Experimental and theoretical study of dynamic polarizabilities in the $5S_{1/2}$-$5D_{5/2}$ clock transition in rubidium-87 and determination of E1 matrix elements

TL;DR

This paper combines experimental and theoretical approaches to accurately determine the dynamic polarizabilities, magic wavelength, and E1 matrix elements for the $5S_{1/2}$-$5D_{5/2}$ transition in rubidium-87, improving atomic clock precision.

Contribution

It provides the first combined experimental and theoretical determination of the magic wavelength and E1 matrix element for this transition, resolving previous discrepancies.

Findings

Magic wavelength of 776.179(5) nm experimentally

E1 matrix element of 1.80(6) $ea_0$ experimentally

Agreement between experimental and theoretical values

Abstract

The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light-shift. These light-shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light-shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5S_{1/2}$-$5D_{5/2}$ transition in rubidium-87 over the range 770 nm to 800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5P_{3/2}$-$5D_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5P_{3/2}$-$5D_{5/2}$ resonance, and the corresponding reduced E1 matrix element 1.80(6) $ea_0$ (experimental) and 1.96(15) $ea_0$ (theoretical). These values resolve a previous discrepancy between theory and experiment.