Prospects for precision measurements of atomic helium using direct frequency comb spectroscopy

. We analyze several possibilities for precisely measuring electronic transitions in atomic helium by the direct use of phase-stabilized femtosecond frequency combs. Because the comb is self-calibrating and can be shifted into the ultraviolet spectral region via harmonic generation, it offers the prospect of greatly improved accuracy for UV and far-UV transitions. To take advantage of this accuracy an ultracold helium sample is needed. For measurements of the triplet spectrum a magneto-optical trap (MOT) can be used to cool and trap metastable 2 3 S state atoms. We analyze schemes for measuring the two-photon 2 3 S →4 3 S interval, and for resonant two-photon excitation to high Rydberg states, 2 3 S →3 3 P →n 3 S, D. We also analyze experiments on the singlet-state spectrum. To accomplish this we propose schemes for producing and trapping ultracold helium in the 1 1 S or 2 1 S state via intercombination transitions. A particularly intriguing scenario is the possibility of measuring the 1 1 S →2 1 S transition with extremely high accuracy by use of two-photon excitation in a magic wavelength trap that operates identically for both states. We predict a “triple magic wavelength” at 412 nm that could facilitate numerous experiments on trapped helium atoms, because here the polarizabilities of the 1 1 S, 2 1 S and 2 3 S states are all similar, small, and positive.