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Journal of Modern Optics

Generation of Even and Odd Coherent States in the Intensity Dependent Jaynes—Cummings Model

Khalid Zaheer, Mohamed Ridza Wahiddin

Published Jan 1, 1994• 25 citations
Publisher

Abstract

We study the evolution of the wavefunction in the intensity dependent Jaynes—Cummings model. It is shown that apart from the periodic revivals indicated by the dynamics of inversion, half-time revivals of the wavefunction take place in the limit of [nbar] ≫ 1. The decoupled atomic state is a superposition of the upper and lower levels and is independent of the initial atomic condition. The decoupled field state is an even or odd coherent state with a spiked distribution function, depending on the initial atomic state.

DOI
10.1080/09500349414550161

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We study the evolution of the wavefunction in the intensity dependent Jaynes—Cummings model. It is shown that apart from the periodic revivals indicated by the dynamics of inversion, half-time revivals of the wavefunction take place in the limit of [nbar] ≫ 1. The decoupled atomic state is a superposition of the upper and lower levels and is independent of the initial atomic condition. The decoupled field state is an even or odd coherent state with a spiked distribution function, depending on the initial atomic state.
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The pure-state evolution of the atomic as well as the field states in the resonant two-photon Jaynes-Cummings model with the field initially in the coherent state is studied. Analytic expressions for various quantities involved are obtained under the large-n\ifmmode\bar\else\textasciimacron\fi{} approximation. It is shown that the atom as well as the field are approximately in the pure state for gt=k\ensuremath{\pi}/4, where k is an integer and in a completely pure state for gt=k\ensuremath{\pi}. The field states generated at the times gt=k\ensuremath{\pi}/4 are shown to be a quantum superposition of the coherent states for a particular choice of the relative phase. The interference between these states leads to a spiked photon-number distribution but the field is still Poissonian.
For large initial fields, the evolution of the Jaynes-Cummings model is shown to simplify considerably. For two special initial atomic states (the eigenstates of the semiclassical problem) one finds a disentangled, quasipure-state evolution for both the field and atom. For an arbitrary initial atomic state the evolution is a linear super-imposition of these two privileged alternative paths. New results include the fact that the state of the atom at half-revival time is pure and independent of the initial state (nonunitary evolution), and that the state of the field at that time is a coherent super-imposition of macroscopically distinct states (Schrodinger cat).
An expression for the population inversion in the Jaynes-Cummings model and the most general initial state of the atom-field system is presented. States that maintain the same level of population inversion when the atom and the field are initially decoupled are found. When the atom is prepared in a coherent superposition of its states and the field is in an eigenstate of the Susskind-Glogower phase operator, for a certain choice of the relative phase between the atomic dipole and the field, coherent trapping occurs. The evolution of the squeezing of the field for these states is given, and the dependence on the phase and on the mean photon number of the field is studied.