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

TL;DR

This paper calculates magic wavelengths for helium's $2^3S o 2^1S$ transition, identifying key wavelengths where polarizabilities match, aiding laser-based experiments with minimal theoretical complexity.

Contribution

It provides ab initio based calculations of magic wavelengths for helium isotopes without advanced techniques, including continuum contributions and isotope shifts.

Findings

Identified magic wavelengths around 320 nm for helium isotopes.

Achieved better than 1% accuracy with simple extrapolation methods.

Demonstrated minimal isotope shift effects on magic wavelengths.

Abstract

We have calculated ac polarizabilities of the $2 \ ^3S$ and $2 \ ^1S$ 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.