Tayloring Bose-Einstein condensate environments for a Rydberg impurity

TL;DR

This paper develops a theoretical framework to understand and quantify how Rydberg atoms embedded in Bose-Einstein condensates interact with phonons, highlighting their extreme tunability and potential for controlled open quantum systems.

Contribution

It provides analytical and numerical calculations of Rydberg-phonon coupling coefficients, bath correlation functions, and spectral densities, advancing the modeling of Rydberg impurities in condensates.

Findings

Bath correlation amplitude scales as ν^{-5}

Re-organisation energies scale as ν^{-3}

Rydberg impurities offer highly tunable open quantum systems

Abstract

Experiments have demonstrated that atoms excited to specific Rydberg states within Bose-Einstein condensates cause significant excitation of phonons. If the Rydberg atom is brought into an electronic superposition state, this coupling to phonons leads to decoherence. We provide the theoretical basis for the treatment of the latter. To this end, we evaluate Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities and re-organisation energies. All these quantify the influence of the environment and form essential inputs for follow up open quantum system techniques. We find that the amplitude of bath correlations scales like the power law $\nu^{-5}$ with the principal quantum number $\nu$, while re-organisation energies scale like $\nu^{-3}$, reflecting the extreme tunability of Rydberg atomic properties. Rydberg impurities in condensates thus constitute a non-trivial open-quantum system with exceptionally controlled system, coupling and environmental Hamiltonians.