Monte Carlo simulation to study fluctuation in magneto-optical traps with various laser beam configurations. First, the temperature and the radius of a lithium trap are calculated with the assumption of exactly counterpropagating beams. The results are compared with previously reported experimental data [Opt. Commun. 158, 263 (1998)]. Subsequently, the role of fluctuation in the transition from a ball- to a ring-shaped spatial distribution of atoms is investigated. This transition occurs when the laser beams in the xy plane are progressively misaligned. Finally, the temperature of the atoms in a ring-shaped distribution is determined, and its dependence with the misalignment of the beams is analyzed.

© 2001 Optical Society of America

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  1. P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
    [CrossRef]
  2. J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
    [CrossRef] [PubMed]
  3. Y. Castin and K. Mølmer, “Monte Carlo wave-function analysis of 3D optical molasses,” Phys. Rev. Lett. 74, 3772–3775 (1995).
    [CrossRef] [PubMed]
  4. Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
    [CrossRef]
  5. U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
    [CrossRef]
  6. D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
    [CrossRef]
  7. L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).
  8. V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).
  9. T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
    [CrossRef] [PubMed]
  10. M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
    [CrossRef] [PubMed]
  11. D. Felinto and S. S. Vianna, “Orbital modes in low-density magneto-optical traps,” J. Opt. Soc. Am. B 17, 681–689 (2000).
    [CrossRef]
  12. F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
    [CrossRef]
  13. A. S. Arnold and P. J. Manson, “Atomic density and temperature distributions in magneto-optical traps,” J. Opt. Soc. Am. B 17, 497–506 (2000).
    [CrossRef]
  14. V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
    [CrossRef] [PubMed]
  15. D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).
  16. M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
    [CrossRef]
  17. 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, 169–172 (1988).
    [CrossRef] [PubMed]
  18. A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231–236 (1991).
    [CrossRef]
  19. S. Chu and C. Wieman, eds., Feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2020–2278 (1989).
  20. M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
    [CrossRef]
  21. C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, A. Kumarakrishnan, P. L. Gould, and J. Javanainen, “Measurements of temperature and spring constant in a magneto-optical trap,” J. Opt. Soc. Am. B 11, 703–711 (1994).
    [CrossRef]
  22. C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
    [CrossRef] [PubMed]
  23. J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
    [CrossRef]
  24. S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
    [CrossRef]
  25. I. Guedes, M. T. Araujo, D. M. B. P. Milori, G. I. Surdutovich, V. S. Bagnato, and S. C. Zilio, “Forces acting on magneto-optically trapped atoms,” J. Opt. Soc. Am. B 11, 1935–1940 (1994).
    [CrossRef]
  26. D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
    [CrossRef]

2000 (2)

1999 (2)

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
[CrossRef]

1998 (2)

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

1996 (2)

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

1995 (4)

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

Y. Castin and K. Mølmer, “Monte Carlo wave-function analysis of 3D optical molasses,” Phys. Rev. Lett. 74, 3772–3775 (1995).
[CrossRef] [PubMed]

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

1994 (3)

1993 (1)

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

1992 (3)

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

1991 (3)

A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231–236 (1991).
[CrossRef]

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
[CrossRef]

1990 (1)

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

1989 (2)

1988 (1)

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, 169–172 (1988).
[CrossRef] [PubMed]

Araujo, M. T.

Arimondo, E.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Arnold, A. S.

Bagnato, V. S.

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

I. Guedes, M. T. Araujo, D. M. B. P. Milori, G. I. Surdutovich, V. S. Bagnato, and S. C. Zilio, “Forces acting on magneto-optically trapped atoms,” J. Opt. Soc. Am. B 11, 1935–1940 (1994).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

Cardoso, G. C.

J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
[CrossRef]

Castin, Y.

Y. Castin and K. Mølmer, “Monte Carlo wave-function analysis of 3D optical molasses,” Phys. Rev. Lett. 74, 3772–3775 (1995).
[CrossRef] [PubMed]

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Chu, S.

Clairon, A.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Colla, M.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Cooper, C. J.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Dalibard, J.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

de Araujo, M. T.

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

Dinneen, T. P.

Drewsen, M.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Edwards, N. H.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Engler, H.

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Felinto, D.

D. Felinto and S. S. Vianna, “Orbital modes in low-density magneto-optical traps,” J. Opt. Soc. Am. B 17, 681–689 (2000).
[CrossRef]

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

Fioretti, A.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Foot, C. J.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231–236 (1991).
[CrossRef]

Gould, P. L.

