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Europhysics Letters (EPL)

Atomic-Cascade Experiment with Detection of the Recoil Atom

Susana F. Huelga, Miguel Ferrero, Emilio Santos

Published Jul 20, 1994• 13 citations
Publisher

Abstract

Bell's inequalities cannot be violated in atomic-cascade experiments, even with ideal apparatus, due to the three-body character of the atomic decay. Here we propose a new experiment that would block this loophole by means of a suitable selection of an ensemble of photon pairs. A threshold value for the quantum efficiency is found which may allow the discrimination between quantum mechanics and local-hidden-variables theories. Experimental requirements for performing such a test are discussed.

DOI
10.1209/0295-5075/27/3/002

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Bell's inequalities cannot be violated in atomic-cascade experiments, even with ideal apparatus, due to the three-body character of the atomic decay. Here we propose a new experiment that would block this loophole by means of a suitable selection of an ensemble of photon pairs. A threshold value for the quantum efficiency is found which may allow the discrimination between quantum mechanics and local-hidden-variables theories. Experimental requirements for performing such a test are discussed.
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.
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.
The tests of Bell's inequality to date have failed to be definitive because of the ``detection loophole,'' due to the inefficiency of photodetectors. An idealized experiment using pairs of two-level Rydberg atoms, correlated with the help of a quantized cavity field, was proposed by Oliver and Stroud [J. Opt. Soc. Am. B 4, 1426 (1987)] for the purpose of blocking this loophole. We develop their proposal by removing their idealizations. We carefully define the ensemble of atom pairs by imposing conditions on arrival times at the analyzers of the atoms. We take into account the spread of velocities of the atoms, which implies that the ensemble must be described quantum mechanically by a statistical operator rather than a pure state, and we show that with detector efficiencies of 0.9 or better, quantum mechanics implies a strong violation of Bell's inequality in the ensemble. Upper and lower bounds on ensemble averages can be inferred from experimental averages, thereby permitting an experimental test of Bell's inequality in the ensemble. \textcopyright{} 1996 The American Physical Society.
An atomic cascade experiment is proposed that includes the detection of a recoil atom after the emission of two photons. This would permit testing of the Bell inequality without the need for additional assumptions, provided that the quantum efficiency of single-photon detectors exceeds a threshold of 0.92. The atomic source consists of calcium atoms, first trapped and then accelerated by gravity, whose velocity is controlled before they reach the interaction region with the two counterpropagating laser beams. The procedure allows a relatively high background in the photodetectors.