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 derive analytically the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a method of infinite determinants to find the modes which diagonalize the linearized time-dependent dynamical problem. This allows obtaining 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.

24 pages, 3 figures, v2 adds citations and small corrections

References in corpus (6)

• Complete methods set for scalable ion trap quantum information processing
• Fabrication and heating rate study of microscopic surface electrode ion traps
• Double wells, scalar fields and quantum phase transitions in ions traps
• Two-Dimensional Arrays of RF Ion Traps with Addressable Interactions
• Translational cooling and storage of protonated proteins in an ion trap at subkelvin temperatures
• Fast and robust quantum computation with ionic Wigner crystals

Cited by in corpus (10)

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• Controlling two-dimensional Coulomb crystals of more than 100 ions in a monolithic radio-frequency trap
• Classical and Quantum Modes of Coupled Mathieu Equations
• Quantum Computation under Micromotion in a Planar Ion Crystal
• Imaging the collective excitations of an ultracold gas using statistical correlations
• Revealing quantum statistics with a pair of distant atoms
• High Fidelity Quantum Gates for Trapped Ions under Micromotion
• Two-dimensional spectroscopy for the study of ion Coulomb crystals
• Simulation of Motion of Many Ions in a Linear Paul Trap
• An open-endcap blade trap for radial-2D ion crystals