Precision Measurement of the 2$^{3}$S$_{1}$-2$^{3}$P$_{J}$ Transitions in $^{4}$He using an Optical Frequency Comb*

One promising way to measure the fine structure constant $\alpha $ and test Quantum Electrodynamics in an atomic system is to measure the $^{4}$He fine structure splitting of the 2$^{3}$P level into the J=0,1,2 sublevels. We recently reported the most accurate experimental measurements of these intervals, with uncertainties of 500 Hz and 700 Hz for the small (2P$_{1}$-2P$_{2}$, 2.2 GHz) and large (2P$_{0}$-2P$_{1}$, 29.6 GHz) intervals, respectively [1]. Our approach uses saturated absorption laser spectroscopy at 1083 nm to excite metastable $^{4}$He atoms in a variable-pressure discharge cell to the 2P$_{J}$ states. Several changes to the experiment have improved our resolution by a factor of 5 to less than 100 Hz. Most significant, a new iodine frequency reference at 532 nm is 40 times more stable than an existing $^{3}$He reference. The stability of this reference is transferred to 1083 nm using an optical frequency comb. Simultaneously, the comb lets us accurately measure the optical frequencies of the 2S-2P$_{J}$ transitions with respect to the SI second. We present preliminary measurements of both the improved $^{4}$He 2P fine structure splittings and the 2S-2P$_{J}$ transitions using the iodine-stabilized frequency comb as the frequency reference for the experiment. Systematics and their limitations on accuracy are discussed. [1] T. Zelevinsky, D. Farkas, and G. Gabrielse, \textit{Phys. Rev. Lett}., \textbf{95}, (2005).