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arXiv:quant-ph/0202041 · Physical Review A

Entanglement and the SU(2) phase states in atomic systems

M. Ali Can, Alexander A. Klyachko, A.S. Shumovsky

Published Aug 19, 2002• 19 citations
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Abstract

We show that a system of $2n$ identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU(2) phase states. In particular, violation of classical realism in terms of the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimoni-Holt conditions is proved. We discuss a property of entanglement expressed in terms of local measurements. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions and that the parasitic influence of cavity detuning can be compensated through the use of Kerr medium.

DOI
10.1103/physreva.66.022111

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We show that a system of 2n2n2n identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU(2) phase states. In particular, violation of classical realism in terms of the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimoni-Holt conditions is proved. We discuss a property of entanglement expressed in terms of local measurements. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions and that the parasitic influence of cavity detuning can be compensated through the use of Kerr medium.
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We construct a Bell inequality from the Clauser-Horne-Shimony-Holt inequality for two qubits that provides a stronger bound on the correlations of entangled states than allowed by the CHSH inequality. The argument involved here can be generalized to nnn qubits. The inequalities obtained are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits.
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A simple classical non-local dynamical system with random initial conditions and an output projecting the state variable on selected axes has been defined to mimic a two-channel quantum coincidence experiment. Non-locality is introduced by a parameter connecting the initial conditions to the selection of the projection axes. The statistics of the results shows violations up to 100% of the Bell's inequality, in the form of Clauser-Horne- Shimony-Holt (CHSH), strongly depending on the non-locality parameter. Discussions on the parallelism with Bohmian mechanics are given.