Dispersive optical nonlinearities in an EIT-Rydberg medium

TL;DR

This paper explores how Rydberg excitation blockade induces dispersive optical nonlinearities in cold Rydberg gases, providing exact and scalable methods to evaluate the nonlinear response in various regimes.

Contribution

It introduces a universal scaling formula for dispersive nonlinearities and a novel technique to simplify Rydberg interaction effects using two-body correlations.

Findings

Third-order nonlinearities can be exactly evaluated at steady state.

A universal scaling formula relates Rydberg interactions to optical nonlinearity.

A new method simplifies the treatment of nonlocal Rydberg interactions.

Abstract

We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be exactly evaluated in a steady state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple "universal scaling" formula to determine the dispersive optical nonlinearity of the medium. We also develop a novel technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that only involve two-body correlations, which can be solved numerically. All average populations and coherences are then obtained straightforwardly.