Abstract

We present an experimental study of the spatial diffusion of a single ion in a polarization gradient field. A 24Mg+ ion was radially confined in a two-dimensional radio-frequency (rf) trap, while an optical lattice superimposed on a weak electric potential was applied along the free axis. With the help of a statistical analysis of single ion trajectories, a spatial diffusion constant was obtained as a function of optical potential depth. The results are compared to semiclassical theoretical models for trapped ions and neutral atoms.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. H. Katori, S. Schlipf, L. Perotti, and H. Walther, to be published.

Other

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]

J. Dalibard and C. Cohen{Tannoudji, J. Opt. Soc. Am. B 6, 2023 (1989).

G. Grynberg and S. Triche, in Proceedings of the International School of Physics Enrico Fermi, Course CXXXI, edited by A. Aspect et al. IOS Press, Amsterdam (1996).

Y. Castin, J. Dalibard and C. Cohen-Tannoudji, in Proceedings of the LIKE workshop, edited by L. Moi et.al. ETS Editrice, Paris (1991).

J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
[CrossRef]

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

S. Marksteiner, K. Ellinger, and P. Zoller, Phys. Rev. A53, 3409 (1996)

H. Katori, S. Schlipf, and H. Walther, Phys. Rev. Lett. 79, 2221 (1997).
[CrossRef]

T. W. Hodapp, C. Gerz, C. Furtlehner, C. I. Westbrook, W. D. Phillips, and J. Dalibard, Appl. Phys. B 60, 135 (1995).
[CrossRef]

C. Jurczak, B. Desruelle, K. Sengstock, J.-Y. Courtois, C. I. Westbrook, and A. Aspect, Phys. Rev. Lett. 77, 1727 (1996).
[CrossRef] [PubMed]

P. Pax, W. Greenwood, and P. Meystre, Phys. Rev. A56, 2109 (1997).

I. Waki, S. Kassner, G. Birkl, and H. Walther, Phys. Rev. Lett. 68 2007 (1992).
[CrossRef] [PubMed]

H. Katori, S. Schlipf, L. Perotti, and H. Walther, to be published.

Supplementary Material (1)

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Figures (4)

Figure 1.
Figure 1.

Sketch of the ring trap. The shape of the electrostatic and optical potentials is depicted in the inset. The electrostatic potential is formed by two additional electrodes which are not shown in the figure. The lower picture shows a trajectory measurement. In this special case another ion enters the observation region defined by the electrostatic potential from the left (see text for details). The kinetic energy of the ions corresponds to a temperature of roughly 1 mK.

Figure 2.
Figure 2.

Results for the position autocorrelation functions for different optical potential depths. The oscillation at the U 0 = 37ER is due to the motion of the ion in the external electric potential. For all the curves the laser intensity is I = 4ISat .

Figure 3.
Figure 3.

The spatial diffusion coefficient Dx as a function of optical potential depth U 0. The symbols mark measurements taken on different days.

Figure 4.
Figure 4.

Comparison between theory and experiment. The experimental data are identical to the ones plotted in Fig. 3. The theory from Ref. [9] is marked with FPK. This treatment neglects localization by an optical potential. The difference between the two Monte-Carlo simulations is that in the ion case the superimposed external electric potential is included.

Equations (5)

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ϕ ( τ ) = [ x ( t + τ ) x ( t ) ] 2 = 2 x 2 2 x ( 0 ) x ( τ ) ,
m x ̈ + γ x ̇ + m ω ext 2 x = F ( t ) .
ϕ ( τ ) = 2 k B T m ω ext 2 [ 1 exp ( m ω ext 2 τ γ ) ] .
ϕ ( 0 ) = 2 k B T γ = 2 D X .
ϕ ( τ ) = 2 k B T m ω ext 2 [ 1 exp ( γτ 2 m ) cos ( ω ext τ ) ] ,

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