Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution

TL;DR

This paper develops a mean field theoretical model based on nearest-neighbor distribution to analyze weakly-interacting Rydberg polaritons in an EIT system, providing analytical formulas for key optical properties validated by experimental data.

Contribution

It introduces a novel mean field model for weakly-interacting Rydberg polaritons in EIT systems, extending theoretical understanding beyond strongly-interacting regimes.

Findings

Analytical formulas for attenuation and phase shift derived

Model predictions agree with experimental data

Provides a tool for designing EIT-based quantum devices

Abstract

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weaklyinteracting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weaklyinteracting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons, and for evaluating experimental feasibility.