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Physical Review A

Proposal for a loophole-free test of the Bell inequalities

Edward S. Fry, Thomas Walther, Shifang Li

Published Dec 1, 1995• 177 citations
Publisher

Abstract

A proposal for an experimental realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment is described. Two $^{199}\mathrm{Hg}$ atoms, each with nuclear spin 1/2, are produced in an entangled state with total nuclear spin zero. Such a state is obtained by dissociation of dimers of the $^{199}\mathrm{Hg}_{2}$ isotopomer using a spectroscopically selective stimulated Raman process. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two-photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition.

DOI
10.1103/physreva.52.4381

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A proposal for an experimental realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment is described. Two 199Hg^{199}\mathrm{Hg}199Hg atoms, each with nuclear spin 1/2, are produced in an entangled state with total nuclear spin zero. Such a state is obtained by dissociation of dimers of the 199Hg2^{199}\mathrm{Hg}_{2}199Hg2​ isotopomer using a spectroscopically selective stimulated Raman process. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two-photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition.
The status of our experimental realization of Bohm’s spin-1/2 particle version of the Einstein-Podolsky-Rosen gedankenexperiment is discussed. This new experiment provides a definitive test of the, as yet, untested strong Bell inequalities. It closes the two widely recognized loopholes associated with previous experiments, and has the interesting new feature that the entangled state exists for milliseconds rather than nanoseconds. The spin one-half particles are two 199 Hg atoms in an entangled nuclear spin state with total nuclear spin zero. Measurement of the nuclear spin correlation is achieved by detection of each atom using a spin state selective two photon excitation-ionization scheme.
Abstract An experimental realization of Bohm's spin-1/2 EPR gedanken-experiment is possible using the spin-1/2 nuclei of the isotope 199 Hg. The dissociation of dimers of the 199 Hg 2 isotopomer, using a spectroscopically selective stimulated Raman process, leads to the generation of an entangled state between the two 199 Hg atoms. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two photon excitation-ionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition. Effects of imperfect analyzers will also be discussed.
All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described.
We present recent progress in the implementation of experimental realization of a loophole-free test of Bell inequalities for entangled 111Cd atoms. The experimental approach is a modified version of the proposal of FRY and co-workers (Phys. Rev. A 52(6), 1995, p. 4381) for the realization of Bohm’s 1/2-spin particle version of the Einstein–Podolsky–Rosen (E-P-R) experiment and is based on the production of entangled atoms by photodissociation of the 111Cd2 isotopologue in a supersonic expansion beam using the spectroscopically selective stimulated Raman process.
Most experimental tests of Bell inequalities have involved measurements of correlations between two photons. One of the first definitive experiments involved the linear polarization correlation between two photons in an atomic cascade of 200 Hg. That experiment is discussed in depth in this paper. The form of the initial state density matrix was a critical part of that experiment; and the experimental and theoretical determination of the density matrix, including finite solid-angle effects is discussed. However, all Bell inequality experiments to date have two widely recognized loopholes, detector efficiency and locality. This paper concludes with a very brief description of an experiment that will close both of these loopholes. In contrast to existing experiments with photons, this new test involves spin correlations between the nuclei of two 199 Hg atoms; it is an exact experimental realization of Bohm's version of the Einstein-Podolsky-Rosen gedankenexperiment.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.