Determination of the hyperfine structure constants of the Rb87 and Rb85 4D5/2 state and the isotope hyperfine anomaly

The hyperfine structure (hfs) splittings of the $4{D}_{5/2}$ state for two isotopes of $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ atoms are measured based on double-resonance optical pumping spectra in a $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{5/2}$ ladder-type atomic system. The frequency calibration is performed by employing a wideband fiber-pigtailed phase-type electro-optic modulator together with a Fabry-P\'erot cavity to cancel the error arising from nonlinear frequency scanning. The hfs magnetic dipole constant $A$ of the $4{D}_{5/2}$ state is determined to be \ensuremath{-}16.801 \ifmmode\pm\else\textpm\fi{} 0.005 MHz for $^{87}\mathrm{Rb}$ and \ensuremath{-}4.978 \ifmmode\pm\else\textpm\fi{} 0.004 MHz for $^{85}\mathrm{Rb}$. The hfs electric quadrupole constant $B$ of the $4{D}_{5/2}$ state is determined to be 3.645 \ifmmode\pm\else\textpm\fi{} 0.030 MHz for $^{87}\mathrm{Rb}$ and 6.560 \ifmmode\pm\else\textpm\fi{} 0.052 MHz for $^{85}\mathrm{Rb}$. The values of $A$ and $B$ for the $^{87}\mathrm{Rb}4{D}_{5/2}$ state are twice as accurate as previous work with thermal atoms using a femtosecond laser comb and the values of $A$ and $B$ for the $^{85}\mathrm{Rb}4{D}_{5/2}$ state are 3 times and 25 times more accurate than previous work in laser-cooled atoms using Fabry--P\'erot interferometer, respectively. According to this high precision of the hfs constants and the previously measured nuclear $g$ factors of the two isotopes, the value of the $d$-electron hyperfine anomaly $^{87}\mathrm{\ensuremath{\Delta}}{}^{85}(4{D}_{5/2})$ is derived to be \ensuremath{-}0.0041 \ifmmode\pm\else\textpm\fi{} 0.0009.