Jaynes-Cummings model in a finite Kerr medium

TL;DR

This paper models a finite Kerr medium using a spin system to study the intensity-dependent atom-field interactions and their quantum properties, with a focus on the effects of a bounded number of excitations.

Contribution

It introduces a novel spin-based model that captures the main features of a Kerr medium with a finite number of excitations, extending previous infinite models.

Findings

Quantum properties depend on the maximum number of excitations

Behavior of atomic and field states varies with excitation limit

Model provides insights into finite-size Kerr medium dynamics

Abstract

We introduce a spin model which exhibits the main properties of a Kerr medium to describe an intensity dependent coupling between a two-level atom and the radiation field. We select a unitary irreducible representation of the su(2) Lie algebra such that the number of excitations of the field is bounded from above. We analyze the behavior of both the atomic and the field quantum properties and its dependence on the maximal number of excitations.