Splitting of the three-body F\"orster resonance in Rb Rydberg atoms as a measure of dipole-dipole interaction strength

TL;DR

This paper investigates the splitting of three-body F"orster resonances in Rb Rydberg atoms, revealing how the splitting measures the dipole-dipole interaction strength, which is crucial for quantum gate implementation.

Contribution

It provides a detailed analysis and analytical formulas describing the splitting of three-body F"orster resonances and its relation to dipole-dipole interaction strength in Rb Rydberg atoms.

Findings

Splitting of the resonance depends on the interatomic distance R.

The splitting is a measure of the dipole-dipole exchange interaction energy.

Analytical formulas describe the resonance behavior based on R.

Abstract

Three-body F\"orster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms in optical traps using their laser excitation into strongly interacting Rydberg states. In our recent theoretical paper [Zh. Eksper. Teor. Fiz. 168(1), 14 (2025)] it was found that the proposed earlier three-body F\"orster resonance $3\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2} $ in Rb Rydberg atoms has a splitting, with one of the split components having weaker dependence of the resonant electric field (and the corresponding dynamic shift) on the distance $R$ between the atoms. Here we study this effect in more detail, since such a resonance is the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the F\"orster resonance depending on $R$. It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states $S$ and $P$.