Hello all. I am trying to determine what is the effect of having photons that are distinguishable undergoing a quantum interference process. To do that, I try to generalize the Hong-Ou-Mandel effect, and try to determine what are the terms that appear as a function of the product of the creation...
Hi Simon, I guess I did sort it out, thanks to the help of the geniuses in here :-) I think I succeeded to work out the math for the HOM effect in Directional Couplers (DCs) as well. DCs are a way to integrate BSs in photonic chips and the main difference is a phase shift of 90 degrees between...
I just found out another thread called "Photon position again", where the subject of photons' observables is discussed. Or, rather, the lack of observables for photons positions. That may explain partly my confusion, or, at least, tells me I am not the only one confused by this :-)
Well, I am trying to figure out what is the observable matrix for the BS. First I thought it would be the transformation matrix:
|1 1|
|1 -1|
But then I realized it doesn´t have eigen-states and corresponding eigen-values. Or, at least, I can not find them :-)
I also don´t understand why the...
Hello vanhess71, thank you for the feedback! What is the minimal statistical interpretation? Concerning observables, do you think it would be possible to say that, in the case of transformation of a photon by a 50:50 BS, the observable hermitian operator would take the form of a sigma-3 Pauli...
Thank you so much Simon! Before I saw your math I had worked out some equations for the Hong-Ou-Mandel Effect. I based myself mainly on Wikipedia, so I am not sure if it is 100% correct, though the general idea seems to agree with your equations. The equations and set-up are here (I haven´t...
Hello Dr.! Thank you for your feedback. Yes, no doubt about that, the perfect timing of input photons is definately a big issue. Taking that in consideration parametric down conversion really seems simpler. There are some proposals that use semiconductors to generate entangled photon pairs with...
Hello, thank you very much! Ok, I think I understood that :-) In your opinion would be possible to mesure simmultaneously the presence and phase of output photons in that hypothetical setup I mentioned? Thanks again!
Hi Simon, thank you! I agree with you entirely, such a BS doesn´t exist. I am new to Quantum Photonics, so forgive my lack of understanding :-). I meant the proposal as a kind of thought experiment, but since came across a very interesting quantum effect related to quantum interference of photon...
Thank you for your reply. Actually there are some proposals to use semiconductors to generate entangled photon pairs that seem promissing (https://arxiv.org/abs/1702.08823). I am not familiar with the physical process involved but hope to understand it a little better after reviewing the...
Two photons arrive at a hypothetical 50:50 Beam-Splitter with no phase shift between reflected and transmitted modes. One enters the Left side and the other the Bottom side of the BS as shown in Fig.1 of the link below:
https://drive.google.com/open?id=0B5JsDLKoUSA5emk5Qk9nUHVIelE
Each photon...