The first two-photon entanglement experiment performed 50 years ago by Kocher and Commins (KC) provided isolated pairs of entangled photons from an atomic three-state fluorescence cascade. In view of questioning of Bell’s theorem, data from these experiments are re-analyzed and shown sufficiently precise to confirm quantum mechanical and dismiss semi-classical theory without need for Bell’s inequalities. Polarization photon correlation anisotropy (A) is useful: A is near unity as predicted quantum mechanically and well above the semi-classic range, 0 6 A 6 1=2. Although yet to be found, one may envisage a three-state molecule emitting entangled photon pairs, in analogy with the KC atomic system. Antibunching in fluorescence from single molecules in matrix and entangled photons from quantum dots promise it be possible. Molecules can have advantages to parametric down-conversion as the latter photon distribution is Poissonian and unsuitable for producing isolated pairs of entangled photons. Analytical molecular applications of entangled light are also envisaged.

Introduction

Statistical characterization of quantum correlations has been guided for half a century by Bell’s inequalities [10,11]. In 1935, in a provocative paper, Einstein, Podolsky and Rosen suggested a hypothetical experiment capable of testing some apparently paradoxical predictions of quantum theory, the EPR paradox [12]. Einstein believed quantum mechanical descriptions of physical systems to be correct only if supplemented with statistical distributions involving certain hidden variables but von Neumann [13] presented a mathematical proof that any hidden-variable theory must be in conflict with quantum mechanics. Bell argued that the proofs, although mathematically correct, rested upon physically unrealistic assumptions and showed that regardless of choice of hidden-parameter framework expectation values will obey certain inequalities [10,11]. The EPR paradox is philosophically interesting and has led also to a paradigmatic concept: ‘‘entanglement” (Schrödinger: ‘‘Verschränkung”) [۱۴] with roots in the wave-particle duality, today finding spreading applicability as briefly reviewed here. In 1950 Wu and Shaknow [15], based on a suggestion by Wheeler [16], demonstrated that the angular correlation of annihilation radiation from positron-electron pairs quantitatively fulfills the asymmetry predicted by quantum pair theory. I will along similar lines consider the asymmetry of the first polarized photon correlation experiments with visible light and show that these are sufficiently precise to rule out local hidden-variable theories with reasonable statistical accuracy, and useful in general (e.g., molecular) contexts. Today’s quantum photon theory and technology follows in my view from mainly two strands of seminal experiments: 1. The discovery by Hanbury Brown and Twiss [17,18] that photons from a thermal source have a tendency to arrive in bunches – an effect characteristic of thermal bosons which can be explained in terms of classical fields. 2. Photon bunching studies by Mandel and coworkers [19,20] with the discovery of photon antibunching by Kimble, Dagenais and Mandel [21], predicted by Fano [22], Glauber [23] and Stoler [24] as a purely quantum field phenomenon. A seminal experiment by Kocher and Commins [1] demonstrated the generation of isolated pairs of entangled photons by an atomic fluorescence cascade and is the focus of this communication. In its wake followed several studies using this technique combined with a suggestion by Clauser, Horne, Shimony and Holt how to test Bell’s inequality by measuring at four combinations of orientations of the polarizers [25–۲۷]. Also two-photon correlation experiments using laser parametric down-conversion technique were reported strongly violating the Bell inequality, however, also substantially the classical probability [28].