Sideband cooling of a $\hbox {Ca}^+$–$\hbox {In}^+$ ion chain toward the quantum logic spectroscopy of $\hbox {In}^+$

Abstract

Indium ions (${}^{115}\hbox {In}^+$) are a promising candidate for an optical clock with a frequency inaccuracy below $10^{-17}$. Quantum logic spectroscopy (QLS) plays a fundamental role in realizing such a clock by supplying a high-fidelity fast quantum state detection method. Initializing a phonon mode of an ion chain consisting of $\hbox {In}^+$ and an ancillary ion to the ground state is a fundamental step toward the implementation of QLS. We report experimental results of the sideband cooling and heating rate measurements of a ${}^{40}\hbox {Ca}^+$–${}^{115}\hbox {In}^+$ chain using optical transitions in $\hbox {Ca}^+$. The sideband cooling of the out-of-phase mode of the axial motion down to an estimated phonon number of 0.096 is demonstrated.