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Journal of Modern Optics

Realization of GHZ states and the GHZ test via the interaction of atoms with cavity field states

E. S. Guerra

Published Jun 2, 2006• 1 citation
Publisher

Abstract

In this article we discuss the realization of atomic GHZ states involving Rydberg atoms interacting with superconducting cavities and we show explicitly how to perform the GHZ test in which it is possible to decide between local realism theories and quantum mechanics.
DOI
10.1080/09500340600551606

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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.
From the hypotheses of realism and stationarity, the latter related to the Leggett-Garg assumption of non-invasive measurability, we derive inequalities, involving three autocorrelation functions, to be fulfilled by any two-state stochastic process. We seek to test a broad class of realist theories against quantum mechanics for a system consisting of a Rydberg atom interacting with a single quantized mode in a superconducting resonant cavity. Departures from quantum predictions are enhanced when the temperature is decreased to about 0.5 K and the state of the cavity approximates a Fock state.
We demonstrate how a new exactly soluble cavity QED model can be used to test local realism associated with three-particle entangled states, as proposed by Mermin. These states embody the correlations described by Greenberger, Horne, and Zeilinger (GHZ) and provide a stronger refutation of local hidden variable theories than is possible with Bell inequalities. It is shown that two photons distributed in the model’s four cavity modes coupled with a two-level atom can effectively produce three independent spin-1/2 particle states. We discuss preparation of the desired perfectly correlated GHZ state and a method to perform measurement on various field modes and atomic level correlations equivalent to a spin component along any direction.