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

摘要

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} $ statedecaying 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 measurementsequence for laser control and highly efficient quantum state detection forquantum jumps. The measured branching ratio and improved lifetime are,respectively, 0.9992(80) and 1.1652(46) s, which yield the value of thequadrupole transition matrix element (in absolute value) 9.737(43)~$ea_{0}^{2}$with the uncertainty at the level of 0.44\%. The measured quadrupole transitionmatrix element is in good agreement with the most precise many-body atomicstructure calculations. Our method can be universally applied to measurementsof transition matrix elements in single ions and atoms of similar structure.