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

Abstract

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 $2 ^3S$ state atoms. We analyze schemes for measuring the two-photon $2 ^3S \to 4 ^3S$ interval, and for resonant two-photon excitation to high Rydberg states, $2 ^3S \to 3 ^3P \to n^3S,D$. We also analyze experiments on the singlet-state spectrum. To accomplish this we propose schemes for producing and trapping ultracold helium in the $1 ^1S$ or $2 ^1S$ state via intercombination transition. A particularly intriguing scenario is the possibility of direct singlet state spectroscopy, including a measurement of the $1 ^1S \to 2 ^1S$ 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 $1 ^1S$, $2 ^1S$ and $2 ^3S$ states are all similar, small, and positive.