Jaynes–Cummings model

The Jaynes–Cummings model (JCM) is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity, with or without the presence of light (in the form of a bath of electromagnetic radiation that can cause spontaneous emission and absorption). The JCM is of great interest in atomic physics, quantum optics, and solid-state quantum information circuits, both experimentally and theoretically.

This model was originally proposed in 1963 by Edwin Jaynes and Fred Cummings in order to study the relationship between the quantum theory of radiation and the semi-classical theory in describing the phenomenon of spontaneous emission.

In the earlier semi-classical theory of field-atom interaction, only the atom is quantized and the field is treated as a definite function of time rather than as an operator. The semi-classical theory can explain many phenomena that are observed in modern optics, for example the existence of Rabi cycles in atomic excitation probabilities for radiation fields with sharply defined energy (narrow bandwidth). The JCM serves to find out how quantization of the radiation field affects the predictions for the evolution of the state of a two-level system in comparison with semi-classical theory of light-atom interaction. It was later discovered that the revival of the atomic population inversion after its collapse is a direct consequence of discreteness of field states (photons). This is a pure quantum effect that can be described by the JCM but not with the semi-classical theory.

Twenty four years later, in 1987, a beautiful demonstration of quantum collapse and revival was observed in a one-atom maser by Rempe, Walther, and Klein. Before that time, research groups were unable to build experimental setups capable of enhancing the coupling of an atom with a single field mode, simultaneously suppressing other modes. Experimentally, the quality factor of the cavity must be high enough to consider the dynamics of the system as equivalent to the dynamics of a single mode field. With the advent of one-atom masers it was possible to study the interaction of a single atom (usually a Rydberg atom) with a single resonant mode of the electromagnetic field in a cavity from an experimental point of view, and study different aspects of the JCM.

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