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arXiv:quant-ph/9903085 · Physics Letters A

Quantum entangled supercorrelated states in the Jaynes–Cummings model

A. K. Rajagopal, Kevin L. Jensen, F.W. Cummings

Published Aug 1, 1999• 24 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(99)00404-1

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An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local $2\ifmmode\times\else\texttimes\fi{}2$ projections of the full $2\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called ``supercorrelated'' states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed.
ABSTRACT In this paper, we investigate steady‐state quantum squeezing and entanglement in a generalized Dicke model, which features Jaynes–Cummings (JC) and anti–Jaynes–Cummings (AJC) interactions with different strengths, by taking into account of single‐atom spontaneous emission and continuous homodyne detection of the cavity field. We find that a reduction in the strength of the AJC interaction can lead to atomic squeezing, which is otherwise absent when the strengths of the two interactions are equal. Likewise, cavity‐field squeezing and atom‐field entanglement can be enhanced as the strength of the AJC interaction is reduced. Furthermore, continuous measurement is shown to significantly enhance both the squeezing and entanglement in both normal and superradiant phases. In addition, it is revealed that under certain conditions, single‐atom spontaneous emission can also improve the squeezing and entanglement. Our results reveal distinctive characteristics of quantum correlations in the open Dicke model and suggest a promising route for realizing robust nonclassical states in such systems.