Experimental and theoretical study of the 3d ²D–level lifetimes of ⁴⁰Ca⁺

We report measurements of the lifetimes of the 3d ²D_5∕2 and 3d ²D_3∕2 metastable states of a single laser-cooled ⁴⁰Ca⁺ ion in a linear Paul trap. We introduce a measurement technique based on high-efficiency quantum state detection after coherent excitation to the D_5∕2 state or incoherent shelving in the D_3∕2 state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the D_5∕2 state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the D_3∕2 state is measured with a single ion and yields 1176(11) ms which improves the statistical uncertainty of previous results by a factor of four. We compare these experimental lifetimes to high-precision ab initio all order calculations [D_3∕2 state: 1196(11) ms; D_5∕2 state: 1165(11) ms] and find a very good agreement. These calculations represent an excellent test of high-precision atomic theory and will serve as a benchmark for the study of parity nonconservation in Ba⁺ which has similar atomic structure.