Entropy exchange and entanglement in the Jaynes-Cummings model

Abstract

The Jaynes-Cummings model is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight (S. J. D. Phoenix, P. L. Knight, Annals of Physics 186, 381). 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 anti-correlated. 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 anti-correlation 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.