Entangled photon apparatus for the undergraduate laboratory (2002)
arxiv.org
arxiv.org
Being more specific, if I have a pair of entangled photons, does their interfering constructively, in the classical sense, have anything to do with the probability that a photon would be detected there?
Since we are talking about fields, both classical and quantum are subject to it.
In QED, the absorption of a photon during detection mean is due to the coupling between electric field and electron field.
This coupling involve the field value (the term ieAmu) and not the square of the field value. Therefore the interference classical will also happen in the quantum case.
When coupling photons to electrons you have to sum the influence (their phase) of all photons before computing the interaction with the electron.
With Feynman diagrams, you could order the events in time, have the first photon push the electron forward a little and the second photon backward a little, after a tons of integrals over space and frequencies you will notice that the effects should cancel. What matters is that when the dust is settled, the various conserved quantities like momentum and energy are conserved. If you push your model further you can investigate the various absorption times of the various photons, whether the detection of what you define as an entangled pair of photons usually fall in the same coincidence time-window.
Question is, for photons not random, but entangled, could they be persuaded to drop their energy quanta more selectively?
You can interfere a photon with its entangled photon. You can interfere it with itself too. As soon as your first photon get absorbed, in your calculations about the second photon you incorporate the new information you got about the first, and you update your probability distribution accordingly (but that's not a physical process it's just your way of computing the probability).
When the first photon is absorbed the second is not necessarily so and he can go its merry way. (If you use the information you gain from the observation of the first photon about its polarization, and you have set-up your experiment so that you have time to orient a polarizer in the right orientation so that your photon can pass, you can catch the second photon 100% of the time).
There have been tons of experiments, where you entangle the photons n-way, split them multiple times, and interfere them in various ways.
Feynman propagator conserve various quantities allows you to evolve your probability distributions forward and backward in time. When you compute the conditional probabilities that correspond to your observations, you can shift them all back to the same instant where the entangled pair was produced.
You can't expect to change conserved quantities, because they are continuously conserved. For quantities that are not subject to specific conservation law like for example the time of detection of the photon, you can compute correlations, but there are also subject to conservation of information.
You could also theoretically imagine experiments where you entangle photons and have them interact with entangled pairs of electrons. But it's more for the intellectual pleasure of trying to do complex calculations correctly.
Personal unorthodox conviction : It's not the way the universe does the computation. The universe has its (finite) configuration it is in which is continuously (and locally) evolved through time, but which as an observer inside the universe you can't have access to (think of it like the seed of a random number generator). It doesn't need the results of your experiments to evolve through time. The way you can compute the same way the universe does is through Monte-Carlo simulations of the joint probability, but from inside the universe you have to generate a lot of (possibly infinite) candidate trajectories (aka possible universes) and do the sum (or filter to match the observation to the universe you are in).
I 3D-printed a lot of the optical hardware, re-purposed older electronics that we had in storage, and the photon detectors have significantly dropped in price. I think all told I got it together for about 8000 USD.
The linked paper by Dehlinger and Mitchell is one of the most important papers in conceptually bringing quantum entanglement experiments to nearly any undergraduate physics lab. Mark Beck applied their ideas and nearly single-handedly taught all of us how to actually perform the experiments. (I had the privilege of taking one of his workshops.)