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, A. Kumarakrishnan, P. L. Gould, and J. Javanainen, “Measurements of temperature and spring constant in a magneto-optical trap,” J. Opt. Soc. Am. B 11, 703–711 (1994).
[CrossRef]

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, 169–172 (1988).
[CrossRef] [PubMed]

Grego, S.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Grimm, R.

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Grison, D.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Guedes, I.

Habesch, R.

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

Horowicz, R. J.

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

Javanainen, J.

Kaiser, R.

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

Kumarakrishnan, A.

Laurent, Ph.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Lett, P. D.

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

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, 169–172 (1988).
[CrossRef] [PubMed]

Lezama, A.

J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
[CrossRef]

Lin, Z.

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Manson, P. J.

Marcassa, L. G.

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

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, 169–172 (1988).
[CrossRef] [PubMed]

Milori, D.

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

Milori, D. M. B. P.

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

I. Guedes, M. T. Araujo, D. M. B. P. Milori, G. I. Surdutovich, V. S. Bagnato, and S. C. Zilio, “Forces acting on magneto-optically trapped atoms,” J. Opt. Soc. Am. B 11, 1935–1940 (1994).
[CrossRef]

Mølmer, K.

Y. Castin and K. Mølmer, “Monte Carlo wave-function analysis of 3D optical molasses,” Phys. Rev. Lett. 74, 3772–3775 (1995).
[CrossRef] [PubMed]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Muller, J. H.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Nadir, A.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Nunes, F. Dias

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

Oriá, M.

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

Perrin, H.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Phillips, W. D.

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

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, 169–172 (1988).
[CrossRef] [PubMed]

Rolston, S. L.

Salomon, C.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Santarelli, G.

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Schünemann, U.

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Sesko, D.

D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
[CrossRef]

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

Shimizu, F.

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Shimizu, K.

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Silva, J. F.

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

Steane, A. M.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231–236 (1991).
[CrossRef]

Surdutovich, G. I.

I. Guedes, M. T. Araujo, D. M. B. P. Milori, G. I. Surdutovich, V. S. Bagnato, and S. C. Zilio, “Forces acting on magneto-optically trapped atoms,” J. Opt. Soc. Am. B 11, 1935–1940 (1994).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

Szriftgiser, P.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Tabosa, J. W. R.

J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
[CrossRef]

Takuma, H.

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Tan, K. Y. N.

Tanner, C. E.

Townsend, C. G.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Tuboy, A.

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

Tuboy, A. M.

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

Verkerk, P.

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

Vianna, S. S.

D. Felinto and S. S. Vianna, “Orbital modes in low-density magneto-optical traps,” J. Opt. Soc. Am. B 17, 681–689 (2000).
[CrossRef]

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

Vitlina, R.

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

Walker, T.

D. Sesko, T. Walker, and C. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
[CrossRef]

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

Wallace, C. D.

Watts, R. N.

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

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, 169–172 (1988).
[CrossRef] [PubMed]

Weidemüller, M.

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Westbrook, C. I.

P. D. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

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, 169–172 (1988).
[CrossRef] [PubMed]

Wieman, C.

Zetie, K. P.

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

Zhan, M.

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Zielonkowski, M.

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Zilio, S. C.

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

I. Guedes, M. T. Araujo, D. M. B. P. Milori, G. I. Surdutovich, V. S. Bagnato, and S. C. Zilio, “Forces acting on magneto-optically trapped atoms,” J. Opt. Soc. Am. B 11, 1935–1940 (1994).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

Appl. Phys. B (1)

M. Drewsen, Ph. Laurent, A. Nadir, G. Santarelli, A. Clairon, Y. Castin, D. Grison, and C. Salomon, “Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap,” Appl. Phys. B 59, 283–298 (1994).
[CrossRef]

Braz. J. Phys. (1)

L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, S. C. Zilio, and V. S. Bagnato, “Magneto-optical trap of sodium atoms from a vapor cell and observation of spatial modes,” Braz. J. Phys. 22, 3–6 (1992).

Europhys. Lett. (1)

A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magneto-optical trap,” Europhys. Lett. 14, 231–236 (1991).
[CrossRef]

J. Opt. Soc. Am. B (7)

Jpn. J. Appl. Phys. (1)

Z. Lin, K. Shimizu, M. Zhan, F. Shimizu, and H. Takuma, “Laser cooling and trapping of Li,” Jpn. J. Appl. Phys. 30, L1324–L1326 (1991).
[CrossRef]

Laser Phys. (2)

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, “Spatial distributions of optically trapped cooled neutral atoms,” Laser Phys. 2, 172–177 (1992).

