In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon:
- Measurement of the transverse spatial quantum state of light at the single-photon level. B.J. Smith et al. Opt. Lett. 30, 3365 (2005), arXiv:quant-ph/0507142
- Direct measurement of the quantum wavefunction. J.S. Lundeen et al. Nature 474, 188 (2011), arXiv:1112.3575
- Compressive Direct Measurement of the Quantum Wave Function. M. Mirhosseini, et al. Phys. Rev. Lett. 113, 090402 (2014), arXiv:1404.2680
- Hologram of a single photon. R. Chrapkiewicz et al. Nature Photon. 10, 576 (2016), arXiv:1509.02890
Most of them refer to a Iwo Bialynicki-Birula's paper "Photon wave function" [Prog. Opt. 36, 245 (1996), arXiv:quant-ph/0508202] when describe the measured object (or don't refer to anything). Having read these papers and some other literature discussion, as well as this forum (see links below), I still cannot really understand of what exactly was measured by the authors of the experimental papers and weather it makes sense to call that a "photon wavefunction", so I assume I am missing something important.
I wonder if
they've measured the electric field / amplitude of Maxwell mode with a single-photon in it (then what's so quantum about that, other than you have to do long counting)?
they've measured the spatial momentum quantum state, but by the means of Fourier optics transformed it into distribution over spatial points (they why to call it the way they do)
there is a reason to introduce a real quantum spatial wave-function of a single photon (than how it lines up with the absence of position operator for a photon and other problems discussed in the topics below?)
and I would greatly appreciate if someone can help.