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We report measurements of the lifetimes of the 3d $^2$D$_{5/2}$ and 3d$^2$D$_{3/2}$ metastable states of a single laser-cooled $^{40}$Ca$^+$ ion in alinear Paul trap. We introduce a new measurement technique based onhigh-efficiency quantum state detection after coherent excitation to theD$_{5/2}$ state or incoherent shelving in the D$_{3/2}$ state, and subsequentfree, unperturbed spontaneous decay. The result for the natural lifetime of theD$_{5/2}$ state of 1168(9) ms agrees excellently with the most precisepublished value. The lifetime of the D$_{3/2}$ state is measured with a singleion for the first time and yields 1176(11) ms which improves the statisticaluncertainty of previous results by a factor of four. We compare theseexperimental lifetimes to high-precision ab initio all order calculations andfind a very good agreement. These calculations represent an excellent test ofhigh-precision atomic theory and will serve as a benchmark for the study ofparity nonconservation in Ba$^+$ which has similar atomic structure.Comment: 13 pages, 8 figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Experimental and theoretical study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mi>d</mml:mi><mml:mspace width="0.3em" /><mml:mmultiscripts><mml:mi>D</mml:mi><mml:mprescripts /><mml:none /><mml:mn>2</mml:mn></mml:mmultiscripts></mml:math>–level lifetimes of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Ca</mml:mi><mml:none /><mml:mo>+</mml:mo><mml:mprescripts /><mml:none /><mml:mn>40…

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