Tailoring Rydberg interactions via F\"orster resonances: state combinations, hopping and angular dependence

TL;DR

This paper explores how F"orster resonances can be used to precisely control the strength and angular dependence of Rydberg atom interactions, with a detailed search method and analysis of various quantum state combinations.

Contribution

It introduces a comprehensive search method for F"orster resonances in Rydberg states and quantifies their interaction strength using a new figure of merit, enabling tailored interaction control.

Findings

Identified strong F"orster resonances across a range of quantum states.

Quantified interaction strength with a new figure of merit $ ilde C_3$.

Discussed the angular dependence and tunability of interactions near resonances.

Abstract

F\"orster resonances provide a highly flexible tool to tune both the strength and the angular shape of interactions between two Rydberg atoms. We give a detailed explanation about how F\"orster resonances can be found by searching through a large range of possible quantum number combinations. We apply our search method to $SS$, $SD$ and $DD$ pair states of $^{87}$Rb with principal quantum numbers from 30 to 100, taking into account the fine structure splitting of the Rydberg states. We find various strong resonances between atoms with a large difference in principal quantum numbers. We quantify the strength of these resonances by introducing a figure of merit $\tilde C_3$ which is independent of the magnetic quantum numbers and geometry to classify the resonances by interaction strength. We further predict to what extent excitation exchange is possible on different resonances and point out limitations of the coherent hopping process. Finally, we discuss the angular dependence of the dipole-dipole interaction and its tunability near resonances.