$C_6$ coefficients for interacting Rydberg atoms and alkali-metal dimers

TL;DR

This paper calculates and analyzes the van der Waals $C_6$ coefficients for interactions between Rydberg alkali-metal atoms and alkali-metal dimers, revealing how these coefficients depend on quantum states and principal quantum numbers, with high accuracy.

Contribution

It provides detailed $C_6$ coefficients for atom-molecule pairs involving Rydberg atoms and alkali-metal dimers, including polynomial fits and state-dependent interaction characteristics.

Findings

$C_6$ coefficients accurately fitted to $O(n^7)$ polynomial for $40 \\leq n \\leq 150$

Rydberg states $n^2S_j$ and $n^2P_j$ produce attractive potentials

$n^2D_j$ states can lead to repulsive potentials depending on pairs

Abstract

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2L_j$; $L\leq 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^1\Sigma^+$; $v=0$, $J=0$). We compute the associated $C_6$ dispersion coefficients of atom-molecule pairs involving $^{133}$Cs and $^{85}$Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O(n^7)$ over the range of principal quantum numbers $40\leq n\leq 150$. For all atom-molecule pairs considered, Rydberg states $n^2S_j$ and $n^2P_j$ result in attractive $1/R^6$ potentials. In contrast, $n^2D_j$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as $n^{-5}$ for $n>40$. For intermediate values of $n\lesssim40$, both repulsive and attractive interaction energies in the order of $ 10-100 \,\mu$K can be achieved with specific atomic and molecular species. The accuracy of the reported $C_6$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\Delta C_6/C_6$ estimated to be no greater than 1\% on average.