Cross-Kerr interaction in a four-level atomic system

TL;DR

This paper derives the form of the cross-Kerr interaction in a four-level atomic system, showing it can produce strong nonlinear coupling between weak probe fields, surpassing optical fiber capabilities.

Contribution

It introduces a method to calculate the cross-Kerr interaction in a four-level atomic system using perturbation theory, extending known solutions from three-level systems.

Findings

Cross-Kerr interaction can be significantly enhanced in a four-level system.

Strong nonlinear coupling is achievable between weak probe fields.

Interaction strength exceeds that of optical fibers.

Abstract

We derive the form of the cross-Kerr interaction in a four-level atomic system in the N-configuration. We use time-independent perturbation theory to calculate the eigenenergies and eigenstates of the Schrodinger equation for the system. The system is considered as a perturbation of a Raman resonant three-level lambda scheme for which exact solutions are known. We show that within the strong control field limit the cross-Kerr interaction can arise between two weak probe fields. The strength of this nonlinear coupling is several orders of magnitude larger than that achievable using optical fibres.