Quantum pinhole camera

Question

Sorry this question may be silly as posed by a non-physicist. But, here goes.

In an attempt to conjure up a device that could image extra-solar planets, one faces the daunting task of trying image an object that is separated from a much brighter source (the parent star) by an extremely small angular distance. Airy disks, diffraction related to the wave nature of light spoils the any chance at imaging except in the rare instances of distantly orbiting Jupiter sized planets around dim stars.

But, what about utilizing the quantum nature of light? Picture a long thin chamber with special pinhole at one end which only allows one photon to enter the chamber at a time. I'm not even sure if such a "pinhole" is technologically feasible. However, supposing that this can be done, the other end would have a dense array tiny detectors. The chamber itself would be cooled to near 0, to reduce black body radiation from the side walls of the chamber to avoid contaminating light. The chamber would be made from a special material to reduce the scattering of photons entering the chamber. One could then use signals from the detectors at the other end of the chamber to deduce the angle at which photons enter the chamber, thus distinguishing between photons originating from the planet versus the star. Over a period of time of seconds / minutes perhaps, one could then reconstruct an image (even a accurately positioned dot would be good enough to observe its orbital motions) of the planet separate from the star.

There might be some basic problems with this concept. First, pinhole itself. Knowing the exact position of this "pinhole" might lead to uncertainty in momentum (including incident angle) of the photon entering through it. However, conversely, making a detection at the other end (assuming one could measure the position of the detection event on the opposite end precisely enough) does constrain the incident angle of the entering photon knowing that it could only have entered through one point in the chamber.

Secondly, there would be real issues with scattering within the chamber itself.

Any thoughts?

Answer 1

Simple answer: you cannot defeat the "classical" resolution limits with the one photon at a time method - nor with any other "quantum"-grounded method.

This is because the propagation equations of a light field in a one photon state are Maxwell's equations: you would calculate the probability of photon registration at your detector array from the appropriate solution of Maxwell's equations with the total energy in all space normalized to unity. I say more about the use of the Maxwell equations to describe one-photon light states in this answer here and here in those they link to.

You may be a little confused by recent discussions of optical superresolution and sensationalist claims that techniques such as STED "overcome the classical resolution limits". They do no such thing. They make use of other information together with optical measurement to locate a source even though the optics is only resolving to within the Abbe diffraction limit. For example, STED involves source preparation, whereby an excited fluorescent medium is selectively relaxed by a pulsed probe field which has a "doughnut" shapen waist region at the focus. When the fluorescence measurement is made after the probe pulse, one can use the a priori knowledge that the fluorescence must have come from the "hole" region in the doughnut field to infer the position of the fluorescent source more accurately than the diffraction limit alone.

Whilst observing stars, one has no opportunity to prepare the sources in any way that would allow superresolution.