Iterative precision measurement of branching ratios applied to 5P states in 88Sr

We report and demonstrate a method for measuring the branching ratios of dipole transitions of trapped atomic ions by performing nested sequences of population inversions. This scheme is broadly applicable to species with metastable lambda systems and can be generalized to find the branching of any state to lowest states. It does not use ultrafast pulsed or narrow linewidth lasers and is insensitive to experimental variables such as laser and magnetic field noise as well as ion heating. To demonstrate its effectiveness, we make the most accurate measurements thus far of the branching ratios of both and states in 88Sr+ with sub-1% uncertainties. We measure 17.175(27) for the – branching ratio, 15.845(71) for –, and 0.056 09(21) for –. These values represent the first precision measurement for –, as well as ten- and thirty-fold improvements in precision respectively for – and – over the best previous experimental values.