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

TL;DR

This paper reports the first precise experimental measurement of the quadrupole transition matrix element in a single trapped $^{40}$Ca$^{+}$ ion, using advanced laser control and quantum detection techniques, with results aligning well with theoretical calculations.

Contribution

First experimental determination of the $^{40}$Ca$^{+}$ quadrupole transition matrix element using a novel synchronized measurement method.

Findings

Branching ratio of 0.9992(80)

Lifetime of 1.1652(46) seconds

Matrix element value of 9.737(43) $ea_{0}^{2}$

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)~$ea_{0}^{2}$ 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.