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10
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For example, although Braunstein and Mann have shown that the detection efficiency requirement can be reduced to 71%, this is only in the limit of no background and a large number of entangled particles
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(1993)
Phys. Rev. A
, vol.47
, pp. R2427
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Braunstein, S.L.1
Mann, A.2
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In [7], Hardy also discusses non-maximally-entangled states, for use in a demonstration of nonlocality without inequalities. However, in the absence of supplementary assumptions, his scheme would require detector efficiencies greater than 98%.
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Hardy has also proposed a scheme which employs two nonlinear crystals, in a different geometry than that discussed here [, ]. Specifically, he proposes directing the down-converted photons from one crystal through a second crystal, such that one cannot determine from which crystal a pair originated. However, as he points out, his scheme requires near-perfect alignment to function adequately (the best results reported so far with such a scheme displayed only 30% visibility [, 67, 318), ]: to violate a Bell's inequality, one needs greater than 71% visibility, assuming 100% detection efficiency and no background. The fact that we use photons which are (very nearly) collinear reduces our alignment difficulties considerably., Phys. Rev. Lett.
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(1991)
L. Hardy, Phys. Lett. A
, vol.161
, pp. 326
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Zou, X.Y.1
Wang, L.J.2
Mandel, L.3
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A very different proposal has been made by Edward Fry, in Proceedings of the International Conference on Lasers '93, edited by C. P. Wang (STS Press, McLean, VA, 1993), using dissociated mercury dimers as the correlated particles. The advantage is that detection efficiencies of 95% are possible by photoionizing the atoms and detecting the photoelectrons. Although it may be that this scheme is a viable one, it is still untested; it should be noted that none of Bell's inequality experiments to date have relied on entangled atoms.
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and references therein.
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In contrast to the cascade situation, the polarizations remain well defined even for noncollinear down-converted pairs. One consequence is that extra means must be used to prepare a polarization-entangled state. (Due to energy conservation, the photons are automatically produced in an energy -entangled state [13 – 15].)
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Hardy has pointed out that one could use the full state (1) if one's detectors could reliably distinguish between one- and two-photon states [e.g., if a two-photon detection resulted in a pulse twice as high as a single-photon detection, cf., ], thereby allowing one to account for the cases in which both photons went the same way (private communication).
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(1987)
Appl. Phys. Lett.
, vol.51
, pp. 406
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Petroff, M.D.1
Stapelbroek, M.G.2
Kleinhans, W.A.3
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In these tests as well, half of the counts are discarded (electronically) to eliminate a noninterfering background [14,15].
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Although in this scheme [16] there is in principle no necessity of discarding half of the counts, in practice the small irises needed for high visibility fringes severely reduce the effective detection efficiency.
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In experiments performed with gamma-ray photons (produced from positronium annhilation, for instance) the actual detector efficiencies are very high, but available polarizers are very poor [2].
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Actually, this leaves a factor of 2 safety margin. Ideally, one would desire that the backward light cones of the detection apparatuses and the particle source not overlap, lest it be argued that the apparatus settings share some common cause. Practically, this is impossible (since all must lie within the future light cone of this paper), and the best one could achieve would be to base the analyzer settings on random signals from astronomical objects outside each other's light cones (e.g., quasars on opposite sides of the universe). This compromise would rule out all local theories short of ``superdeterminism,'' which amounts to the claim that there is no nonlocality since all events are predetermined, but they are predetermined to precisely mimic a nonlocal theory. Such a metaphysical viewpoint is clearly outside the scope of science.
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Using the two-crystal source, one could in principle perform a Franson-type experiment [13 – 15], without the need to electronically discard counts that arise from the noninterfering processes where one photon travels the short path in its unbalanced Mach-Zehnder interferometer and the other photon travels the long path [28]. To do this, one simply uses polarizing beam splitters in the interferometers, oriented to prevent these processes, i.e., force one long path to be associated with horizontal polarization and the other long path to be associated with vertical polarization. Half-wave plates in two of the paths can be used to rotate all polarizations to vertical, say, restoring coherence. A standard nonpolarizing beam splitter can then be used to recombine the paths.
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Franson has argued that the pump coherence time might also come into play [34]. However, this is also of the nanosecond time scale.
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45
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and references therein].
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46
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V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, in Handbook of Nonlinear Optical Crystals, edited by A. E. Siegman, Springer Series in Optical Sciences Vol. 64, (Springer-Verlag, New York, 1991).
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47
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Actually, it is sufficient that the vectors k vec1times n vec1 and k vec2times n vec2 (where k veci and n veci are the pump beam and optic axis directions, respectively, associated with crystal i) be mirror symmetric about this plane.
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By ``background'' we mean all detector counts not arising from our correlated photons, i.e., stray light, detector dark counts, etc.
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Note that p3p( α ) varies as sinα2 + |f| cosalpha2, so any attempt to simply average the signals from the p and s channels, for example, by adding (6) to a similar inequality for the s-channel counts, as in the CHSH inequality [, ], will remove the benefit of unbalancing the entanglement.
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(1969)
Phys. Rev. Lett.
, vol.23
, pp. 880
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Clauser, J.F.1
Holt, R.A.2
Horne, M.A.3
Shimony, A.4
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and [37]], in which the two-photons from a down-conversion crystal always take the same port of a 50-50 beam splitter.
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