Effective Field Theory for Rydberg Polaritons

TL;DR

This paper develops an effective field theory to describe the propagation and interactions of Rydberg polaritons in one dimension, revealing the importance of effective range corrections and long-range interactions for understanding many-body quantum phenomena.

Contribution

The paper introduces a novel EFT framework for Rydberg polaritons, incorporating effective range corrections and analyzing the impact of long-range Rydberg interactions on many-body dynamics.

Findings

Effective range corrections dominate near scattering resonances.

Long-range Rydberg interactions induce strong N-body effects.

Mapping propagation to a non-equilibrium quench simplifies analysis.

Abstract

We develop an effective field theory (EFT) to describe the few- and many-body propagation of one dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a non-equilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective $N$-body interactions between Rydberg polaritons. These results pave the way towards studying non-perturbative effects in quantum field theories using Rydberg polaritons.