Precise Frequency Measurement of the 2$^{1}$S$_{0}$-3$^{1}$D$_{2}$ Two-Photon Transition in atomic $^{4}$He

We present the first precise frequency measurement of the 2$^{1}$S$_{0}$-3$^{1}$D$_{2}$ two-photon transition in $^{4}$He at 1009 nm. The laser source at 1009 nm is stabilized on an optical frequency comb to perform the absolute frequency measurement. The absolute frequency of 2$^{1}$S$_{0}$-3$^{1}$D$_{2}$ transition is experimentally determined to be 594 414 291 803(13) kHz with a relative uncertainty of 1.6 $\times$ 10$^{-11}$ which is more precise than previous determination by a factor of 25. Combined with the theoretical ionization energy of the 3$^{1}$D$_{2}$ state, the ionization energy of the 2$^{1}$S$_{0}$ state is determined to be 960 332 040 866(24) kHz. In addition, the deduced 2$^{1}$S$_{0}$ and 2$^{3}$S$_{1}$ Lamb shifts are 2806.817(24) and 4058.8(24) MHz respectively which are 1.6 times better than previous determinations.