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arXiv:1609.04177 · Physical Review A

Precise determination of the quadrupole transition matrix element of Ca+40 via branching-fraction and lifetime measurements

H. Shao, Yao Huang, H. Guan, Chengbin Li, Tao Shi, K. Gao

Published May 24, 2017• 17 citations
arXivHTMLPDF

Abstract

We report the experimental determination of the $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ $\ensuremath{\leftrightarrow}$ $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ quadrupole transition matrix element in $^{40}\mathrm{Ca}^{+}$ by measuring the branching fraction of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state decaying into the ground state $4s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and the lifetime of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state, using a technique of a highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching fraction and improved lifetime are, respectively, 0.998(12) and 1.1649(44) s, which yield the value of the quadrupole transition matrix element (in absolute value) of 9.733(52) $e{a}_{0}^{2}$ with an uncertainty of 0.54%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.

DOI
10.1103/physreva.95.053415

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