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- On the biphoton wavelength

From Eq. 6 and experimental results presented in previous section, it is clear that the wavelength associated to the coincidence patterns can be continuously varied and that it can assume any value, even a fraction or a multiple of the single photon one. This fact can be explained by the phase entanglement between signal and idler photons. It also seems that it has no implications on the energy of the individual photons neither on the total energy of the biphotons. It is clear from all experiments utilizing twin photons from the parametric down-conversion, that the process behind all quantum effects is entanglement. The entanglement is a consequence of a process that we could call transfer of spectrum from the pump beam to the biphotons. A particular case of that is the transfer of angular spectrum described in Ref. [11] dealing with the transverse degrees of freedom of the field. In the experiment we present here, it is nice to be able to understand the main features in connection with entanglement and transfer of angular spectrum for a simple case utilizing a monomode approach. This is one of the virtues of the interferometer presented.

It is interesting however, to analyze some possible interpretations. When aaaalways (the probability is much bigger) emitted by the same crystal and never (the probability is much smaller) by different ones. This corresponds to having both photons passing through one of the slits and never one photon through each slit. For this reason, it is not necessary to change the pump laser beam profile. But the analogy is complete.

When a, for example, it is not possible to assign some physical meaning to the wavelength observed by one of the detectors anymore. For the same set of measurements, the wavevector is three times larger than the single photon one (corresponding to a wavelength three times smaller than the single photon one) from the point of view of the conjugated detector. This result shows that assigning a wavelength to something we call biphoton can be dangerous. The energy of each individual photon is not changed during the interference process, neither during the detection process, and the discussion about this apparent wavelength may turn into speculation. However, diffraction properties are actually changed and that may have consequences in imaging and other applications. Some possible applications can be envisaged. For example, the coincidence patterns could be used for measuring the refraction index for some material placed in the path of the beams. Differential measurements could be performed in a collinear configuration with both beams passing through the sample. We could also think of twin beams with crossed polarizations used for birefringence measurements. The interferometer is quite useful for fundamental research on the production, detection and manipulation of entangled states. Recently, it was used in our laboratory for producing position entangled states wich were coupled to polarization entanglement so that we were able to measure the plarization entanglement thorugh position interference [14]. Experiments currently in progress show that it is also suitable for studying quantum distilation, purification and decoherence.

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