Abstract

We have measured the low-density characteristics of a magneto-optical trap for both isotopes of rubidium. Trapped-atom temperatures are measured by the time-of-flight technique and are similar to temperatures in optical molasses. They are below the Doppler limit in most cases and increase linearly with the ratio of laser intensity to laser detuning. A slight difference between the two isotopes is observed. The data agree well with three-dimensional, multistate, semiclassical simulations. Spring constants of the trap are inferred from careful measurements of the size of the trapped-atom cloud. The spring constant is seen to increase with intensity at low intensity, becoming independent of intensity at high intensity. This trend is consistent with sub-Doppler cooling mechanisms.

© 1994 Optical Society of America

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  17. S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
    [CrossRef] [PubMed]
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  27. We are assuming a small enough value of B that we can ignore the effects of different ground- and excited-state Landé g factors discussed in Refs. 19 and 20.
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    [CrossRef]
  29. J. Werner, H. Wallis, G. Hillenbrand, and A. Steane, J. Phys. B 26, 3063 (1993).
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  30. A. Hemmerich, M. Weidemuller, T. Esslinger, and T. W. Hansch, Europhys. Lett. 21, 445 (1993).
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  31. E. Riis, D. S. Weiss, K. A. Moler, and S. Chu, Phys. Rev. Lett. 64, 1658 (1990).
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    [CrossRef]

1993 (6)

H. Wallis, J. Werner, and W. Ertmer, Comments At. Mol. Phys. 28, 275 (1993).

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

J. Werner, H. Wallis, G. Hillenbrand, and A. Steane, J. Phys. B 26, 3063 (1993).
[CrossRef]

A. Hemmerich, M. Weidemuller, T. Esslinger, and T. W. Hansch, Europhys. Lett. 21, 445 (1993).
[CrossRef]

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

1992 (8)

A. M. Steane, G. Hillenbrand, and C. J. Foot, J. Phys. B 25, 4721 (1992).
[CrossRef]

J. Javanainen, Phys. Rev. A. 46, 5819 (1992).
[CrossRef] [PubMed]

T. P. Dinneen, C. D. Wallace, and P. L. Gould, Opt. Commun. 92, 277 (1992).
[CrossRef]

C. Valentin, M. C. Gagne, J. Yu, and P. Pillet, Europhys. Lett. 17, 133 (1992).
[CrossRef]

M. Walhout, J. Dalibard, S. L. Rolston, and W. D. Phillips, J. Opt. Soc. Am. B 9, 1997 (1992).
[CrossRef]

J. Werner, H. Wallis, and W. Ertmer, Opt. Commun. 94, 525 (1992).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, T. T. Grove, and P. L. Gould, Phys. Rev. Lett. 69, 897 (1992).
[CrossRef] [PubMed]

A. M. Steane, M. Chowdhury, and C. J. Foot, J. Opt. Soc. Am. B 9, 2142 (1992).
[CrossRef]

1991 (5)

A. M. Steane and C. J. Foot, Europhys. Lett. 14, 231 (1991).
[CrossRef]

S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
[CrossRef] [PubMed]

J. Javanainen, Opt. Commun. 86, 475 (1991).
[CrossRef]

D. Sesko, T. Walker, and C. Wieman, J. Opt. Soc. Am. B 8, 946 (1991).
[CrossRef]

K. Molmer, Phys. Rev. A 44, 5820 (1991).
[CrossRef] [PubMed]

1990 (4)

E. Riis, D. S. Weiss, K. A. Moler, and S. Chu, Phys. Rev. Lett. 64, 1658 (1990).
[CrossRef] [PubMed]

J. Nellessen, J. Werner, and W. Ertmer, Opt. Commun. 78, 300 (1990).
[CrossRef]

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

T. Walker, D. Sesko, and C. Wieman, Phys. Rev. Lett. 64, 408 (1990).
[CrossRef] [PubMed]

1989 (5)

1988 (1)

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

1986 (1)

Buch, P.

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Castin, Y.

