Eur. Phys. J. D 32, 233-239 (2005)
https://doi.org/10.1140/epjd/e2004-00171-6

A proposal to test Bell's inequalities with mesoscopic non-local states in cavity QED

¹ Laboratoire Kastler Brossel, Département de Physique de l'École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Edward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
³ Collège de France, 11 place Marcelin-Berthelot, 75005 Paris, France

Corresponding author: ^a jmr@lkb.ens.fr

Received: 4 June 2004
Published online: 30 November 2004

Abstract

We propose a cavity quantum electrodynamics (CQED) experiment to test the violation of a Bell-type inequality using non-local mesoscopic states (NLMS). These states involve coherent field superpositions stored in two spatially-separated high-Q cavities. The inequality is expressed in terms of the measured Wigner function of the entangled two-field-mode system at four points in phase space, as proposed in [Banaszek and Wódkiewicz, Phys. Rev. Lett. 82, 2009 (1999)]. We examine the production of these entangled NLMS and the measurement of their Wigner function. The experiment involves circular Rydberg atoms and superconducting millimeter-wave cavities. We present a detailed numerical study of the optimal inequality violation and of the effect of decoherence. We discuss the range of experimental parameters making it possible to observe a locality violation and show that they correspond to realistic, albeit demanding, conditions.