You appear to not accept the PDC technology as being any more persuasive to you than Aspect's when it comes to pair production. Is that accurate?
The phenomenologial PDC hamiltonian used in Quantum Optics computations has been reproduced perfectly within the Stochastic Electrodynamics (e.g. see papers from Marshall & Santos group; recent editions of well respected Yariv's QO textbook have an extra last chapter which for all practical purposes recognizes this equivalence).
Also, is it your opinion that photons are not quantum particles, but are instead waves?
Photons in QED are quantized modes of EM field. For a free field you can construct these in any basis in Hilbert space, so the "photon number" operator [n] depends on basis convention. Consequently the answer to question "how many photons are here" depends on the convention for the basis. (No different than you asking me what is the speed number on your car, and if I say 2300; this obviously is meaningless, since you need to know what convention I use for my speed units.)
For example if you have plane wave as a single mode, in its 1st excited state (as harmonic oscillator), in that particular base you have single photon, the state is an eigenstate of this [n]. But if you pick other bases, then you'll have a superposition of generally infinitely many of their "photons" and the plane wave is not the eigenstate of their [n].
The QO convention then calls "single photon" any superposition of the type |Psi.1> = Sum(k) of Ck(t) |1_k>, where sum goes over wave vectors k (a 4-vector) k=(w,kx,ky,kz) and |1_k> are eigenstates of some [n] with eigenvalue 1. This kind of photon is quasi-localized (with spread stretching across many wavelengths). Obviously, here you don't have any more E=hv relation since there is no single ferquency v superposed into the "single photon" state |Psi.1>. If the localization is very rough (many wavelengths superposed) then you could say that approximately |Psi.1> has some dominant and average v0, and one could say approximately E=hv0.
But there is no position operator for a point-like photon (and it can't be constructed in QED) and no QED process generates QED "single photon", the Fock state |1> for some basis and its [n], (except as an approximation in the lowest order of perturbation theory). Thus there is no formal counterpart in QED for a point-like entity hiding somewhere inside EM field operators, much less of some such point being exclusive. A "photon" for laser light streches out for many miles.
The equations these QED and QO "photons" follow in Heisenberg picture are plain old Maxwell equations for free fields or for any linear optical elements (mirrors, beam splitters, polarizers etc). For the EM interactions, the semiclassical and QED formalisms agree to at least alpha^4 order effects (as shown by Barut's version of semiclassical fields which include self-interaction). That is 8-9 digits of precision (it could well be more if one were to carry out the calculations).
Barut unfortunately died in 1994, so that work has stalled. But their results up to 1987 are described in http://library.ictp.trieste.it/DOCS/P/87/248.pdf . ICTP has scanned 149 of his preprints, you can
get pdfs here (type Barut in "author"; also interesting is his paper on http://library.ictp.trieste.it/DOCS/P/87/157.pdf ; his semiclassical approach starts in papers from 1980 and on).
In summary, you can't count them except by convention, they appear and disappear in interactions, there is no point they can be said to be at, they have no position but just approximate regions of space defined by a mere convention of "non-zero values" for field operators (one can call these wave packets as well, since they move by the plain Maxwell wave equations, anyway; and they are detected by the same square-law detection as semiclassical EM wave packets).
One can think, I suppose of point photons as a heuristics, but one has to watch not to take it too far and start imagining, as these AJP authors apparently did, that you have some genuine kind of exclusivity one would have for a particle. That exclusivity doesn't exist either in theory (QED) or in experiments (other than via misleading presentation or outright errors as in this case).
The theoretical non-existence was [post=529314]already explained[/post]. In brief, the "quantum" g2 of (AJP.8-11 for n=0) corresponds to a single photon in the incident field. This "single photon" is |Psi.1> = |T> + |R> where |T> and |R> correspond to regions of the "single photon" field in T and R beams. The detector which (AJP.8) models is Glauber's ideal detector, which counts 1 if and only if it absorbs the whole single photon, leaving the vacuum EM field. But this "absorbtion" is (derived by Glauber in [4]) purely dynamical process,
local interaction of quantized EM field of the "photon" with the atomic dipole and for the "whole photon" to be absorbed, the "whole EM field" of the "single photon" has to be absorbed (via resonance, a la antenna) with the dipole. (Note that the dipole can be much smaller than the incident EM wavelength, since the resonance absorption will absorb the surrounding area of the order of wavelength.)
