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arXiv:0709.1493 · Journal of Physics A Mathematical and Theoretical

Marginal and density atomic Wehrl entropies for the Jaynes–Cummings model

Faisal A A El-Orany

Published Jan 4, 2008• 7 citations
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Abstract

In this paper, we develop the notion of the marginal and density atomic Wehrl entropies for a two-level atom interacting with the single mode field, i.e. the Jaynes–Cummings model. For this system we show that there are relationships between these quantities and both the information entropies and the von Neumann entropy.
DOI
10.1088/1751-8113/41/3/035303

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The concept of the classical-like Wehrl entropy is shown to be a very sensitive and informative measure describing the time evolution of a quantum system. Its applications to the Jaynes-Cummings model reveal relevant aspects of the field dynamics. The Wehrl entropy provides a compact one-parameter description giving, among other things, a clear signature for the splitting of the Q function. It gives also a clear indication of the phase randomization of the coherent electromagnetic field states during the interaction with a two-level atom.
The behavior of atoms in the Jaynes–Cummings model has been discussed and analyzed extensively to date in terms of transition probability and entropy. In this paper, the Jaynes–Cummings model is described in terms of a quantum-mechanical channel expressing the state transition. For this channel, von Neumann entropy and quantum mutual entropy are derived. By means of these quantities, the variation of the atomic state and its nonreciprocity in this model are discussed. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(1): 95–103, 2001
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