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Journal of Modern Optics

Sir Peter Knight and the Jaynes–Cummings model

Bruce W. Shore

Published Sep 10, 2007• 7 citations
Publisher

Abstract

A 1993 review article (B.W. Shore and P.L. Knight, J. Mod. Opt. 40 1195 (1993)) on the Jaynes–Cummings model (JCM) has proven to be one of the most useful articles co-authored by Sir Peter Knight, to judge by the number of citations to this in other publications. I will comment on how that review has been useful to subsequent researchers, and on some of the applications of the JCM that were not foreseen at that time.

DOI
10.1080/09500340701303501

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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.

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A 1993 review article (B.W. Shore and P.L. Knight, J. Mod. Opt. 40 1195 (1993)) on the Jaynes–Cummings model (JCM) has proven to be one of the most useful articles co-authored by Sir Peter Knight, to judge by the number of citations to this in other publications. I will comment on how that review has been useful to subsequent researchers, and on some of the applications of the JCM that were not foreseen at that time.
The Jaynes–Cummings Model (JCM) has been at the forefront of modern physics as one of the simplest, yet intricately nonlinear, models of light–matter interaction. Focusing on the omnipresence of the JCM across a range of disciplines, this significantly updated and comprehensive review conveys to the reader the fundamental generality of its formalism, looking at a wide range of applications in specific physical systems and across disciplines including atomic physics, quantum optics, solid-state physics and quantum information sciences. An ideal reference for researchers in quantum physics and quantum optics, the book also comprises an accessible introduction for students engaged with non-equilibrium quantum phase transitions, quantum computing and simulation, quantum many-body physics, cavity, circuit and waveguide quantum electrodynamics. Part of IOP Series in Quantum Technology. Key features • Collects JCM physics and applications scattered across literature and different applications. • The exposition guides the reader through a rich and appealing landscape interlacing quantum optics and condensed-matter physics. • All chapters discuss theory and experiment, linked historically to the development of the various directions stemming from JC physics. This is accompanied by a thorough list of references to the key publications. • The presentation is kept concise, while continuous text is interspersed with various illustrations and an economical use of mathematical expressions.
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.