The coherent interaction between matter and radiation - A tutorial on the Jaynes-Cummings model

TL;DR

This tutorial provides a comprehensive overview of the Jaynes-Cummings model, detailing its Hamiltonian, eigenstates, and dynamics, including Rabi oscillations and collapse-revival phenomena, within the context of cavity QED and quantum information.

Contribution

It offers a complete, pedagogical description of the JC model, including analysis of its Hamiltonian and experimental realizations, enhancing understanding of matter-radiation coherence.

Findings

Analysis of the JC Hamiltonian and eigenstates

Description of Rabi oscillations and collapse-revival effects

Overview of key cavity QED experiments

Abstract

The Jaynes-Cummings (JC) model is a milestone in the theory of coherent interaction between a two-level system and a single bosonic field mode. This tutorial aims to give a complete description of the model, analyzing the Hamiltonian of the system, its eigenvalues and eigestates, in order to characterize the dynamics of system and subsystems. The Rabi oscillations, together with the collapse and revival effects, are distinguishing features of the JC model and are important for applications in Quantum Information theory. The framework of cavity quantum electrodynamics (cQED) is chosen and two fundamental experiments on the coherent interaction between Rydberg atoms and a single cavity field mode are described.