Precision Measurement of the Quadrupole Transition Matrix Element in a Single Trapped ${}^{40}$Ca${}^{+}$

Abstract

We report the first experimental determination of the $4s{}^2{S}_{1/2}$ $\leftrightarrow$ $3d{}^2{D}_{5/2}$ quadrupole transition matrix element in ${}^{40}$Ca${}^{+}$ by measuring the branching ratio of the $3d{}^2{D}_{5/2}$ state decaying into the ground state $4s{}^2{S}_{1/2}$ and the lifetime of the $3d{}^2{D}_{5/2}$ state, using a technique of highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching ratio and improved lifetime are, respectively, 0.9992(80) and 1.1652(46) s, which yield the value of the quadrupole transition matrix element (in absolute value) 9.737(43)~$e{a}_0^2$ with the uncertainty at the level of 0.44\%. 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.

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Cited by in corpus (2)

• Radiative Transition Properties of Singly Charged Magnesium, Calcium, Strontium and Barium Ions
• Combining experiments and relativistic theory for establishing accurate radiative quantities in atoms: the lifetime of the ${}^2$P${}_{3/2}$ state in ${}^{40}$Ca${}^{+}$