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Physical Review A

Preparation of a four-atom Greenberger-Horne-Zeilinger state

Christopher C. Gerry

Published Jun 1, 1996• 28 citations
Publisher

Abstract

I propose a method to prepare four atoms in an entangled state of the type discussed by Greenberger, Horne, and Zeilinger [in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989), p. 107]. The method involves two micromaser cavities, each supporting two modes initially prepared in a nonlocalized two-photon state by an atom undergoing a two-photon transition. Subsequently, two atoms pass through each cavity, becoming entangled in a Greenberger-Horne-Zeilinger state leaving the cavities in the vacuum. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.4591

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I propose a method to prepare four atoms in an entangled state of the type discussed by Greenberger, Horne, and Zeilinger [in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989), p. 107]. The method involves two micromaser cavities, each supporting two modes initially prepared in a nonlocalized two-photon state by an atom undergoing a two-photon transition. Subsequently, two atoms pass through each cavity, becoming entangled in a Greenberger-Horne-Zeilinger state leaving the cavities in the vacuum. \textcopyright{} 1996 The American Physical Society.
We propose a way for generating nnn-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states with a three-level qubit system and $(n\ensuremath{-}1)$ four-level qubit systems in a cavity. This proposal does not require identical qubit-cavity coupling constants and thus is tolerant to qubit-system parameter nonuniformity and nonexact placement of qubits in a cavity. The proposal does not require adjustment of the qubit-system level spacings during the entire operation. Moreover, it is shown that entanglement can be deterministically generated using this method and the operation time is independent of the number of qubits. The present proposal is quite general, which can be applied to physical systems such as various types of superconducting devices coupled to a resonator or atoms trapped in a cavity.
A proposal is made for obtaining a mesoscopic realization of the Greenberger-Horne-Zeilinger (GHZ) "all or nothing" contradiction between quantum mechanics and local realism in the context of cavity QED. The proposed experiment involves three separated micromaser cavities, each initially prepared in a coherent state, which are then entangled by dispersive atom-field interactions followed by selective ionization of a single atom that has passed through all three cavities. The cavities are then probed individually by single atoms manipulated to obtain a measurement of the parity of the cavity fields. Using an isomorphism between coherent-state cavity fields and a spin-\textonehalf{} system, we show how this experiment gives rise to violations of local realism in the manner of GHZ.