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

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.

22 pages, 7 figures. Tutorial. Submitted to a special issue of EPJ - ST devoted to the memory of Federico Casagrande

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• Generalized rotating-wave approximation for arbitrarily large coupling
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• Revisiting the Jaynes-Cummings model with time-dependent coupling
• Tripartite multiphoton Jaynes-Cummings model: Analytical solution and Wigner nonclassicalities
• Renormalisation group flow of the Jaynes-Cummings model
• Structured beam controlled super-resolution in quantum dots via rapid adiabatic passage