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arXiv:0705.4373

Relationship between the linear entropy, the von Neumann entropy and the atomic Wehrl entropy for the Jaynes-Cummings model

Faisal A. A. El-Orany

Published May 30, 2007• 2 citations
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Abstract

The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.

DOI
10.48550/arxiv.0705.4373

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The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.
The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.
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
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