Radium single-ion optical clock

Abstract

We explore the potential of the electric quadrupole transitions $7s{}^2{S}_{1/2}$ - $6d{}^2{D}_{3/2}$, $6d{}^2{D}_{5/2}$ 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 $7s{}^2{S}_{1/2}(F=2,m_F=0)$ - $6d{}^2{D}_{3/2}(F=0,m_F=0)$ 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.

20 pages, 1 figure