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Journal of Modern Optics

Entangled fields in multiple cavities as a testing ground for quantum mechanics

János A. Bergou

Published Oct 1, 1997• 12 citations
Publisher

Abstract

Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and post-selective quantum mechanics, QND measurements, complementarity, and tests of mechanics itself against, e.g. the so-called causal communication constraint. We show how to produce nonlocal entangled states of multiple cavity fields. We first discuss two-cavity entanglement, namely the generation of the Bell basis states for this system, when there is at most one photon in either of the cavities. We then discuss a straightforward generalization to similar N-cavity states. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review a proposal to test quantum mechanics against the causal communication constraint using the two-cavity state and a test of pre- and post-selective quantum mechanics using a three-cavity state and the close connection of the latter to the consistent histories interpretation. Finally we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation and quantum copying.

DOI
10.1080/09500349708231858

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Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and post-selective quantum mechanics, QND measurements, complementarity, and tests of mechanics itself against, e.g. the so-called causal communication constraint. We show how to produce nonlocal entangled states of multiple cavity fields. We first discuss two-cavity entanglement, namely the generation of the Bell basis states for this system, when there is at most one photon in either of the cavities. We then discuss a straightforward generalization to similar N-cavity states. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review a proposal to test quantum mechanics against the causal communication constraint using the two-cavity state and a test of pre- and post-selective quantum mechanics using a three-cavity state and the close connection of the latter to the consistent histories interpretation. Finally we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation and quantum copying.
Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and post-selective quantum mechanics, QND measurements, complementarity, and tests of mechanics itself against, e.g. the so-called causal communication constraint. We show how to produce nonlocal entangled states of multiple cavity fields. We first discuss two-cavity entanglement, namely the generation of the Bell basis states for this system, when there is at most one photon in either of the cavities. We then discuss a straightforward generalization to similar N-cavity states. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review a proposal to test quantum mechanics against the causal communication constraint using the two-cavity state and a test of pre- and post-selective quantum mechanics using a three-cavity state and the close connection of the latter to the consistent histories interpretation. Finally we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation and quantum copying.
Highly entangled states of more than one quantum system are necessary for tests of local hidden-variable theories and of quantum mechanics itself. We show how to produce field states, which are located in several cavities and are highly entangled, by sending apropriately prepared atoms through the cavities. We discuss both a two-cavity and a three-cavity state in which either each cavity is in a one-photon number state or each is in the vacuum state. Finally, a test of quantum mechanics using the two-cavity state is presented.
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.
We provide a scheme by utilizing a two-cavity setup to generate useful quantum mechanically entangled states of two cavity fields, which themselves are prepared in Schrodinger cat states. The underlying atom-field interaction is considered off-resonant and three atoms are successively sent through the cavities, initially fed with coherent fields. Analytical solution of the protocol, followed by conditional measurements on the atoms, produce a family of eight such entangled states. Entanglement properties of the obtained states are characterized by the Von Neumann entropy. We reveal the parameter domain for tuning the entanglement, the prime tuning parameters being the atom-field interaction time and the field amplitudes. The parameter domains for both quasi-Bell and non quasi-Bell states are discussed. We also present a Wigner phase space representation of the reduced state of the cavity, showing negative values and interference patterns similar to those of a compass state, used in quantum precision measurements, and despite its large entropy.