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.

9 pages, 5 figures

References in corpus (7)

• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Calculation of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium
• High-precision spectroscopy of the forbidden 2 3S1 - 2 1P1 transition in quantum degenerate metastable helium
• Magic wavelengths for the $2{}^{3}S\to 2{}^{1}S$ transition in helium
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• QED and relativistic nuclear recoil corrections to the 413 nm tune-out wavelength for the $2{}^3{S}_1$ state of helium