Magic wavelengths for the $2{}^{3}S\to 2{}^{1}S$ transition in helium

Abstract

We have calculated ac polarizabilities of the $2{}^{3}S$ and $2{}^{1}S$ states of both ${}^4$He and ${}^3$He in the range 318 nm to 2.5 $\mu$m and determined the magic wavelengths at which these polarizabilities are equal for either isotope. The calculations, only based on available ab initio tables of level energies and Einstein A coefficients, do not require advanced theoretical techniques. The polarizability contribution of the continuum is calculated using a simple extrapolation beyond the ionization limit, yet the results agree to better than 1% with such advanced techniques. Several promising magic wavelengths are identified around 320 nm with sufficient accuracy to design an appropriate laser system. The extension of the calculations to ${}^3$He is complicated due to the additional hyperfine structure, but we show that the magic wavelength candidates around 320 nm are predominantly shifted by the isotope shift.

arXiv comment9 pages, 3 figures

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• A simple 2 W continuous-wave laser system for trapping ultracold metastable helium atoms at the 319.8 nm magic wavelength
• Efficient production of an 87Rb F = 2, mF = 2 Bose-Einstein condensate in a hybrid trap
• Pauli blocking of stimulated emission in a degenerate Fermi gas
• Towards implementation of a magic optical-dipole trap for confining ground-state and Rydberg-state cesium cold atoms
• Quantum-State Controlled Penning Ionization Reactions between Ultracold Alkali and Metastable Helium Atoms
• An ultracold, optically trapped mixture of {87}Rb and metastable {4}He atoms
• Simple method for producing Bose-Einstein condensates of metastable helium using a single beam optical dipole trap
• Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths
• A hybrid quantum system formed by trapping atoms in the near-field of a levitated nanosphere
• Nonrelativistic quantum electrodynamic approach to polarizabilities of light atoms