Tuesday 1 December 2015

optics - Spatial wave-function of a single photon and its measurement


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:



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.




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