Y. Castin, J. Dalibard, and C. Cohen-Tannoudji, in Light Induced Kinetic Effects on Atoms, Ions, and Molecules 1990, L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and F. Strumia, eds. (ETS Editrice, Pisa, 1991), p. 5.

Chowdhury, M.

Chu, S.

E. Riis, D. S. Weiss, K. A. Moler, and S. Chu, Phys. Rev. Lett. 64, 1658 (1990).
[CrossRef] [PubMed]

P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989).
[CrossRef]

D. S. Weiss, R. Riis, Y. Shevy, P. J. Ungar, and S. Chu, J. Opt. Soc. Am. B 6, 2072 (1989).
[CrossRef]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Clairon, A.

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

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Cohen-Tannoudji, C.

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Y. Castin, J. Dalibard, and C. Cohen-Tannoudji, in Light Induced Kinetic Effects on Atoms, Ions, and Molecules 1990, L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and F. Strumia, eds. (ETS Editrice, Pisa, 1991), p. 5.

Csambal, C.

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Dalibard, J.

M. Walhout, J. Dalibard, S. L. Rolston, and W. D. Phillips, J. Opt. Soc. Am. B 9, 1997 (1992).
[CrossRef]

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

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).
[CrossRef]

Y. Castin, J. Dalibard, and C. Cohen-Tannoudji, in Light Induced Kinetic Effects on Atoms, Ions, and Molecules 1990, L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and F. Strumia, eds. (ETS Editrice, Pisa, 1991), p. 5.

Dinneen, T. P.

T. P. Dinneen, C. D. Wallace, and P. L. Gould, Opt. Commun. 92, 277 (1992).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, T. T. Grove, and P. L. Gould, Phys. Rev. Lett. 69, 897 (1992).
[CrossRef] [PubMed]

Drewsen, M.

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Ertmer, W.

H. Wallis, J. Werner, and W. Ertmer, Comments At. Mol. Phys. 28, 275 (1993).

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

J. Werner, H. Wallis, and W. Ertmer, Opt. Commun. 94, 525 (1992).
[CrossRef]

J. Nellessen, J. Werner, and W. Ertmer, Opt. Commun. 78, 300 (1990).
[CrossRef]

Esslinger, T.

A. Hemmerich, M. Weidemuller, T. Esslinger, and T. W. Hansch, Europhys. Lett. 21, 445 (1993).
[CrossRef]

Foot, C. J.

A. M. Steane, G. Hillenbrand, and C. J. Foot, J. Phys. B 25, 4721 (1992).
[CrossRef]

A. M. Steane, M. Chowdhury, and C. J. Foot, J. Opt. Soc. Am. B 9, 2142 (1992).
[CrossRef]

A. M. Steane and C. J. Foot, Europhys. Lett. 14, 231 (1991).
[CrossRef]

Gagne, M. C.

C. Valentin, M. C. Gagne, J. Yu, and P. Pillet, Europhys. Lett. 17, 133 (1992).
[CrossRef]

Gerz, C.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

Gould, P. L.

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, T. T. Grove, and P. L. Gould, Phys. Rev. Lett. 69, 897 (1992).
[CrossRef] [PubMed]

T. P. Dinneen, C. D. Wallace, and P. L. Gould, Opt. Commun. 92, 277 (1992).
[CrossRef]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Grison, D.

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Grove, T. T.

C. D. Wallace, T. P. Dinneen, K. Y. N. Tan, T. T. Grove, and P. L. Gould, Phys. Rev. Lett. 69, 897 (1992).
[CrossRef] [PubMed]

Guellati, S.

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

Hansch, T. W.

A. Hemmerich, M. Weidemuller, T. Esslinger, and T. W. Hansch, Europhys. Lett. 21, 445 (1993).
[CrossRef]

Haubrich, D.

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

Hemmerich, A.

A. Hemmerich, M. Weidemuller, T. Esslinger, and T. W. Hansch, Europhys. Lett. 21, 445 (1993).
[CrossRef]

Hillenbrand, G.

J. Werner, H. Wallis, G. Hillenbrand, and A. Steane, J. Phys. B 26, 3063 (1993).
[CrossRef]

A. M. Steane, G. Hillenbrand, and C. J. Foot, J. Phys. B 25, 4721 (1992).
[CrossRef]

Hodapp, T. W.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

Hope, A.

