Magic wavelengths of the Sr ($5s^2\;^1\!S_0$--$5s5p\;^3\!P_1$) intercombination transition near the $5s5p\;^3\!P_1$--$5p^2\;^3\!P_2$ transition

TL;DR

This study combines theoretical calculations and precise measurements to determine magic wavelengths near 473 nm for the Sr intercombination transition, validating atomic matrix element predictions crucial for optical trapping.

Contribution

The paper provides the first combined theoretical and experimental determination of magic wavelengths near 473 nm for Sr's intercombination transition, testing and validating atomic matrix element calculations.

Findings

Measured magic wavelengths: 473.361(4) nm and 473.133(14) nm.

Theoretical predictions: 473.375(22) nm and 473.145(20) nm.

Excellent agreement validates the matrix element calculations.

Abstract

Predicting magic wavelengths accurately requires precise knowledge of electric-dipole matrix elements of nearby atomic transitions. As a result, measurements of magic wavelengths allow us to test theoretical predictions for the matrix elements that frequently can not be probed by any other methods. Here, we calculate and measure a magic wavelength near $473$ nm of the $5s^2\,^1\!S_0 - 5s5p\,^3\!P_1$ intercombination transition of ${}^{88}$Sr. Experimentally, we find $473.361(4)$ nm for $\Delta m=0$ ($\pi$ transition) and $473.133(14)$ nm for $\Delta m=-1$ ($\sigma^{-}$ transition). Theoretical calculations yield $473.375(22)$~nm and $473.145(20)$ nm, respectively. The $^3\!P_1$ polarizability is dominated by the contributions to the $5p^2\, ^3\!P$ levels and excellent agreement of theory and experiment validates both theoretical values of these matrix elements and estimates of their uncertainties.