Measurement of dipole matrix elements with a single trapped ion

Abstract

We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion interactions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4${}^2$S${}_{1/2}\leftrightarrow$ 4${}^2$P${}_{1/2}$ transition of ${}^{40}$Ca${}^{+}$, for which we find the value 2.8928(43) ea${}_0$. Moreover, the method allows us to deduce the lifetime of the 4${}^2$P${}_{1/2}$ state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a longstanding discrepancy between calculated values and experimental results.

5 + 14 pages, 4 + 2 figures; v2: supplemental material added; v3: structure improved, typos corrected, uncertainty calculations corrected;