Abstract
The distribution function for Brownian motion of a parametric oscillator is calculated exactly with the help of continued fraction expansions in the long time limit. We derive expressions for the energy and the widths of the spatial and velocity distribution. Our results are relevant to understand confinement of particles in radio frequency ion traps.
Similar content being viewed by others
References
Ince, E.L.: Ordinary differential equations. New York: Longmans 1977
Mc Lachlan, N.W.: Theory and application of Mathieu functions. Oxford: Clarendon Press 1947
Wang, M.C., Uhlenbeck, G.E.: Rev. Mod. Phys.17, 323 (1945)
Risken, H.: The Fokker Planck equation: methods of solution and applications. In: Springer Series in synergetics. Vol. 18. Berlin, Heidelberg, New York, Tokyo: Springer-Verlag 1984
Kampen, N.G. van: Stochastic processes in physics and chemistry. Amsterdam: North-Holland 1981
Dehmelt, H.G.: Adv. At. Mol. Phys.3, 53 (1967)
Wineland, D.J., Itano, W.M., Dyck, R.S. van, jr.: Adv. At. Mol. Phys.19, 135 (1983)
Meixner, T., Schäffke, F.W.: Mathieu'sche Funktionen und Sphäroidfunktionen. Berlin, Göttingen, Heidelberg: Springer-Verlag 1954
Knight, R.D., Prior, M.H.: J. Appl. Phys.50, 3044 (1979)
Schaaf, H., Werth, G.: Appl. Phys.25, 249 (1981)
Toschek, P.E.: Les Houches XXXVIII. 383 (1984). Amsterdam, Oxford, New York, Tokyo: North-Holland 1984
For a review on laser cooling see Stenholm, S.: Rev. Mod. Phys. (to be published)
Cook, R., Shankland, D.G., Wells, A.L.: Phys. Rev. A31, 564 (1985)
Haken, H.: Laser theory. In: Encyclopedia of Physics. Vol. XXV/2c. Berlin, Heidelberg, New York: 1970
Ichimaru, S.: Basic principles of plasma physics: a statistical approach. In: Frontiers in Physics Lecture Note Series. Reading, Ma.: Benjamin/Cummings 1973
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Blatt, R., Zoller, P., Holzmüller, G. et al. Brownian motion of a parametric oscillator: A model for ion confinement in radio frequency traps. Z Phys D - Atoms, Molecules and Clusters 4, 121–126 (1986). https://doi.org/10.1007/BF01437349
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01437349