Proposal for suppressing the ac Stark shift in the He(23S1 → 33S1) two-photon transition using magic wavelengths

Motivated by recent direct measurement of the forbidden 2(3)S(1) -> 3(3)S(1) transition in helium [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) -> 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 He-4 [or 1265.683 9(2) nm for He-3] can be used to design an optical dipole trap; the magic wavelength of 934.234 5(2) nm for He-4 [or 934.255 4(4) nm for He-3] 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 x 10(4) W/cm(2). Alternatively, by selecting detuning frequencies relative to the 2(3)P state in the region of 82-103 THz, as well as adjusting the intensity ratios of the two lasers, the ac Stark shift in the 2(3)S(1) -> 3(3)S(1) two-photon transition can be canceled.