Grassmann phase space theory and the Jaynes–Cummings model
The Jaynes–Cummings model of a twolevel atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an nphoton Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a highQ microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and nphoton states and deriving coupled equations for the amplitudes are a wellknown and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by cnumber phase space variables, with the density operator representedmore »
 Authors:

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 ARC Centre for Quantum–Atom Optics (Australia)
 (Australia)
 Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN19QH (United Kingdom)
 Department of Physics, University of Strathclyde, Glasgow, G40NG (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22220747
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 334; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ANNIHILATION; ANNIHILATION OPERATORS; ATOMS; CREATION OPERATORS; DISTRIBUTION FUNCTIONS; FERMIONS; FIELD OPERATORS; LANGEVIN EQUATION; MANYBODY PROBLEM; MATHEMATICAL SOLUTIONS; MICROWAVE RADIATION; PHASE SPACE; PHOTONS; SPIN; STOCHASTIC PROCESSES