Quantum optical non-linearities induced by Rydberg-Rydberg interactions: a perturbative approach

TL;DR

This paper presents a perturbative theoretical analysis of quantum optical non-linearities caused by Rydberg-Rydberg interactions in an atomic medium within an optical cavity, revealing new resonant features and proposing a simplified three-boson model.

Contribution

It introduces an analytic perturbative approach valid for weak fields and resonant intermediate states, and proposes an effective three-boson model to elucidate the underlying physics.

Findings

Analytic expressions for quantum statistical properties under weak driving fields.

Identification of new resonant features due to Rydberg interactions.

A simplified three-boson model capturing the system's essential physics.

Abstract

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant. Therefore they allow us to investigate quantitatively new features associated with the resonant behaviour of the system. We also propose an effective non-linear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.