The Jaynes-Cummings Model

TLDR

The Jaynes‑Cummings model is a solvable quantum description of an atom interacting with a field, originally used to study spontaneous emission and Rabi oscillations, and has since revealed non‑classical photon statistics such as antibunching while remaining attractive due to its analytical tractability and extensibility. The authors aim to use the JCM to clarify quantum correlations (entanglement) and further explore the classical–quantum relationship, presenting an overview of its theory and extensions. They provide a theoretical overview of the JCM and its many analytic and numerical extensions and generalizations. Analytic solutions show that with suitable initial conditions the Rabi oscillations revive repeatedly, evidencing photon discreteness, and recent work has found that during collapsed intervals the atom–field system forms a macroscopic Schrödinger‑cat superposition.

Abstract

Abstract The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it has been found that during the quiescent intervals of collapsed Rabi oscillations the atom and field exist in a macroscopic superposition state (a Schrödinger cat). This discovery offers the opportunity to use the JCM to elucidate the basic properties of quantum correlation (entanglement) and to explore still further the relationship between classical and quantum physics. The relative simplicity of the JCM and the ease with which it can be extended through analytic expressions or numerical computation continues to motivate attention, as evidenced by the growing abundance of publications. We here present an overview of the theory of the JCM and some of the many extensions and generalizations that have appeared.