Finding the ultra-narrow $^3\!P_2 \rightarrow \, ^3\!P_0$ electric quadrupole transition in Ni$^{12+}$ ion for an optical clock

Charles Cheung; Sergey G. Porsev; Dmytro Filin; Marianna S. Safronova; Malte Wehrheim; Lukas J. Spieß; Shuying Chen; Alexander Wilzewski; José R. Crespo López-Urrutia; Piet O. Schmidt

arXiv · 2502.05386

Finding the ultra-narrow $^3\!P_2 \rightarrow \, ^3\!P_0$ electric quadrupole transition in Ni$^{12+}$ ion for an optical clock

Charles Cheung·Sergey G. Porsev·Dmytro Filin·Marianna S. Safronova·Malte Wehrheim·Lukas J. Spieß·Shuying Chen·Alexander Wilzewski·José R. Crespo López-Urrutia·Piet O. Schmidt

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Abstract

The Ni$^{12+}$ ion features an electronic transition with a natural width of only 8 mHz, allowing for a highly stable optical clock. We predict that the energy of this strongly forbidden $3s^2 3p^4\, ^3\!P_2 \rightarrow 3s^2 3p^4 \, ^3\!P_0$ electric quadrupole transition is 20081(10) cm$^{-1}$. For this, we use both a hybrid approach combining configuration interaction (CI) with coupled-cluster (CC) method and a pure CI calculation for the complete 16-electron system, ensuring convergence. The resulting very small theoretical uncertainty of only 0.05\% allowed us to find the transition experimentally in a few hours, yielding an energy of 20078.984(10) cm$^{-1}$. This level of agreement for a 16-electron system is unprecedented and qualifies our method for future calculations of many other complex atomic systems. While paving the way for a high-precision optical clock based on Ni$^{12+}$, our theory and code development will also enable better predictions for other highly charged ions and other complex atomic systems.

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Charles Cheung, Sergey G. Porsev, Dmytro Filin, Marianna S. Safronova, Malte Wehrheim, Lukas J. Spieß, Shuying Chen, Alexander Wilzewski, José R. Crespo López-Urrutia, Piet O. Schmidt. 2025-02-08. Finding the ultra-narrow $^3\!P_2 \rightarrow \, ^3\!P_0$ electric quadrupole transition in Ni$^{12+}$ ion for an optical clock. https://arxiv.org/abs/2502.05386

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