# Double silt experiment with one circular polarizer in front of only one slit in the which-way perspective?

If one puts in front of a double slit two quarter-wave circular polarizers (QWP) in front of each slit, say one with 45° and the other with -45° orientation (fast and slow axis - i.e. clock- and anti-clockwise circular polarization) and shines linear polarized light on the slits, one does not get the typical interference pattern but the Gaussian-shaped diffraction pattern. This is the result of the overlap of the fringe- and anti-fringe patterns which, summed up, furnish the typical bell-shaped figure (these result from the two QWP induced pi-phase shift which causes the interference pattern with the central peak to be shifted left and right, respectively, with maxima overlapping minima and vice-versa). One can see this also from the perspective of the which-way question in quantum mechanics which states that by placing the two QWP in front of the slits we have 'marked' the photons and we could recover the which-way information which leads to the loss of the interference pattern. However, what happens if one places only one QWP in front of only one slit? As I understand it, the interference pattern would reappear as only one fringe or anti-fringe (right? Well, maybe not... this is part of my question). I'm in doubt, because if one would analyze this in the which-way perspective photons are still 'labeled', that is, photons going through the slit without the QWP would be linearly polarized, those going through the slit with the QWP are circularly polarized and one could in principle recover the which way information, i.e. one expects still only the diffraction without interference pattern. So, a contradiction arises that hints possibly at a mistake or misunderstanding from my side, but can't find out where it is. Can anyone help?

• How do you recover which-way information? The circularly polarized and linearly polarized states are not orthogonal, so you can't know exactly which way each photon went. And the pattern on screen will be a blurred double-slit pattern (a mixture of double- and single-slit patterns), since circular polarization can be thought of as a superposition of two orthogonal linear polarizations. Jan 16 '19 at 14:26
• Hmmm... I feel you might be right but I'm still not getting it. Say the incoming light front has vertical polarization. In front of the detector screen one places a filter for horizontal polarization. So no photon coming from the slit with light having vertical pol. can get through while if you see a photon getting through it can be only that coming from the slit with the QWP. So, this allows for which-way tracking.... not?
– Mark
Jan 16 '19 at 18:04