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When multiple harmonic oscillators are coupled, they exhibit normal modes, which can be either delocalized or localized. The delocalized modes are used to exchange information between qubits in a Paul trap for quantum information processing, while localized modes can be used for frequency-resolved addressing. In this work, we observe both delocalized and localized normal modes depending on the coupling regime of a tapered Paul trap. We present the radial dynamics of multiple trapped ions, including the radial eigenfrequencies and eigenvectors of two and three calcium ions, studied both theoretically and experimentally [1]. A transition from delocalized to localized radial oscillations was observed as the axial confinement of the trap was decreased. The emergence of the localized modes at lower axial confinements is a direct consequence of the funnel-shaped potential of the tapered ion trap [2]. This behavior is fundamentally different from that of linear ion traps. This work lays the foundation for studying many-body phenomena with trapped ions and for advancing future quantum technologies.
[1] M. Bhardwaj, M. Göb, B. S. Nikolova, B. Bauerhenne, P. A. Ivanov, and K. Singer, “Transition from Collective to Local Radial Motional Modes in a Tapered Paul Trap”, arXiv: 2605.25125 (2026).
[2] B. Deng, M. Göb, M. Masuhr, J. Roßnagel, G. Jacob, D. Wang, and K. Singer, “A comprehensive study on a tapered Paul trap: from design to potential applications”, Quantum Science and Technology 10, 015017 (2024).