D. M. B. P. Milori, A. M. Tuboy, L. G. Marcassa, R. Habesch, S. C. Zilio, and V. S. Bagnato, “Transitions between stable spatial distributions of atoms in a magneto-optical trap,” Laser Phys. 8, 1163–1166 (1998).

Opt. Commun. (4)

M. T. de Araujo, R. J. Horowicz, D. Milori, A. Tuboy, R. Kaiser, S. C. Zilio, and V. S. Bagnato, “Time of flight technique to determine temperature of atoms in a ring-shaped trap,” Opt. Commun. 119, 85–89 (1995).
[CrossRef]

J. W. R. Tabosa, A. Lezama, and G. C. Cardoso, “Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry,” Opt. Commun. 165, 59–64 (1999).
[CrossRef]

S. Grego, M. Colla, A. Fioretti, J. H. Muller, P. Verkerk, and E. Arimondo, “A cesium magneto-optical trap for cold collisions studies,” Opt. Commun. 132, 519–526 (1996).
[CrossRef]

U. Schünemann, H. Engler, M. Zielonkowski, M. Weidemüller, and R. Grimm, “Magneto-optic trapping of lithium using semiconductor lasers,” Opt. Commun. 158, 263–272 (1998).
[CrossRef]

Phys. Rev. A (5)

M. T. de Araujo, L. G. Marcassa, S. C. Zilio, and V. S. Bagnato, “Double-ring structure: another variant in the spatial distribution of cold sodium atoms,” Phys. Rev. A 51, 4286–4288 (1995).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, D. Milori, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, “Spatial distribution of atoms in a magneto-optical trap,” Phys. Rev. A 48, 3771–3775 (1993).
[CrossRef] [PubMed]

D. Felinto, L. G. Marcassa, V. S. Bagnato, and S. S. Vianna, “Influence of the number of atoms in a ring-shaped magneto-optical trap: observation of bifurcation,” Phys. Rev. A 60, 2591–2594 (1999).
[CrossRef]

C. G. Townsend, N. H. Edwards, C. J. 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, 1423–1440 (1995).
[CrossRef] [PubMed]

F. Dias Nunes, J. F. Silva, S. C. Zilio, and V. S. Bagnato, “Influence of laser fluctuations and spontaneous emission on the ring-shaped atomic distribution in a magneto-optical trap,” Phys. Rev. A 54, 2271–2274 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

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, 169–172 (1988).
[CrossRef] [PubMed]

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Y. Castin and K. Mølmer, “Monte Carlo wave-function analysis of 3D optical molasses,” Phys. Rev. Lett. 74, 3772–3775 (1995).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Top, radius in the xy plane σr. Bottom, temperature T as a function of laser detuning for various intensities; the dashed line shows the minimum Doppler temperature for lithium (140 µK). The other parameters, for both top and bottom, are w=6.5 mm and b=14 G/cm. The error bars are of the size of or smaller than the symbols.

Fig. 2
Fig. 2

Simulated trajectory of an atom in the xy plane forming a ring. The trap parameters are b=10 G/cm, δ=-4Γ, I=Is, w=5 mm, and d=3 mm (s0=0.2). The dashed lines with arrows show the directions of the wave vectors of the four beams in the center of their respective Gaussian profiles.

Fig. 3
Fig. 3

(a) Average and (b) variance of the radius in the xy plane versus misalignment. The other parameters are b=8 G/cm, δ=-2.5Γ, I=0.2Is, and w=5 mm. Filled squares, results for an observation time of 0.8 s; the observation times for the open circles are ∼15 s. The curves are guides for the eye.

Fig. 4
Fig. 4

Radial distribution of atoms for various misalignments. The other parameters are the same as in Fig. 3, and the curves are guides for the eye.

Fig. 5
Fig. 5

Variation of Ω and ΔΩ with the misalignment. The other parameters are the same as in Fig. 3. The curves guides for the eye.

Fig. 6
Fig. 6

Radial, tangential, and axial temperatures of a MOT as a function of misalignment. The parameters are the same as in Fig. 3. The curves are guides for the eye.

Equations (3)

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

n1R=n2(R+Γ),
sx+=sin2 θ2 2I(r)4(δ+kvx)2+1+(1+cos θ)24 2I(r)4(δ+kvx+μB)2+1+(1-cos θ)24 2I(r)4(δ+kvx-μB)2+1,
kbT=Γ4 1+6I/Is+(2δ/Γ)22|δ|/Γ,

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