So, to absorb "single photon" |Psi.1> = |T> + |R>, the Glauber detector has to capture both branches of this single field, T and R, interact with them and resonantly absorb them, leaving EM vacuum as result, and counting 1. But to do this, the detector will have to be spread out to capture both T and R beams. Any second detector will get nothing, and you indeed have perfect anticorrelation, g2=0, but it is entirely trivial effect, with nothing non-classical or puzzling about it (semi-classical detector will do same if defined to capture full photon |T>+|R>).
You could simulate this Glauber detector capturing "single photon" |T>+|R> by adding an OR circuit to outputs of two regular detectors DT and DR, so that the combined detector is Glaber_D = DT | DR and it reports 1 if either one or both of DT and DR trigger. This, of course, doesn't add anything non-trivial since this Glauber_D is one possible implementation of Glauber detector described in previous paragraph -- its triggers are exclusive relative to a second Glauber_Detector (e.g. made of another pair of regular detectors placed somewhere, say, behind the first pair).
So the "quantum" g2=0 eq (8) (it is also semiclassical value, provided one models the Glauber Detector semiclassically), is valid but trivial and it doesn't correspond to the separate detection and counting used in this AJP experiment or to what the misguided authors (as their students will be after they "learn" it from this kind of fake experiment) had in mind.
You can get g2<1, of course, if you subtract accidentals and unpaired singles (the DG triggers for which no DT or DR triggered). This is in fact what Glauber's g2 of eq. (8) already includes in its definition -- it is defined to predict the subtracted correlation, and the matching operational procedure in Quantum Optics is to compare it to subtracted measured correlations. That's the QO convention. The classical g2 of (AJP.2) is defined and derived to model the non-subtracted correlation, so let's call it g2c. The inequality (AJP.3) is g2c>=1 for non-subtracted correlation.
Now, nothing is to stop you from defining another kind of classical "correlation" g2cq which includes subtraction in its definition, to match the QO convention. Then this g2cq will violate g2cq>=1, but there is nothing surprising here. Say, your subtractions are defined to discard the unpaired singles. Therefore in your new eq (14) you will put N(DR)+N(DT) (which was about 8000 c/s) instead of N(G) (which was 100,000 c/s) in the numerator of (14) and you have now g2cq which is 12.5 times smaller than g2c, and well below 1. But no magic. (The Chiao Kwiat paper recognizes this and doesn't claim any magic from their experiment.) Note that these subtracted g2's, "quantum" or "classical" are not the g2=0 of single photon case (eq AJP.11 for n=1), as that was a different way of counting where the perfect anticorrelation is entirely trivial.
Therefore, the "nonclassicality" of Quantum Optics is a term-of-art, a verbal convention for that term (which somehow just happens to make their work sound more ground-breaking). Any well bred Quantum Optician is thus expected to declare a QO effect as "nonclassical" whenever its subtracted correlations (predicted via Gn or measured and subtracted) violate inequalities for correlations computed classically for the same setup, but without subtractions. But there is nothing genuinely nonclassical about any such "violations".
These verbal gimmick kind of "violations" have nothing to do with theoretically conceivable genuine violations (where QED still might disagree with semiclassical theory). The genuine violations would have to be for the perturbative effects of orders alpha^5 or beyond, some kind of tiny difference beyond 8-9th decimal place, if there is any at all (unknown at present). QO operates mostly with 1st order effects, all its phenomena are plain semiclassical. All their "Bell inequality violations" with "photons" are just creatively worded magic tricks of the described kind -- they compare subtracted measured correlations with the unsubtracted classical predictions, all wrapped into whole lot of song and dance on "fair sampling" or "momentary technological detection loophole" or "non-enhancement hypothesis"... And after all the song and dance quiets down, lo and behold, the "results" match the subtracted prediction of Glauber's correlation function Gn (Bell's QM result cos^2() for correlations for photons are a special case Gn()) and violate nonsubtracted classical prediction. Duh.