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Physical Review A

Loophole-free test of the Bell inequality

Susana F. Huelga, Miguel Ferrero, Emilio Santos

Published Jun 1, 1995• 35 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.51.5008

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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.
The nonlocality inherent in quantum mechanics has been tested experimentally, but the nonlocal interpretation of all the relevant experiments can be challenged. All past tests of Bell's inequalities have required supplementary assumptions, without which the experimental results satisfy the inequalities, in agreement with the notion of local realism. There are basically three loopholes that need to be closed; neither the cascade sources nor the parametric down-conversion sources of correlation photons used to date are capable of closing all of them, even if the detectors used had been 100% efficient. We propose a two-crystal down-conversion source, relying on type-II collinear phase matching, which should permit a violation of Bell's inequalities without the need for supplementary assumptions. As the source can produce a true singletlike state, it is also relevant for quantum cryptographic applications.
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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.
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.
The proof of Nature's nonlocality through Bell-type experiments is a topic of longstanding interest. Nevertheless, no experiments performed thus far have avoided the so-called 'detection loophole,' arising from low detector efficiencies and angular-correlation difficulties. In fact, most, if not all, of the systems employed to date can never close this loophole, even with perfect detectors. In addition, another loophole involving the non-rapid, non-random switching of various parameter settings exists in all past experiments. We discuss a proposal for a potentially loophole-free Bell's inequality experiment. The source of the EPR-correlated pairs consists of two simultaneously-pumped type-2 phase-matched nonlinear crystals and a polarizing beam splitter. The feasibility of such a scheme with current detector technology seems high, and will be discussed. We also present a single-crystal version, motivated by other work presented at this conference. In a separate experiment, we have measured the absolute detection efficiency and time response of four single-photon detectors. The highest observed efficiencies were 70.7 plus or minus 1.9 percent (at 633 nm, with a device from Rockwell International) and 76.4 plus or minus 2.3 percent (at 702 nm, with an EG&G counting module). Possible efficiencies as high as 90 percent were implied. The EG&G devices displayed sub-nanosecond time resolution.
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.