Precision measurement of the3dD3/22–state lifetime in a single trappedCa+40

Abstract

We present a high-precision measurement of the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--state lifetime in a single trapped $^{40}\mathrm{Ca}^{+}$. The measurement was performed using a high-efficiency quantum-state detection technique to monitor quantum jumps and a high-precision and highly synchronous measurement sequence for laser control. A feature in our measurement is the pumping rate of the 729-nm laser that was corrected in a real-time way. The $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--state lifetime was obtained through the measurement of the spontaneous decay rate after incoherent shelving of the ion to the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$ state with a wait time. Systematic errors, such as collisions with background gases, heating effects, impurity components, the shelving and pumping rates, and state detection, were carefully analyzed and estimated. We determined an improved value of the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}$--state lifetime to be ${\ensuremath{\tau}}_{3/2}=1.195(8)$ s. Furthermore, the $3d\phantom{\rule{4pt}{0ex}}^{2}D_{3/2}\ensuremath{\rightarrow}4s\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}$ quadrupole transition matrix element was measured to be ${S}_{ki}=7.936(26)e{a}_{0}^{2}$, and the ratio between the lifetimes of $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}$ and $3d{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{5/2}$ was determined to be 1.018(11). Our method can be universally applied to lifetime measurements of other single ions and atoms with a similar structure.