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Violations of a new inequality for classical fields

J. D. Franson

Published Feb 1, 1992• 0 citations
OpenAlex

Abstract

Two entangled photons incident upon two distant interferometers can give a coincidence counting rate that depends nonlocally on the sum of the phases of the two interferometers. It has recently been shown that experiments of this kind may violate a simple inequality that must be satisfied by any classical or semi-classical field theory. The inequality provides a graphic illustration of the lack of objective realism of the electric field. The results of a recent experiment which violates this inequality and in which the optical path length between the two interferometers was greater than 100 m are briefly described.

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Two entangled photons incident upon two distant interferometers can give a coincidence counting rate that depends nonlocally on the sum of the phases of the two interferometers. It has recently been shown that experiments of this kind may violate a simple inequality that must be satisfied by any classical or semi-classical field theory. The inequality provides a graphic illustration of the lack of objective realism of the electric field. The results of a recent experiment which violates this inequality and in which the optical path length between the two interferometers was greater than 100 m are briefly described.
We have performed an EPR-type experiment first proposed by Franson,1 resulting in two-particle interference that is both nonclassical and nonlocal. We used photon pairs produced in an entangled state of energy via spontaneous down-conversion. Each photon enters an unbalanced interferometer, and we detect singles and coincidence rates at the output ports. If the long- and short-arm path-length difference is much greater than the photons’ coherence lengths, no fringes are seen in singles as the arm lengths are varied. Yet when the difference between the path-length differences of the two interferometers is less than these coherence lengths, fringes are observed in coincidence, resulting from an interference of the (indistinguishable) “long–long” and “short–short" coincidence possibilities. If the electronic resolution is sufficient to eliminate the background of "short–long" and "long–short” coincidences, the visibility may be as high as 100%.2 For V > 71%, with certain reasonable auxiliary assumptions, Bell’s inequalities can be violated. The interpretation is that no local, realistic model can yield the observed results. The use of this type of entangled state is significant because it is much closer to the original EPR paradox than the spin-singlet case commonly considered.
In the study of systems that can not be explained classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality - originally derived in 1969 - and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements - that is, any system where only one possible result of a pair of potential outcomes can be registered. This encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. This experiment constitutes the first violation of local realism with such high quanta. We thus demonstrate the versatility of this inequality under very lossy conditions.
A two-photon correlation experiment of the kind that was proposed by Franson and has recently been carried out by two groups is analyzed. In this experiment two simultaneously produced photons are directed along two paths to two photodetectors without mixing. An unbalanced interferometer with delay time that is much longer than the coherence time of the light is inserted in each path. Yet the rate of two-photon detection by the two detectors in coincidence exhibits interference as the path difference is changed. The question of whether classical field theory can account for these observations is discussed. We show that no ergodic classical field is able to reproduce the experimental results, although a nonergodic field can give rise to interference through the artifice of generating an ensemble by initializing repeatedly.