Abstract

Multiple scattering is studied in a Cs magneto-optical trap (MOT). We use two Abel inversion algorithms to recover density distributions of the MOT from fluorescence images. Deviations of the density distribution from a Gaussian are attributed to multiple scattering.

© 2005 Optical Society of America

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References

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Appl. Opt. (2)

Appl. Phys. B (1)

M. Drewsen, P. 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 (1994).
[CrossRef]

Europhys. Lett. (1)

C. Gabbanini, A. Evangelista, S. Gozzini, A. Lucchesini, A. Fioretti, J. H. Muller, M. Colla and E. Arimondo, “Scaling laws in magneto-optical traps,” Europhys. Lett. 37, 251 (1997).
[CrossRef]

J. Opt. B: Quant. Semiclass. Opt. (1)

T.M. Brzozowski, M. Maczynska, M. Zawada, J. Zachorowski and W. Gawalik, “Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances,” J. Opt. B: Quant. Semiclass. Opt., 4, 62 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

J. Quant. Spect. Radiat. Transfer (1)

L. M. Smith, D. R. Keefer and S. I. Sudharsanan, “Abel Inversion Using Transform Techniques,” J. Quant. Spect. Radiat. Transfer 39, 367 (1988).
[CrossRef]

Opt. Commun. (1)

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

Phys. Rev. A (3)

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 (1995).
[CrossRef] [PubMed]

G. Hillenbrand, C. J. Foot and K. Burnett, “Heating due to long-range photon exchange interactions between cold atoms,” Phys. Rev. A 50, 1479 (1994).
[CrossRef] [PubMed]

K. Lindquist, M. Stephens and C. Wieman, ”Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap,” Phys. Rev. A , 4082 (1992).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (3)

C. R. Gebhardt, T. P. Rakitzis, P. C. Samartzis, V. Ladopoulos and T. N. Kitsopoulos, “Slice imaging: A new approach to ion imaging and velocity mapping,” Rev. Sci. Instrum. 72, 2001 (2001).
[CrossRef]

V. Dribinski, A. Osssadtchi, V. A. Mandelshtam and H. Reisler, “Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634 (2002).
[CrossRef]

K. R. Overstreet, J. Franklin and J. P. Shaffer, “Zeeman effect spectroscopically locked Cs diode laser system for atomic physics,” Rev. Sci. Instrum. 75, 4749 (2004).
[CrossRef]

SIAM J. Matrix Anal. Appl. (1)

G. H. Golub, P. C. Hansen and D. P. O’Leary, “Tikhonov Regularization and Total Least Squares,” SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

Other (3)

J.P. Shaffer, Ph.D. Thesis, University of Rochester (1999).

K. Iizuka, Engineering Optics (Springer-Verlag, 1987).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Mapping of a 3-D distribution onto a 2-D plane. Also depicted is the projection of a slice at constant z.

Fig. 2.
Fig. 2.

(a.) MOT density versus Natoms trapped. (b.) MOT volume versus Natoms trapped. (c.) Natoms1/3 versus MOT radius. (d.) Temperature as a function of detuning as measured from time-of-flight velocity distributions for I = 30mW/cm2 and magnetic field gradient dB/dz= 15G/cm. Open triangles (△) represent data analyzed using the BASEX transform, closed circles (●) were analyzed using the Fourier-Hankel transform.

Fig. 3.
Fig. 3.

Comparison of raw image to the Fourier-Hankel and BASEX transform methods. Additional structure is visible in both transformed images. The raw image was taken for Natoms = 2.0×106, a laser intensity of 30mW/cm2, and a magnetic field gradient dB/dz = 15G/cm.

Fig. 4.
Fig. 4.

Correlation of the (a.) raw images, (b.) Fourier-Hankel transform (●) and BASEX (⊕) to a Gaussian fit. The inset in (b.) shows an adjacent averaging of the R2 data.

Equations (16)

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R h ¯ ω L Γ 2 C 1 2 Ω tot 2 2 δ 2 + Γ 2 4 + C 2 2 Ω tot 2 2 ,
f ( x , y , z ; v x , v y , v z , t ) i = x , y , z e ( i v i t ) 2 / 2 σ i 2 e m v i 2 / 2 k B T .
f ( z , t ) e m z 2 / 2 σ z ( t ) 2 .
P ( x , z ) = 2 x I ( r , z ) r r 2 x 2 d r ,
I ( r , z ) = 1 π r d P ( x , z ) / d x x 2 r 2 d x .
F { P ( x ) } = I ( x 2 + y 2 ) e 2 πixk d x d y .
F { P ( x ) } = 2 π 0 r I ( r ) J 0 ( 2 πkr ) d r .
I ( r ) = 2 π 0 k J 0 ( 2 πkr ) P ( x ) e 2 πixk d x d k .
P ( x , z ) = Abel { I ( r , z ) } = k = 0 N 1 C k Abel { f k ( r , z ) } = k = 0 N 1 C k G k ( x , z ) .
P ij = k = 0 K 1 C k G ij ( k ) ,
G ij ( k ) = 2 h ( x x i , z z j ) x r f k ( r , z ) r 2 x 2 d x d z d r ,
X mi = 2 h x ( x x i ) x r ρ m ( r ) r 2 x 2 d x d r
Z nj = h z ( z z j ) ξ n ( z ) d z .
P ij = m = 0 N x 1 n = 0 N z 1 C mn X mi Z nj
ρ m ( r ) = ( e m 2 ) m 2 ( r σ ) 2 m 2 e ( r / σ ) 2 ,
B ( k ) = 1 1 + ( k k 0 ) 2 n ,

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