Sympathetic electromagnetically induced transparency ground state cooling of a ⁴⁰Ca ⁺– ²⁷Al ⁺ pair in an ²⁷Al ⁺ clock

We report on electromagnetically induced transparency cooling of ⁴⁰Ca ⁺ to sympathetically cool the three-dimensional secular modes of motion in a ⁴⁰Ca ⁺– ²⁷Al ⁺ two-ion pair near the ground state. We observe simultaneous ground state cooling across all radial modes and axial modes of a ⁴⁰Ca ⁺– ²⁷Al ⁺ ion pair, occupying a broader cooling range in frequency space over 3 MHz. The cooling time is observed to be less than 1 ms. The mean phonon number and heating rates of all motional modes are measured. This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ²⁷Al ⁺ optical clock, but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.