Abstract
We solve numerically the classical equations of motion [1] for two damped (laser-cooled) ions in a Paul r.f. trap [2]. These equations are very similar to those describing two coupled, driven anharmonic Duffing oscillators and suggest that the two-trapped ion system may be a suitable test system for studies of nonlinear dynamics and chaos on the atomic level. These studies are of interest in part because of the extensive recent experiments with modifications of the original Paul r.f. quadrupole design [3] in order to miniaturize and simplify the trap structure or with the intent of making frequency standards; for frequency standard purposes chaotic motion is something to be studied and avoided. In addition, the possibility has arisen recently of laser cooling trapped ions down to their lowest quantum states with the possibility of generating nonclassical states of motion and even in using stored ions in constructing quantum logic gates [4].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
See, for example, J.W. Emmert, M. Moore and R. Blümel, Phys. Rev. A 48, R1757 (1993)
J. Hoffnagle, R.G. DeVoe, L. Rayna and R.G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
For a survey of recent work with trapped ions including their potential for frequency standards and fundamental measurements, see, for example R. Blatt, P. Gill and R.C. Thompson, J. Modern Optics 39, 193 (1992)
R. Blatt, in Atomic Physics 14, AIP Conference Proceedings #323 (1995), p. 219.
E.g., N. Yu, H. Dehmelt and W. Nagourney, Proc. Natl. Acad. Sci. 86, 5672 (1989)
M.G. Raizen, et al. 45, 6493 (1992)
C.A. Schrama, E. Peik, W.W. Smith and H. Walther, Optics Commun. 101, 32 (1993).
J. Cirac, et al. Phys. Rev. A 49, R3174 (1994); J. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); C. Monroe et al. (preprint, 1994 ).
See, for example F. Diedrich, et al., Phys. Rev. Lett. 59, 2931 (1987)
R. Blümel, J.M. Chen, E. Peik, W. Quint, W. Schleich, Y.R. Shen and H. Walther, Nature 334, 309 (1988)
D.J. Wineland et al., Phys. Rev. Lett 59, 2935 (1987)
Th. Sauter, et al., Z. Phys. D 10, 153 (1988).
R. Blümel, C. Kappler, W. Quint and H. Walther, Phys. Rev. A 40, 808 (1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this paper
Cite this paper
Mackie, M., Jensen, R.V., Smith, W.W. (1996). Sensitivity to perturbations for two-ion crystals in a Paul trap: fractal phase space boundary. In: Eberly, J.H., Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics VII. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9742-8_229
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9742-8_229
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9744-2
Online ISBN: 978-1-4757-9742-8
eBook Packages: Springer Book Archive