Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths

Abstract

Motivated by recent direct measurement of the forbidden $2{}^3{S}_1\to 3{}^3{S}_1$ transition in helium [K. F. Thomas et al., Phys. Rev. Lett. 125, 013002(2020)], where the ac Stark shift is one of the main systematic uncertainties, we propose a dichroic two-photon transition measurement for $2{}^3{S}_1\to 3{}^3{S}_1$ which could effectively suppress the ac Stark shift by utilizing magic wavelengths: one magic wavelength is used to realize state-insensitive optical trapping, the other magic wavelength is used as one of the two lasers driving the two-photon transition. Carrying out calculations based on the no-pair Dirac-Coulomb-Breit Hamiltonian with mass shift operator included, we report the magic wavelength of 1265.615 9(4) nm for ${}^4$He [or 1265.683 9(2) nm for ${}^3$He] can be used to design an optical dipole trap; the magic wavelength of 934.234 5(2) nm for ${}^4$He [or 934.255 4(4) nm for ${}^3$He] can be as one excitation laser in the two-photon process, and the ac Stark shift can be reduced to less than 100 kHz, as long as the intensity of the other excitation laser does not exceed $1\times 10^{4}W/c{m}^2$. Alternatively, by selecting detuning frequencies relative to the $2{}^{3}P$ state in the region of 82$\sim$103 THz, as well as adjusting the intensity ratios of the two lasers, the ac Stark shift in the $2{}^3{S}_1\to 3{}^3{S}_1$ two-photon transition can be cancelled.

arXiv comment9 pages, 5 figures

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