Well, since we cannot know which of the two signal photons we are measuring, we should indeed sum the amplitudes, and do observe interference. However, consider now a case where we block the path of the first idler photon (). Remarkably, even though signal photons can still originate from either the first or the second crystal, the fringes will disappear!

This may again be explained in terms of distinguishability. In Feynman’s words [3]:

If you cannot distinguish the final states even in principle, then the probability amplitudes must be summed.

Further examination of our system shows that blocking the first idler photon does affect the distinguishability between the two signal photons. If the signal photon is accompanied by an idler photon at the second detector (D2) then we know that it originates from the second crystal. If we don’t measure an idler photon – we know that it has been blocked, and that the signal photon originates from the first crystal. Thus, blocking the first idler photon reduces the indistinguishability between the two signal photons.

This is quite remarkable. Even when both processes have a low flux, and statistically, in no point in time the first idler and the second signal photon co-exist, the mere theoretical possibility of measuring the idler photon from the first crystal affects the coherence properties of the signal photon generated in the second crystal. For this reason, we say that the idler photon induces the coherence of the process.

In 2014, this effect has been utilized in the group of Nobel prize winner Anton Zeilinger, in the context of imaging [4]. Consider that we block only part of the path of this idler photon and swap the single photon detector with a sensitive camera. The area on the camera corresponding to the blocked area will show no interference, while the other area will show interference.

Measuring intensity that depends on the transmittance of an object is of course exactly what we want to do in imaging! Notice however the puzzling fact: the light measured by the camera never passed through the object, and the light hitting the object never reaches the camera!

A second modality for using induced coherence for imaging is for phase imaging: the phase accumulated by the idler photon is simply transferred to the signal photon. Such a modality provides interesting configurations such as where the light hitting the object is at a wavelength not detectable by the used camera. Alternatively, it also works when the object is completely transparent or even completely opaque in the wavelength detected by the camera.  

While this imaging technique is no doubt intriguing, providing materials for many new experiments conducted to this day [5], the exact quantum nature of the method has been debated. Indeed, in [6] it has shown that virtually all the features of the experiment can be realized in a quantum-mimetic fashion using classical light. The discussion has since continued, for example in [7] and [8].

In various undetected photon experiments different nonlinear crystals have been used, such as BBO or PPKTP, but in principle almost any nonlinear process could produce similar results [4]. If you want to join the discussion, get your own crystals at Raicol, where we provide the best world class nonlinear crystals and find your own novel imaging modality!