Timeline for What observable(s) does a mirror operate on?
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| Nov 9, 2019 at 19:15 | comment | added | A_P | Are you sure about that? In the setup you describe, it seems we only have one qubit (position) getting an unconditional shift. We'd need another qubit to act as a control. Or maybe I've just misunderstood you. In either case, I think I get it now. It still feels like there's something "special" (at least in our minds) about position to make people call only position phase shifters simply "phase shifters," but I'm at peace with it. | |
| Nov 9, 2019 at 19:00 | comment | added | glS | @A_P that's right, how you place it does matter, because if you introduce the same phase shift on all of the position modes, it's the same as doing nothing. I don't know if this will help, but if you think of a photon in a superposition of two different spatial modes, then a phase shifter in only one of the two modes is essentially a "controlled-shift operation", in the notation of quantum circuits, because it only applies a phase shift conditionally to the photon being in a specific position state. From this pov, it is a "more complex" operation than a polarisation waveplate | |
| Nov 9, 2019 at 18:51 | comment | added | A_P | Consider the device simply known as a "phase shifter" in quantum optics. Surely we can say that the relevant observable there is position, yes? It cannot introduce a phase shift w.r.t any other observable. Part of what's been hard about getting to that answer is that if we place it just right (so that a whole beam is incident), it's no longer a "phase shifter" at all (at least, w.r.t. that beam). In a sense, it's our choice of positioning that makes it a "position phase shifter," yet it still seems to be intrinsically a position phase shifter. | |
| Nov 9, 2019 at 18:39 | comment | added | glS | indeed, there is no "observable associated with a phase shift". A phase shift between two states can be introduced, roughly speaking, by any operation that treats those two states differently. Note that phase shifts introduced by different operations might be indistinguishable (for example a phase shift on a photon due to a mirror or due to a waveplate). The phase between two states is really a way to quantify how those two states will interfere with each other. Also, different physical devices operate on different degrees of freedoms in different ways, that is to be expected I would say | |
| Nov 9, 2019 at 18:35 | comment | added | A_P | Anyway, I think my confusion is mostly resolved. Thanks! I still have to digest your final paragraph. | |
| Nov 9, 2019 at 18:35 | comment | added | A_P | Thanks very much for the detailed answer! For the PBS, it still has to spatially separate the polarization components to let us operate on them separately, right? Here's another way of stating my initial confusion: to change a mirror's behavior (wrt position modes) you can simply move it, whereas for a waveplate you must modify it (e.g., thicken it). Similarly: a "position phase shifter" is commonly just called a "phase shifter," whereas a "polarization phase shifter" is not. I've asked physicists before which observable a "phase shifter" operates on, and they don't understand the question. | |
| Nov 9, 2019 at 12:50 | history | answered | glS | CC BY-SA 4.0 |