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We theoretically and experimentally examine the effects of anharmonic termsin the trapping potential for linear chains of trapped ions. We concentrate ontwo different effects that become significant at different levels ofanharmonicity. The first is a modification of the oscillation frequencies andamplitudes of the ions' normal modes of vibration for multi-ion crystals,resulting from each ion experiencing a different curvature in the potential. Inthe second effect, which occurs with increased anharmonicity or higherexcitation amplitude, amplitude-dependent shifts of the normal-mode frequenciesbecome important. We evaluate normal-mode frequency and amplitude shifts, andcomment on the implications for quantum information processing and quantumstate engineering. Since the ratio of the anharmonic to harmonic termstypically increases as the ion--electrode distance decreases, anharmoniceffects will become more significant as ion trap sizes are reduced. To avoidunwanted problems, anharmonicities should therefore be taken into account atthe design stage of trap development.

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