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

摘要

In this article, we theoretically study the quantum statistical properties ofthe light transmitted through or reflected from an optical cavity, filled by anatomic medium with strong optical non-linearity induced by Rydberg-Rydberg vander Waals interactions. Atoms are driven on a two-photon transition from theirground state to a Rydberg level via an intermediate state by the combination ofa weak signal field and a strong control beam. By using a perturbativeapproach, we get analytic results which remain valid in the regime of weakfeeding fields, even when the intermediate state becomes resonant. Thereforethey allow us to investigate quantitatively new features associated with theresonant behaviour of the system. We also propose an effective non-linearthree-boson model of the system which, in addition to leading to the sameanalytic results as the original problem, sheds light on the physical processesat work in the system.