Precision laser spectroscopy of the 2S01–3D21 two-photon transition in He3

Abstract

We have measured the absolute frequency of the $2^{1}S_{0}--3^{1}D_{2}$ two-photon transitions in $^{3}\mathrm{He}$ at 1009 nm based on a cesium frequency standard through an optical frequency comb. The measured frequencies are 594 384 961.072(19) MHz for the $2^{1}S_{0,1/2}--3^{1}D_{2,5/2}$ transition and 594 384 821.209(15) MHz for the $2^{1}S_{0,1/2}--3^{1}D_{2,3/2}$ transition with relative uncertainties of $2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $3.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$, respectively. The determination of the $2^{1}S_{0}--3^{1}D_{2}$ two-photon transition frequency, without hyperfine effect, in $^{3}\mathrm{He}$ is 594 384 761.556(12) MHz. The deduced isotope shift between $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ is 29.530246(18) GHz. The difference of the squares of the nuclear charge radii is deduced to be $1.059(25)\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{2}$. Finally, by combining other precise measured transitions, we are able to derive the $3^{3}D_{1}--3^{1}D_{2}$ separation in $^{3}\mathrm{He}$ to be 101 058 203(56) kHz, which is an improvement by a factor of 89 compared to previous work.