Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius

We measure the absolute frequency of seven out of the nine allowed transitions between the 2${}^3${\it S} and 2${}^3${\it P} hyperfine manifolds in a metastable ${}^3$He beam by using an optical frequency comb synthesizer-assisted spectrometer. The relative uncertainty of our measurements ranges from $1\times 10^{-11}$to$5\times 10^{-12}$, which is, to our knowledge, the most precise result for any optical ${}^3$He transition to date. The resulting $2^3${\it P}-2${}^3${\it S} centroid frequency is $276702827204.8(2.4)$kHz. Comparing this value with the known result for the ${}^4$He centroid and performing {\em ab initio} QED calculations of the ${}^4$He-${}^3$He isotope shift, we extract the difference of the squared nuclear charge radii $\delta r^2$ of ${}^3$He and ${}^4$He. Our result for $\delta r^2=1.074(3)$ fm${}^2$ disagrees by about $4\sigma$ with the recent determination [R. van Rooij {\em et al.}, Science {\bf 333}, 196 (2011)].