Direct measurement of excited-state dipole matrix elements using electromagnetically induced transparency in the hyperfine Paschen-Back regime

Applying large magnetic fields to gain access to the hyperfine Paschen-Back regime can isolate three-level systems in a hot alkali metal vapors, thereby simplifying usually complex atom-light interactions. We use this method to make the first direct measurement of the $\vert\langle 5P\vert\vert er\vert\vert 5D\rangle\vert$ matrix element in $^{87}$Rb. An analytic model with only three levels accurately models the experimental electromagnetically induced transparency spectra and extracted Rabi frequencies are used to determine the dipole matrix element. We measure $\vert\langle 5P_{3/2}\vert\vert er\vert\vert 5D_{5/2}\rangle\vert = (2.290\pm0.002_{\rm stat}\pm0.04_{\rm syst})~ea_{0}$ which is in excellent agreement with the theoretical calculations of Safronova, Williams, and Clark [Phys. Rev. A \textbf{69}, 022509 (2004)].