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Acta Physica Sinica

Entropy exchange and entanglement of a moving atom with k-photon Jaynes-Cummings model

Jicheng Wang, Liao Qing-Hong, Yueyuan Wang, Wang Yue-ke, Shutian Liu

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The entropy correlation and the entanglement of a moving atom interacting with k-photon Jaynes-Cummings model are investigated. Entropy exchange between atomic and field subsystems, which is a form of anti-correlated behavior, is explored. Analytical results show that atomic motion, transition number k of field and field-mode structure can influence the entropy exchange between atom and light field. Moreover, the relationship between entropy correlations and entanglement is also discussed.

DOI
10.7498/aps.60.114208

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The entropy correlation and the entanglement of a moving atom interacting with k-photon Jaynes-Cummings model are investigated. Entropy exchange between atomic and field subsystems, which is a form of anti-correlated behavior, is explored. Analytical results show that atomic motion, transition number k of field and field-mode structure can influence the entropy exchange between atom and light field. Moreover, the relationship between entropy correlations and entanglement is also discussed.
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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 dynamics of the two_photon Jaynes_Cummings model with atomic motion are studied by using the quantum information theory, and the quantum echanical channel representing the state change of atom is given; the quantum mutual entropy and reduced entropy of the atom are derived. The influences of the atomic motion and the field structure on the quantum mutual entropy are examined. It is shown that the properties of quantum mechanical channel are strongly dependent on the atomic motion, the field model structure, and the entanglement between the atom and the field.
Using the algebraic dynamical method, the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated. The atomic center-of-mass motion and the field-mode structure are also included in this system. We find that the values of the detuning and the average photon number are larger, the amplitude of the entanglement is smaller, but its period does not increase accordingly. Moreover, with the increase of the field-mode structure parameter and the transition photon number, the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast. Interestingly, a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.