Normal modes of trapped ions in the presence of anharmonic trap potentials

TL;DR

This paper investigates how anharmonic trap potentials affect the normal modes of trapped ions, revealing frequency shifts and implications for quantum information processing, especially as trap sizes decrease.

Contribution

It provides a combined theoretical and experimental analysis of anharmonic effects on ion trap normal modes, highlighting their significance in trap design and quantum applications.

Findings

Anharmonicity causes frequency and amplitude shifts in ion normal modes.

Higher anharmonicity leads to amplitude-dependent frequency shifts.

Anharmonic effects become more prominent as ion-electrode distance decreases.

Abstract

We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity. The first is a modification of the oscillation frequencies and amplitudes of the ions' normal modes of vibration for multi-ion crystals, resulting from each ion experiencing a different curvature in the potential. In the second effect, which occurs with increased anharmonicity or higher excitation amplitude, amplitude-dependent shifts of the normal-mode frequencies become important. We evaluate normal-mode frequency and amplitude shifts, and comment on the implications for quantum information processing and quantum state engineering. Since the ratio of the anharmonic to harmonic terms typically increases as the ion--electrode distance decreases, anharmonic effects will become more significant as ion trap sizes are reduced. To avoid unwanted problems, anharmonicities should therefore be taken into account at the design stage of trap development.