Modes of oscillation in radiofrequency Paul traps

H. Landa*, M. Drewsen, B. Reznik, A. Retzker

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general threedimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We analytically derive the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a recently proposed method to find the modes that diagonalize the linearized time-dependent dynamical problem. This allows one to obtain explicitly the ('Floquet-Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small 'peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained.

Original languageEnglish
Article number093023
JournalNew Journal of Physics
StatePublished - Sep 2012


FundersFunder number
Seventh Framework Programme249958


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