Determination of magic wavelengths for the $7s ~ {^2}S_{1/2}-7p ~ {^2}P_{3/2,1/2}$ transitions in Fr atom

TL;DR

This study refines the calculation of magic wavelengths for specific transitions in francium by incorporating advanced relativistic coupled-cluster calculations, correcting previous estimates, and providing more accurate data for experimental guidance.

Contribution

It improves the accuracy of polarizability calculations for francium's excited states by including core correlation effects and using relativistic coupled-cluster theory, correcting prior results.

Findings

Revised magic wavelengths differ significantly from previous reports.

Static polarizability values show excellent agreement with other theoretical results.

New estimates support different trapping schemes for francium atoms.

Abstract

Magic wavelengthsfor the $7S_{1/2}-7P_{1/2,3/2}$ transitions in Fr were reported by Dammalapati \textit{et al.} in [Phys. Rev. A 93, 043407 (2016)]. These $\lambda_{\rm{magic}}$ were determined by plotting dynamic polarizabilities ($\alpha$) of the involved states with the above transitions against a desired range of wavelength. Electric dipole (E1) matrix elements listed in [J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7P_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\alpha$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P-7S$, $7P-8S$ and $7P-6D$ transitions to $\alpha$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\alpha$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\alpha$ are found to be in excellent agreement with the other available theoretical results; whereas substituting the E1 matrix elements used by Dammalapati \textit{et al.} give very small $\alpha$ values for the $7P$ states. Owing to this, we find disagreement in $\lambda_{\rm{magic}}$ reported by Dammalapati \textit{et al.} for linearly polarized light; especially at wavelengths close to the D-lines and in the infrared region. As a consequence, a $\lambda_{\rm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\alpha$ will be very useful for guiding experiments to carry out their measurements.