Abstract

We investigated how the size of ring-shaped clouds of cold, magneto-optically trapped sodium atoms depends on the trapping parameters: magnetic-field gradient and laser intensity, detuning, and misalignment. The experiments were carried out in the low-density regime (N < 106 atoms), and the ring radius was shown to be independent of the number of trapped atoms. The results are explained with a simple model including a coordinate-dependent vortex force and the usual magneto-optical trap forces.

© 1994 Optical Society of America

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  1. S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
    [CrossRef] [PubMed]
  2. D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
    [CrossRef] [PubMed]
  3. E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
    [CrossRef] [PubMed]
  4. T. Walker, D. Sesko, and C. Wieman, Phys. Rev. Lett. 64, 408 (1990).
    [CrossRef] [PubMed]
  5. D. Sesko, T. Walker, and C. Wieman, J. Opt. Soc. Am. B 8, 946 (1991).
    [CrossRef]
  6. V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).
  7. V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
    [CrossRef] [PubMed]
  8. A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore, 1990), p. 266.
  9. A. M. Steane, M. Chowdhury, and C. Foot, J. Opt. Soc. Am. B 9, 2142 (1992).
    [CrossRef]
  10. K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
    [CrossRef] [PubMed]
  11. P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
    [CrossRef]
  12. C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
    [CrossRef] [PubMed]
  13. W. Fairbank, T. Hänsch, and A. Schawlow, J. Opt. Soc. Am. 65, 199 (1975).
    [CrossRef]
  14. A. Steane and C. Foot, Europhys. Lett. 14, 231 (1991).
    [CrossRef]

1993 (1)

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

1992 (3)

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

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

1991 (2)

1990 (2)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

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

1988 (1)

P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
[CrossRef]

1987 (1)

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

1986 (2)

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

1975 (1)

Ashkin, A.

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

Bagnato, V.

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

Bagnato, V. S.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

Bjorkholm, J.

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

Cable, A.

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

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

Chowdhury, M.

Chu, S.

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

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

Fairbank, W.

Farrel, P. M.

P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
[CrossRef]

Foot, C.

Hänsch, T.

Kazantsev, A. P.

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore, 1990), p. 266.

Lindquist, K.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef] [PubMed]

MacGillivray, W. R.

P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
[CrossRef]

Marcassa, L. G.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

Monroe, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Oriá, M.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

Prentiss, M.

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

Pritchard, D.

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

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

Raab, E.

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

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

Robinson, H.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Schawlow, A.

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]

Standage, M. C.

P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
[CrossRef]

Steane, A.

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

Steane, A. M.

Stephens, M.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef] [PubMed]

Surdutovich, G. I.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore, 1990), p. 266.

Swann, W.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

Vitlina, R.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

Walker, T.

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]

Watts, R.

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

Wieman, C.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef] [PubMed]

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]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

Yakovlev, V. P.

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore, 1990), p. 266.

Zilio, S. C.

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

Europhys. Lett. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, and S. C. Zilio, Laser Phys. 2, 172 (1992).

Phys. Rev. A (3)

V. S. Bagnato, L. G. Marcassa, M. Oriá, G. I. Surdutovich, R. Vitlina, and S. C. Zilio, Phys. Rev. A 48, 3771 (1993).
[CrossRef] [PubMed]

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef] [PubMed]

P. M. Farrel, W. R. MacGillivray, and M. C. Standage, Phys. Rev. A 37, 4240 (1988).
[CrossRef]

Phys. Rev. Lett. (5)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef] [PubMed]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 314 (1986).
[CrossRef] [PubMed]

D. Pritchard, E. Raab, V. Bagnato, C. Wieman, and R. Watts, Phys. Rev. Lett. 57, 310 (1986).
[CrossRef] [PubMed]

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

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

Other (1)

A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, Mechanical Action of Light on Atoms (World Scientific, Singapore, 1990), p. 266.

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Figures (8)

Fig. 1
Fig. 1

Schematic representations of the laser-beam misalignment in the xy plane and of the forces acting on an atom in a stable ring of radius r. The radiation-trapping force Fr leads to a softening of the spring constant, and the vortex force Fv is balanced by the damping force.

Fig. 2
Fig. 2

Calculation of the ring radius as a function of the number of trapped atoms for various misalignments. We used I = 60 mW/cm2, Δ = −7 MHz, w = 6 mm, Is = 5 mW/cm2, and dB/dx = 10 G/cm.

Fig. 3
Fig. 3

Visual observation of the ring structure for a cell temperature of (a) 90 °C, (b) 70 °C, and (c) 30 °C. The conditions used for this experiment are s = 1.2 mm, Δ ~ −20 MHz, dB/dx = 10 G/cm, and I = 20 mW/cm2 (for each beam).

Fig. 4
Fig. 4

(a) Observed ring radius during the charging time at 30 °C, Δ ~ −20 MHz, s = 1.2 mm, and I = 20 mW/cm2 (for each beam). (b) Change of the trap fluorescence intensity with time as a reference for (a). The error bars in the data come from the average of five measurements.

Fig. 5
Fig. 5

Ring radius as a function of the magnetic-field gradient for I = 60 mW/cm2, s = 1.5 mm, and Δ = −10 MHz. The filled circles are experimental data, and the curves represent the radius given by Eq. (10).

Fig. 6
Fig. 6

Ring radius as a function of the misalignment for I = 60 mW/cm2, Δ = −10 MHz, and dB/dx = 10 G/cm. The curves are obtained through Eq. (10).

Fig. 7
Fig. 7

Ring radius as a function of the intensity of each laser beam for s = 1.5 mm, Δ = −10 MHz, and dB/dx = 10 G/cm.

Fig. 8
Fig. 8

Ring radius as a function of the detuning to red of the atomic transition 3S1/2 (F = 2) → 3P3/2 (F′ = 3) for s = 1.5 mm, I = 60 mW/cm2, and dB/dx = 10 G/cm.

Equations (10)

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

m d 2 r d t 2 = - K r - γ d r d t + α N r 2 r ^ + ξ ( r ) z ^ x r .
K = 16 k Γ Δ Ω 0 2 ( d ω / d x ) ( 4 Δ 2 + Γ 2 + 12 Ω 0 2 ) 2 ,
N = N [ η c + η r ln ( 2 η r N / π ) 2 π ] ,
α = I σ L 2 ( σ R / σ L - 1 ) 4 π c ,
Ω ± x 2 ( y , s ) = Ω 0 2 exp [ - 2 ( y ± s ) 2 / w 2 ]
ξ 0 = 8 k Γ ( s / w 2 ) Ω 0 2 4 Δ 2 + Γ 2 + 12 Ω 0 2 .
m r ω 2 = ( K - α N r 3 ) r ,
γ r ω = ξ ( r ) r .
r = [ α N K - m ω 2 ( r ) ] 1 / 3 .
r = { w 2 [ 1 - a γ ξ 0 ( K m ) 1 / 2 ] - 2 s 2 } 1 / 2 ,

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