Experimental and theoretical study of the3dD2–level lifetimes ofCa+40

Abstract

We report measurements of the lifetimes of the $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ and $3d\phantom{\rule{0.3em}{0ex}}^{2}D_{3∕2}$ metastable states of a single laser-cooled $^{40}\mathrm{Ca}^{+}$ 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 ${\mathrm{Ba}}^{+}$ which has similar atomic structure.