Two-dimensional wave-vector correlations in spontaneous parametric downconversion explored with an intensified CCD camera. S. S. R. Oemrawsingh, W. J. v. Drunen, E. R. Eliel and J. P. Woerdman in J. Opt. Soc. Am. B 19:2391 (2002).  What the paper says!?

The paper images SPDC signal and idler from type-I (degenerate) source, demonstrating correlations between $k_{i\perp}$ and $k_{s\perp}$ over the full emission cone of the degenerate pairs.

For the study of spatially extended correlations, conventional single-photon detectors are not ideal because they are point detectors, which possess small (typically 175-μm-diameter) active areas, whereas the downconversion state can have a much more extended spatial profile.

A camera is equivalent to an array of $N(N-1)/2$ pairs of detectors:

A camera consisting of a two-dimensional (2D) array of point detectors offers an obvious advantage here. Specifically, all N pixels of an image can be cross correlated with one another, making one image equivalent to N(N - 1)/2 measurements with two separate point detectors, which would have to be positioned differently for each measurement.

All done in-house:

The camera does not require coincidence circuitry, because the exposure itself acts as such a circuit

They image a single pair (cf. Lantz et al. who image several thousands from the huge spatio-temporal modes imaged by the camera)

we look at a single photon pair with, in principle, 512 × 512 single-photon detectors that are all operated in coincidence; the coincidence window is given by the gate time.

And again on single-pair detection:

To establish the photon correlations unequivocally it is important to avoid the generation of multiple pairs of photons in a single pump pulse.

This is achieved by very low pump pulses. Ultimately:

roughly 1 of every 250 images contains a detected correlated pair

while

the dark count is negligible: Only 1 out of every 25.000 images contains an activated bin that is due to dark counts.

They do suffer, however, from stray light:

In contrast, stray light is far from negligible; we observe an activated bin approximately once every 100 images, i.e., approximately twice as often as we expect to detect a correlated signal–idler pair. Consequently, we detect pairs consisting of a stray photon and one of the signal–idler pair with somewhat larger probability than a quantum correlated signal–idler pair.

☡ Here I'd be careful on their bookkeeping: they say they have 1/237 frames with a coincidence, but only 1/1896 correlated pairs, 1/100 stray-light frames, i.e. a twin purity of about 12.5%: of every eight two-photon frames, one is truely correlated. That makes a factor 19 between stray light vs true coincidences, not 2 as they report.

We acquire approximately 436,000 images, most of which (99.5%) are [...] completely empty or contain only one active bin; all these images are discarded. The majority of the remaining images contains only two active bins.

The geometry of the acquisition: they select $\pm$5° signal/idler pairs and focus them in a ring on the camera.

The crystal is tilted slightly such that the degenerate pairs do not coincide with the transmitted pump beam but rather come out of the crystal in a cone with a top half-angle of 5°. This cone of degenerate photons is selected by a spectral filter with 13-nm bandwidth, centered at 803 nm, and subsequently brought to a ringlike focus on the photocathode of the intensified CCD camera.

Counting mode of their camera:

This allows us to set a discrimination level to impose values of 1 on the pixels that have detected a photon (active pixels) and 0 on the pixels that have not.

Principle of the experiment:

The experiment then consists of repetitively firing the laser and, with each shot, capturing the CCD image.

They bin the data and eventually acquire at the rate of 30Hz. This was an heroic measurement, as they «measured only 1839 coincidences, of which 230 pairs were true twins, in approximately 4h».

They find this beautiful correlation in angle: the photons are opposite the one from the other on the ring:

File:Screenshot 20260724 000205.png

They have another case with better alignment but to me it seems to give the exact same result.

There should also be radial correlations, but they don't see them:

Wave-vector correlations in type I SPDC are not limited to the azimuthal degree of freedom. Wave-vector matching in the downconversion process also gives rise to correlations of signal and idler photons in the radial coordinate. These radial correlations are, however, effectively washed out in our experiment as a result of the considerable bandwidth of our pump laser.

By post-selecting the pairs from the central peak, they form this neater image of the "quantum" ring (which they insist is a ring, also making a somehow forced 1D [azimuthal] to 2D [ring] connection):

File:Screenshot 20260724 002100.png

The multiphoton prospects are obvious but, at the time, limited:

The multiplexing advantage appears when there is information in many pixels; in the present case it is of no use because we cannot afford to detect more than a single pair per image.

They credit Jost et al. for the idea:

The idea of using a single-photonsensitive camera was first explored by Jost et al., who showed that an intensified charge-coupled device (ICCD) has sufficient sensitivity to register the photons generated in SPDC. Their experiment brought to light the fact that it is not trivial to establish the inherent correlations of the twin photons generated in SPDC with such a camera.

But they also distinguish themselves from them in such terms:

However, we note that, in a related experiment on spatial correlations in downconversion, which was not at the single-photon level, Jost et al. did use both the multiplexing and integrating features of a camera by a priori assuming angular correlation between signal and idler photons and then focusing on their radial correlations. In such an approach, only intensity-fluctuation correlations (as opposed to photon correlations) can be studied; it therefore differs fundamentally from the method described here.

It is a bit confusing to imply that photon correlations are not intensity correlations. What they mean is that they correlate two single-photons, while Jost et al. correlated intensities above the single-photon level. Jost also assumed the azimuthal correlation a priori in order to look at radial correlations, which are there explicitly demonstrated.