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

Javanainen, J.

J. Javanainen, Phys. Rev. A. 46, 5819 (1992).
[CrossRef] [PubMed]

J. Javanainen, Opt. Commun. 86, 475 (1991).
[CrossRef]

Jessen, P.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

Jones, K. M.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

Kaenders, W. G.

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

Kohns, P.

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Laurent, P.

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Lett, P. D.

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

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Lounis, B.

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Meschede, D.

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

Metcalf, H.

S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
[CrossRef] [PubMed]

Metcalf, H. J.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Moler, K. A.

E. Riis, D. S. Weiss, K. A. Moler, and S. Chu, Phys. Rev. Lett. 64, 1658 (1990).
[CrossRef] [PubMed]

Molmer, K.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

K. Molmer, Phys. Rev. A 44, 5820 (1991).
[CrossRef] [PubMed]

Muller, G.

A. Hope, D. Haubrich, G. Muller, W. G. Kaenders, and D. Meschede, Europhys. Lett. 22, 669 (1993).
[CrossRef]

Nadir, A.

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Nellessen, J.

J. Nellessen, J. Werner, and W. Ertmer, Opt. Commun. 78, 300 (1990).
[CrossRef]

Nienhuis, G.

S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
[CrossRef] [PubMed]

Phillips, W. D.

C. Gerz, T. W. Hodapp, P. Jessen, K. M. Jones, W. D. Phillips, C. I. Westbrook, and K. Molmer, Europhys. Lett. 21, 661 (1993).
[CrossRef]

M. Walhout, J. Dalibard, S. L. Rolston, and W. D. Phillips, J. Opt. Soc. Am. B 9, 1997 (1992).
[CrossRef]

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

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

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, Phys. Rev. Lett. 61, 169 (1988).
[CrossRef] [PubMed]

Pillet, P.

C. Valentin, M. C. Gagne, J. Yu, and P. Pillet, Europhys. Lett. 17, 133 (1992).
[CrossRef]

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Pritchard, D. E.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Riis, E.

E. Riis, D. S. Weiss, K. A. Moler, and S. Chu, Phys. Rev. Lett. 64, 1658 (1990).
[CrossRef] [PubMed]

P. J. Ungar, D. S. Weiss, E. Riis, and S. Chu, J. Opt. Soc. Am. B 6, 2058 (1989).
[CrossRef]

Riis, R.

Rolston, S. L.

Salomon, C.

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

A. Clairon, P. Laurent, A. Nadir, M. Drewsen, D. Grison, B. Lounis, and C. Salomon, in Proceedings of the VI European Frequency and Time Forum, J. J. Hunt, ed., ESA Spec. Pub. 340 (European Space Agency, European Space Technology Center, Noordwijk, The Netherlands, 1992), p. 27.

Sesko, D.

D. Sesko, T. Walker, and C. Wieman, J. Opt. Soc. Am. B 8, 946 (1991).
[CrossRef]

T. Walker, D. Sesko, and C. Wieman, Phys. Rev. Lett. 64, 408 (1990).
[CrossRef] [PubMed]

Shang, S. Q.

S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
[CrossRef] [PubMed]

Sheehy, B.

S. Q. Shang, B. Sheehy, H. Metcalf, P. van der Straten, and G. Nienhuis, Phys. Rev. Lett. 67, 1094 (1991).
[CrossRef] [PubMed]

Shevy, Y.

Steane, A.

J. Werner, H. Wallis, G. Hillenbrand, and A. Steane, J. Phys. B 26, 3063 (1993).
[CrossRef]

Steane, A. M.

A. M. Steane, G. Hillenbrand, and C. J. Foot, J. Phys. B 25, 4721 (1992).
[CrossRef]

A. M. Steane, M. Chowdhury, and C. J. Foot, J. Opt. Soc. Am. B 9, 2142 (1992).
[CrossRef]

A. M. Steane and C. J. Foot, Europhys. Lett. 14, 231 (1991).
[CrossRef]

Suptitz, W.

