Abstract

The Jaynes–Cummings model (JCM) is used to give a detailed analysis of the long-time behavior of a two-level atom interacting with a (Glauber) coherent-state field. This work is based on the earlier work of J. H. Eberly and collaborators, who drew attention to the collapse and revival of the Rabi oscillations of the atomic inversion. We use the three components S₁, S₂, and S₃ of the pseudospin vector S to analyze the dynamics of the atom within the rotating-wave approximation and exact resonance. We show that, at the times when the revivals peak, the variables σ = |S| and η = S₃/σ become independent of (1) the transition dipole moment of the atom, (2) the intensity of the coherent-state field, and (3) the (common) frequency of the atom and the field. Thus these special values of σ and η are a universal feature of the JCM that should be observed in experiments with any two-level atom in an arbitrarily intense (but resonant) coherent-state field. The derivation of the above results was facilitated by transforming into a rotating coordinate frame in which S₁ = 0 so that S₂ and S₃ are the only dynamical variables. The two-dimensional nature of S in this frame makes it easy to visualize the dynamical changes in the atom. The dynamics of the JCM is clarified by comparison with the closely related Buck–Sukumar model. The relationship of the phenomena discussed here to photon echoes and to quench echoes (in condensed media) is pointed out.

© 1985 Optical Society of America

Extended Jaynes–Cummings model

J. Seke
J. Opt. Soc. Am. B 2(6) 968-970 (1985)

Dynamics of a two-mode two-photon Jaynes–Cummings model interacting with correlated SU(1, 1) coherent states

Christopher C. Gerry and Ronald F. Welch
J. Opt. Soc. Am. B 9(2) 290-297 (1992)

Dynamical symmetries of the vacuum field Jaynes–Cummings model

G. Hu and P. K. Aravind
J. Opt. Soc. Am. B 6(9) 1757-1763 (1989)

Measurement-induced nonclassical states of the Jaynes–Cummings model

Himel Ghosh and Christopher C. Gerry
J. Opt. Soc. Am. B 14(11) 2782-2787 (1997)

Features of collapses and revivals in a two-photon Jaynes–Cummings model with a squeezed field

Lin-sheng He
J. Opt. Soc. Am. B 6(10) 1915-1926 (1989)