Potential of electric quadrupole transitions in radium isotopes for single-ion optical frequency standards

We explore the potential of the electric quadrupole transitions 7s (2)S(1/2)-(6)d (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.