| Summary: | Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, long-range interactions between Rydberg atoms. Combining the two systems is not at all straightforward. Rydberg atoms are severely affected by electric fields which may cause Stark shifts and field ionization, while electric fields are used to trap ions. Thus, a thorough understanding of the physical properties of Rydberg ions due to the trapping electric fields is essential for future applications. Here, we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the trapping electric quadrupole fields which leads to Floquet sidebands in the excitation spectra. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state that results from the strong polarizability of the Rydberg ion. By controlling both effects we observe resonance lines close to their natural linewidth demonstrating an unprecedented level of control of this novel quantum platform.
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