Modes of oscillation in radiofrequency Paul traps
Abstract
We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional 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.
- Publication:
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New Journal of Physics
- Pub Date:
- September 2012
- DOI:
- 10.1088/1367-2630/14/9/093023
- arXiv:
- arXiv:1206.4006
- Bibcode:
- 2012NJPh...14i3023L
- Keywords:
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- Quantum Physics
- E-Print:
- 24 pages, 3 figures, v2 adds citations and small corrections