# "Asking photons where they have been" - Danan et al

This paper https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.111.240402 was discussed briefly in another thread on Klyshko photons. I have a couple of questions to anyone who has studied the work.

The authors themselves note that "...even Maxwell’s equations for the classical electromagnetic field should explain the observed phenomena. Indeed, the Two State Vector Formalism adds no new predictions beyond standard quantum mechanics". Yet they describe some aspects of the experiment as "surprising".

It's easy to explain the important qualitative features of all the experimental setups by applying a bit of ray tracing, some approximate "integration by eye" and some arithmetic. Based on this, my questions are:

[1] The same ray tracing that predicts the experimental results, tells you that photons are passing through the inner interferometer all the time. They are interacting with all the mirrors all the time. Yet the authors say, "Some of [the photons] have been inside the nested interferometer (otherwise they could not have known thefrequencies fA, fB), but they never entered and never left the nested interferometer". This is not very clear.

[2] They say,
"Another surprising feature of the power spectrum of Fig. 2(b) is the presence of peaks at fA and fB and the absence of peaks at fE and fF. The photons passing through the inner interferometer have to be reflected off the mirrors E and F and thus they are expected to yield even higher peaks at frequencies fE and fF".
The ray tracing exercise explains this in a non-surprising way, without implying that the photons do not interact with E and F. Why do the authors conclude that the phtons interact with A and B but not with E and F?

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.Scott
Homework Helper
[1] The same ray tracing that predicts the experimental results, tells you that photons are passing through the inner interferometer all the time. They are interacting with all the mirrors all the time. Yet the authors say, "Some of [the photons] have been inside the nested interferometer (otherwise they could not have known thefrequencies fA, fB), but they never entered and never left the nested interferometer". This is not very clear.
[2] They say,
The ray tracing exercise explains this in a non-surprising way, without implying that the photons do not interact with E and F. Why do the authors conclude that the photons interact with A and B but not with E and F?
They are describing things from the non-QM "intuitive" point of view. In other words, they are saying that on the face of it, you should be able to tell which mirrors the photons are reflecting from based on the frequency of the jitter that they are tagged with. So if your FFT shows a jitter from A and B, but not E and F, then the prima facie (non-QM) interpretation would be that some photons that reached the detector did so by following a path the took them to A and B but not E or F.

Of course, there is no such path. And that is a big part of their point. You can't explain this without QM. You can't explain the results by presuming that photons follow a path or an independent mix of paths from the light source to the detector.

you should be able to tell which mirrors the photons are reflecting from based on the frequency of the jitter that they are tagged with
This is the assumption that they are applying all the time, but is it true? IMHO, not always! -- Not in Fig. 2b and 2c, in any case.

Something that is implied (but not clearly stated) in the paper is that the quad detector is feeding a differential amplifier that gives you a difference signal between the upper and lower sectors of the detector. In fact, I emailed Danan to confirm this, and I am waiting for a reply. But usually, that is how one would use this kind of detector to measure the vertical beam displacement.

Assuming that there is such a differential amplifier, you can't assume that zero output signal equals zero interaction with the mirror. You can't even assume that zero output signal implies no light reaching the detector. Keeping this in mind, we can easily explain why E and F alone can't modulate the final output in Fig. 2c. There is one ray that goes via E --> A --> F --> Detector and another that goes via E --> B --> F --> detector. These two rays (or gaussian profiles, to be more precise) overlap the two halves of the detector. In Fig 2c, the two profiles coincide exactly and their E fields (classically speaking) cancel out -- hence no photocurrent. Any movement of E or F will cause both the beams to move together so they will continue to cancel out -- so, again, no potocurrent! On the other hand, a movement of A will affect only its beam and likewise for B. The upper and lower parts of the detector will each receive a resultant E field that fluctuates according to the relative movement between the two beams A and B. This means that there will be some photocurrent signal from each part of the detector with frequency A and/or B, BUT the difference amplifier will cancel these signals out.

But in figure 2b, we have a large E field via mirror C (call it ##E_C##) plus the fields ##E_A## and ##E_B## which don't cancel exactly when A and B rotate. Let's look at the integrated signal due to the periodic misalignment between A and B, and let's call it ##E_{{\Delta}AB}## The total E field varies between ##E_C+E_{{\Delta}AB}## and ##E_C-E_{{\Delta}AB}##. The actual photocurrents will no longer cancel out at the detector, which explains Fig. 2b.

To sum up, light is passing through E and F all the time, only sometimes the contributions of these mirrors is cancelled out by the specific process at the detector and the difference amplifier.

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