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Motivated by recent direct measurement of the forbidden$2\,^3S_1\rightarrow3\,^3S_1$ transition in helium [K. F. Thomas et al., Phys.Rev. Lett. 125, 013002(2020)], where the ac Stark shift is one of the mainsystematic uncertainties, we propose a dichroic two-photon transitionmeasurement for $2\,^3S_1\rightarrow3\,^3S_1$ which could effectively suppressthe ac Stark shift by utilizing magic wavelengths: one magic wavelength is usedto realize state-insensitive optical trapping, the other magic wavelength isused as one of the two lasers driving the two-photon transition. Carrying outcalculations based on the no-pair Dirac-Coulomb-Breit Hamiltonian with massshift 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 dipoletrap; the magic wavelength of 934.234 5(2) nm for $^4$He [or 934.255 4(4) nmfor $^3$He] can be as one excitation laser in the two-photon process, and theac Stark shift can be reduced to less than 100 kHz, as long as the intensity ofthe other excitation laser does not exceed $1\times10^4~W/cm^2$. Alternatively,by selecting detuning frequencies relative to the $2\,^3P$ state in the regionof 82$\sim$103 THz, as well as adjusting the intensity ratios of the twolasers, the ac Stark shift in the $2\,^3S_1\rightarrow3\,^3S_1$ two-photontransition can be cancelled.

Proposal for suppressing ac Stark shift in the He($2\,^3S_1\rightarrow 3\,^3S_1$) two-photon transition using magic wavelengths