Accurate Modeling of Rydberg Atoms and Their Interactions: Theory and Implementation in PairInteraction

Abstract

Rydberg atoms provide a powerful platform for exploring strongly interacting quantum systems, both in free space and in structured electromagnetic environments, with growing applications in quantum technology. Accurately modeling their single-atom properties and mutual interactions is essential for interpreting experiments and designing new architectures. We present a unified theoretical framework for Rydberg atoms and their interactions based on multi-channel quantum defect theory (MQDT) and static electromagnetic Green's tensors. MQDT provides a precise description of Rydberg states of divalent atoms such as strontium and ytterbium, while the Green's tensor formalism provides a general and flexible approach for calculating interactions between two Rydberg atoms in arbitrary geometries, including modifications induced by nearby surfaces. We implement this framework in an updated version of the open-source PairInteraction software [Weber et al., J.~Phys.~B~50 (2017)]. The implementation leverages high-performance libraries and achieves speedups of one order of magnitude for pair-potential calculations compared to prior software. We demonstrate the capabilities of the framework through example applications to divalent atoms and show excellent agreement with experimental data for an exemplary Stark map of $^{174}$Yb. The modular software architecture enables the community to extend it further.