Speaker
Description
Our group has demonstrated the trapping of parallel chains of ${}^{40}\mathrm{Ca}^+$ ions using a planar-electrode ion trap. By applying two radio-frequency (RF) voltages, a double-well potential is generated, and the distance between ion chains can be controlled by adjusting the ratio of these RF voltages. Ideally, the trapping potential is perfectly harmonic for a one-dimensional ion chain. In practice, however, distortions arise from stray electric fields and electrode asymmetries. These effects become more pronounced in double-well configuration, where more complex electrode structures are required. In this study, we characterize the trapping potential from ion imaging data by extracting higher-order motional eigenmodes. To this end, we develop and demonstrate techniques to optically excite motional modes and perform time-resolved imaging. These methods provide access to higher-order modes and their phase information, enabling detailed characterization of stray fields and nonlinear components of the trapping potential. These techniques are expected to enable accurate estimation of trapping potentials via the mode-structure measurements, extending beyond harmonic confinement to anharmonic potentials and two-dimensional ion configurations.
We define the direction along which ions align in a single chain as the $z$-axis. For a system of $N$ ions confined in a harmonic potential, the total potential consists of the harmonic confinement and the Coulomb interaction between ions. This system exhibits $N$ normal modes of vibration along the $z$-axis. The curvature of the harmonic potential corresponds to the eigenvalue of the fundamental motional mode, known as the center-of-mass (COM) mode, in which all ions oscillate in phase with equal amplitude.
There are two primary methods for measuring motional frequencies. One method is based on sideband spectroscopy, which identifies modes from carrier and sideband transitions, but requires highly stable lasers and precise spectroscopic techniques. The other method is electrical “tickling,” in which forced oscillations are induced by applying an AC signal to a DC electrode. By detecting resonance, the eigenfrequency of a mode can be determined. This method is widely used due to its simplicity; however, because it generates a global excitation field acting on the entire ion chain, it becomes increasingly difficult to excite higher-order modes due to the asymmetry of their eigenvectors. To overcome this limitation, we investigate an alternative approach termed optical tickling, in which motional modes are excited via amplitude modulation of the cooling laser. By individually addressing ions, a localized excitation field is generated, enabling efficient excitation of all normal modes, including higher-order modes that are difficult to access electrically. In parallel, we are developing a time-resolved imaging technique capable of measuring eigenvectors of the excited modes with phase resolution. We have demonstrated this method for COM and stretch modes by using an acousto-optic modulator as a fast optical shutter. In this presentation, we report recent progress in the excitation of higher-order motional modes using optical tickling and their characterization via time-resolved imaging.
| Academic level | PhD student |
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