P. Kohns, P. Buch, W. Suptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Tan, K. Y. N.

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We are assuming a small enough value of B that we can ignore the effects of different ground- and excited-state Landé g factors discussed in Refs. 19 and 20.

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Figures (9)

Fig. 1
Fig. 1

Typical TOF spectrum for 85Rb at |δ|/Γ ≈ 4 and It = 4.0 mW/cm2. The points are experimental data, and the solid curve is a fit for T = 9.8 μK.

Fig. 2
Fig. 2

Typical distribution of atoms in the axial direction. The points are experimental data, and the solid curve is a Gaussian fit with σmeas = 55 μm.

Fig. 3
Fig. 3

Spring constant as a function of axial magnetic field gradient for 85Rb at |δ|/Γ ≈ 2 and It = 20 mW/cm2. The solid curve is the best-fit line through the origin.

Fig. 4
Fig. 4

Temperature as a function of total trap intensity It (sum of all six beams) for 85Rb (in a) and 87Rb (in b). The symbol shape denotes the detuning: |δ|/Γ = 0.95 (◇), 1.87 (□), 3.04 (△), and 4.14 (○). Open symbols are experimental data, solid symbols are numerical simulations. The solid curves are best-fit lines to data points with 0.05 ≤ Ω2/|δ|Γ ≤ 0.9.

Fig. 5
Fig. 5

Same data as in Fig. 4, but plotted as a function of light-shift parameter Ω2/|δ|Γ. The solid curves are best-fit lines to the |δ|/Γ ≈ 4 data with Ω2/|δ|Γ ≥ 0.05.

Fig. 6
Fig. 6

Temperature comparison for the two isotopes at |δ|/Γ ≈ 4: 85Rb (○) and 87Rb (△). The solid curves are best-fit lines to the data with Ω2/|δ|Γ ≥ 0.05.

Fig. 7
Fig. 7

Axial spring constant κ for 85Rb (in a) and 87Rb (in b) as determined from trap size measurements. The symbol shape denotes the detuning: |δ|/Γ = 0.95 (◇), 1.87 (□), and 4.14 (○). The solid curves are three-dimensional simulations based on a Doppler model, whereas the dashed lines are the results of a one-dimensional sub-Doppler model [Eq. (7)] scaled down by a factor of 10 to fit on the graph. For both sets of theoretical curves, the upper (lower) curve denotes the smallest (largest) value of detuning.

Fig. 8
Fig. 8

Axial spring constant for 85Rb (in a) and 87Rb (in b) determined by the imbalance method (solid symbols). Equation (12), corrected by Eq. (13), is combined with the measured displacement to yield κ. The data from Fig. 7 (open symbols) are also plotted for comparison. For clarity, the |δ|/Γ ≈ 1 data are not shown, but the agreement is comparable.

Fig. 9
Fig. 9

Imbalance measurements for 85Rb (in a) and 87Rb (in b) plotted as the magnetic field at the location of the displaced cloud (B) per unit intensity imbalance (w). The solid curve is the best-fit line (through the origin) for the |δ|/Γ ≈ 4 data.

Equations (14)

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κ = 2 k B T / σ 2 .
σ meas 2 = σ 2 + σ 0 2 .
σ meas 2 = b d B z / d z + σ 0 2 ,
k B T Γ = ( C σ + σ - ) Ω 2 δ Γ + C 0 ,
κ = g J μ B k d B z d z α ,
α = c J k 2 2 δ Γ δ 2 + Γ 2 / 4 ,
κ = c J 2 g J μ B d B z d z k δ / Γ ( δ / Γ ) 2 1 / 4 .
v l = s 0 k δ 2 + a Γ 2 A .
s 0 = Ω 2 / 2 δ 2 + Γ 2 / 4 .
z l = Γ μ B d B z d z 1 2 g J A Ω 2 δ Γ .
w = I + - I - I + + I - ,
F = χ J w s 0 k Γ ,
ξ = I s / ( I s ) av { 1 + 6 [ I s / ( I s ) av ] s 0 } 2 .
B w = χ j c J g J Γ μ B Ω 2 δ Γ .

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