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Radium single-ion optical clock

We explore the potential of the electric quadrupole transitions $7s\,^2S_{1/2}$ - $6d\,^2D_{3/2}$, $6d\,^2D_{5/2}$ in radium isotopes as single-ion optical frequency standards. The frequency shifts of the clock transitions due to external fields and the corresponding uncertainties are calculated. Several competitive $^A$Ra$^+$ candidates with $A=$ 223 - 229 are identified. In particular, we show that the transition $7s\,^2S_{1/2}\,(F=2,m_F=0)$ - $6d\,^2D_{3/2}\,(F=0,m_F=0)$ at 828 nm in $^{223}$Ra$^+$, with no linear Zeeman and electric quadrupole shifts, stands out as a relatively simple case, which could be exploited as a compact, robust, and low-cost atomic clock operating at a fractional frequency uncertainty of $10^{-17}$. With more experimental effort, the $^{223,225,226}$Ra$^+$ clocks could be pushed to a projected performance reaching the $10^{-18}$ level.