Modes of oscillation in radiofrequency Paul traps
Abstract
We examine the timedependent 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 wellknown experimental observations. We use a recently proposed method to find the modes that diagonalize the linearized timedependent dynamical problem. This allows one to obtain explicitly the (‘FloquetLyapunov’) 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 timedependent quantum wavefunctions of ion oscillations in such traps can be obtained.
 Publication:

New Journal of Physics
 Pub Date:
 September 2012
 DOI:
 10.1088/13672630/14/9/093023
 arXiv:
 arXiv:1206.4006
 Bibcode:
 2012NJPh...14i3023L
 Keywords:

 Quantum Physics
 EPrint:
 24 pages, 3 figures, v2 adds citations and small corrections