Isotopic effect on collisional widths and shifts of Hg clock transition induced by cold Rb atoms

TL;DR

This paper investigates how isotopic variations affect collisional widths and shifts of the Hg clock transition caused by cold Rb atoms, using quantum and semi-classical models across a wide temperature range.

Contribution

It models the interaction potentials and analyzes the impact of isotopic mass differences on collisional line shape parameters and resonances in Hg-Rb systems.

Findings

Shape resonances cause significant variations in line shape parameters.

Quantum calculations align with semi-classical approximations for widths and shifts.

Inelastic collisions may lead to universal behavior affecting isotopic dependence.

Abstract

We study the isotopic dependence of collisional widths and shifts of the Hg clock transition $^1$S$_0$-$^3$P$_0$ perturbed by the Rb atoms in the temperature range from 1 nK to 1 K. For this purpose, we model the Born-Oppenheimer effective interaction potential by including the leading long-range van der Waals coefficients. For elastic collisions, we show the connection between the dependence of collision line shape parameters on the reduced mass of colliding partners as well as the variation of the scattering length in the excited and ground states of the Hg-Rb system in the $\upmu$K temperature range. We confront the full quantum scattering calculations with a semi-classical approximation for collisional widths and shifts. We show that the shape resonances in excited and ground scattering states lead to significant variations of collisional line shape parameters with the change of the reduced mass of colliding atoms. We also indicate the possible influence of inelastic collisions, which could lead to universal behavior and significantly affect the dependence of collisional broadening and shifting on the isotopic combination of colliding atoms.