The ZWM Study(Mandel 1991). What happens at the idler detector?

[al onestone]

In the ZWM study of early 1991, Mandel (U of Rochester) achieves "induced coherence withouyt induced emmission" between two optically pumped downconversion crystals (figure provided). The explaination of the experiment goes like this:

 

The pump beam goes to the 50/50 beamsplitter (BS) and then pumps one of two downconversion crystals (DC1 and DC2) which transform the photon into two photons (signal and idler) with each having roughly half the frequency/energy. The idler from DC1 is forced to transmit through the DC2 crystal so that it retains coherence between the output of the two crystals. The two signal outputs from DC1 and DC2 are combined at a detector D_s .

There are two types of interference here, first is the interference in the coincidence counter (CC). When one of the optical paths is varied there is interference as a function of the combined phases (φ_s + φ_i). The coincidence interference results from indistinguishability between the combined pathways from DC1 to D_s and D_i -or- from DC2 to D_s and D_i . We cannot tell which way the pump photon went after the beam splitter.

The second interference occurs at detector D_s and is a simple function of the phase. The interference that occurs at this detector is a lower order. It is simply the indistinguishability between the optical paths from the pump photon to detector D_s . If the detector has a count you cannot tell if it came from DC1 or DC2 depending on which path it took after the beam splitter.

The coincidence interference(4th order) requires that all four optical paths to the two detectors be identical (or at least differing by no more than a coherence length). The interference at D_s (2nd order) requires the two optical paths from BS to DC1 to D_s and from BS to DC2 to D_s be identical.

By placing the neutral density filter (NDF) between DC1 and DC2 in the idler path i₁ , the interference at detector D_s vanishes. Why? Because the paths to D_s from the pump are now distinguishable. How? If the pump photon goes to DC1 and downconverts then the signal will go to D_s but the idler will be attenuated by the filter and you will not get a coincidence count at D_i . If the pump photon goes to DC2 and downconverts then the signal will go to D_s and the idler will go to D_i and there will be a coincidence count. So the presence or non-presence of a coincidence count at D_i is the measurement which will determine whether the pump photon went to DC1 or DC2 to downconvert. So by inserting the NDF into the idler path, Mandel has eliminated the interference at detector D_s . And it is worth noting that the interference effect at D_s can only be negated by a distinguishability measurement which occurs at a second detector D_i which is spatially separated from D_s , and that these measurements don’t actually need to be made to negate the interference. Mandel notes that these measurements at D_i need only be in principle possible to negate the interference pattern. He got the same results without even making the distinguishing measurements. Absolutely Brilliant!

 

My question is, what is happening at detector D_i when there is no NDF placed in the idler path? Is there interference (2nd order) at this detector also? Mandel refferred to this detector as "superfluous" to the idler detector, so he gave no analysis of its counting rate. If there is interference at D_i then one should be able to negate this effect by placing a NDF in the signal path s₁ which could be done very close to the detector D_s. In this case we would be affecting what measurements are made at D_i by performing a change in the preparation at D_s?

 

Relevant papers of the study:

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).

L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).

[al onestone]

This does not work. The second paper clarifies the issue. The counting rate at D_i does not display interference because it is not a function of phase. For whatever reason, after the math only D_s displays interference.