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International Journal of Theoretical Physics

Stationary State Entanglement of Two Atoms Inside an Optical Cavity under Noise

Cenap Özel, Erol Yılmaz, Hünkar Kayhan, Aliekber Aktağ

Published Apr 24, 2008• 7 citations
Publisher
DOI
10.1007/s10773-008-9743-9

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The simple system of two atoms couple to single mode optical cavity with the phase decoherence is studied for investigating the entanglement and Bell violation between atoms and cavity or between two atoms. We show that in the resonance case (i) atom-field entanglement rapidly decays with phase decoherence and disappears in the stationary state, (ii) atom-atom entanglement is more robust against phase decoherence and survives in the stationary state. In the nonresonance case, the pairwise atom-atom and atom-field entanglement is sensitive to the detuning parameter and is not completely destroyed during evolution. On the other hand, violation of Bell-CHSH inequality is very fragile against the phase decoherence and finally disappears in the stationary state. The phenomenon that the more Bell violation, the less entanglement, or vice versa in such a realistic physical system, is revealed. This phenomenon maybe is the consequence of the choice of concurrence as the entanglement measure and the observables to build the Bell-CHSH inequality. The genuine three-partite entanglement is also analyzed by making use of the state preparation fidelity. It is shown that the genuine three-partite entanglement can appear in the evolution of the system even in the presence of the phase decoherence.
A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.
We study the feasibility of the commonly used adiabatic techniques in the atom-cavity field interaction to entangle two distant atoms trapped inside an optical cavity. Two techniques are considered: the first involves a highly detuned cavity from the atomic transition frequencies, and the second involves a near resonant but strongly damped cavity. We find that the second technique is more efficient for creation of a controllable entanglement between the atoms. We follow the temporal evolution of the concurrence and show that the system evolves to a single entangled state whose the stationary population is a sensitive function of the initial state of the atoms and strengths of the couplings of the atoms to the cavity mode.