Highly charged Nd$^{9+}$ Ion: A potential candidate of $\upmu$Hz linewidth optical clocks for probing fundamental physics

An active optical clock based on highly charged Nd$^{9+}$ ion is proposed for the first time. The clock can offer ultra-narrow linewidth at the $\upmu$Hz-level which is more than two-order of magnitude below the currently recorded laser linewidth. Operating at 605(90) nm superradiation lasing transition between the $5p^2~4f$ ground state and one of the long-lived $5p~4f^2$ excited state, the proposed active clock is inherently immune against the cavity noise which provides high stability. The clock serves as a sensitive probe with high sensitivity to variation of the fine-structure constant with accuracies below 10$^{-19}$ level. Sophisticated relativistic many-body methods are employed to predict related atomic properties that have corroborated the above findings.