Diagrammatic treatment of few-photon scattering from a Rydberg blockaded atomic ensemble in a cavity

TL;DR

This paper develops a diagrammatic approach to analyze few-photon scattering in a Rydberg atomic ensemble within a cavity, extending previous work to higher photon numbers and correlation functions, revealing complex quantum optical phenomena.

Contribution

It introduces a detailed diagrammatic method for studying multi-photon scattering and correlations in Rydberg media inside cavities, advancing understanding of nonlinear quantum optics.

Findings

Calculated three-photon correlation functions revealing photon interactions.

Extended the theoretical framework to higher photon numbers.

Connected correlation functions to polariton energy levels.

Abstract

In a previous letter we studied the giant optical nonlinearities of a Rydberg atomic medium within an optical cavity, in the Schwinger-Keldysh formalism. In particular, we calculated the non-linear contributions to the spectrum of the light transmitted through the cavity. In this article we spell out the essential details of this calculation, and we show how it can be extended to higher input photon numbers, and higher order correlation functions. As a relevant example, we calculate and discuss the three-photon correlation function of the transmitted light, and discuss its physical significance in terms of the polariton energy levels of the Rydberg medium within the optical cavity.