Quantum theory of Kerr nonlinearity with Rydberg slow light polaritons

TL;DR

This paper develops an analytical model for Rydberg slow light polaritons in atomic media, linking their behavior to Kerr nonlinearity and quantum corrections, and proposes an experiment to measure polariton interactions.

Contribution

It introduces an analytical approach to describe Rydberg polaritons' propagation and their nonlinear interactions, including quantum corrections, and suggests an experimental setup to measure these interactions.

Findings

Dispersion relation described by slow light velocity

Connection established between Rydberg polaritons and Kerr nonlinearity

Proposal for measuring two-body and higher-body interactions

Abstract

We study the propagation of Rydberg slow light polaritons through an atomic medium for intermediate interactions. Then, the dispersion relation for the polaritons is well described by the slow light velocity alone, which allows for an analytical solution for arbitrary shape of the atomic cloud. We demonstrate the connection of Rydberg polaritons to the behavior of a conventional Kerr nonlinearity for weak interactions, and determine the leading quantum corrections for increasing interactions. We propose an experimental setup which allows one to measure the effective two-body interaction potential between slow light polaritons as well as higher body interactions.