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



Jonathan Home, David Hanneke, John D. Jost, Dietrich Leibfried, David J. Wineland


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, which become significant at different levels of anharmonicity. The first is a modification of the frequencies and mode vectors 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 becomes important. We evaluate 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.
New Journal of Physics


anharmonicity, ion trap, normal modes, quantum information


Home, J. , Hanneke, D. , Jost, J. , Leibfried, D. and Wineland, D. (2011), Normal modes of trapped ions in the presence of anharmonic trap potentials, New Journal of Physics, [online],, (Accessed April 23, 2024)
Created July 19, 2011, Updated January 2, 2024