We have carried out coincidence interference patterns for several values of the parameter a
For aFig. 2. While the singles show a nearly gaussian profile, the coincidences show interference fringes. The visibility and the wavevector of the coincidence fringes were obtained by a nonlinear curve fitting with the usual function for the double-slit interference. The wavevector for a0. It is associated to the single photon interference. Note that the absolute value of k0 depends on the geometry. In the analogy with a double-slit experiment, each crystal correspond to one slit. However, the light is not emitted in the direction that would correspond to a central(zero order) maximum. It is emitted in a direction corresponding to a higher order. This means that the associated wavelength is multiplied by a large integer, which is not important in this work. For this reason the wavevectors will be presented in arbitrary units. The procedure is repeated keeping detector A fixed and scanning detector B. The result shows a profile similar to that of Fig. 2, showing the symmetry between scans with one of the detectors fixed. These patterns can be interpreted as single photon wavepacket interference ones. This is a consequence of the fact that only signal or idler paths are changed, when only signal or idler detectors are moved individually.
For aFig. 3. The convention used establishes that the positive aFig. 3 is two times the one in Fig. 2. k+1(signal side) = k+1(idler side) = 2k0. This was predicted by Eq. 6 for aaFig. 3 can be interpreted as a two-photon wavepacket interference. We will address this point again in next section.
For a, detector A was displaced two times slower than detector B. The displacement is performed so that detectors get together to the position corresponding to the coincidence peak detection in previous measurements. With this procedure it is possible to take care for the symmetry of the interference curve. The results are shown in Fig. 4. In Fig. 4a the coincidence counts are plotted as a function of the detector A position and in Fig. 4b, the same coincidence counts are plotted as a function of the detector B position. This is necessary now, because the displacements are different, we do not have a common coordinate anymore, as in previous cases. The fitting of the curves lead to k+(signal side) = [ 3/2] k0, which corresponds to a and k+ (idler side) = 3 k0 which corresponds to ai = + 2 when the phase shift is written in terms of the idler coordinates. This is in agreement with Eq. 6.
For a, detector A is still displaced two times slower than detector B, but now the negative sign indicates that the sense of one of the displacements is changed. Detector A moves towards the pump beam while detector B move backwards the pump beam. The results are shown in Fig. 5. In Fig. 5a the coincidence counts are plotted as a function of the detector A position while in Fig. 5b they are plotted as a function of the detector B position. From the point of view of detector A a and the wavevector is k- (idler side) = k0. From the point of view of detector B as = - 2 and k- (signal side) = k0.