Timeline for Can all quantum superpositions be realized experimentally?
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| Aug 20, 2012 at 5:46 | comment | added | Luboš Motl | Yes, you can definitely construct holes that act as filters. A hole always is a filter, after all. It corresponds to a projection operator that only keeps the particle if its position belongs to a set, the hole. By accelerating the particle or doing something else with it along the path, the position information may be converted to another quantum number such as the momentum. If the initial state of the particle is the same (independent of the history/slit) and the final state is the same up to the final position along the would-be interference pattern, there is always interference. | |
| Aug 19, 2012 at 21:49 | comment | added | Revo | Sorry, but I do not understand what you mean by "arm" let alone "the kinetic energy is ready", "accelerated", and "the arms length" to control the relative phases. Could you please elaborate on that mechanism. Are you saying that we have 2 holes, they act like filters, one will let only particles in the quantum state 1 to pass, and the other will allow only particles in the quantum state 5 to pass, then we let them interfere then collect them in a box? (I guess that would destroy the interference pattern so seems my understanding is wrong) | |
| Aug 18, 2012 at 20:01 | comment | added | Luboš Motl | Let me mention that this technical description sounds very different than a quantum computer or others and it shouldn't be surprising. Your task "prepare a physical system in a particular quantum state" is the quantum counterpart of "prepare a classical system in a particular state". This is an extremely universal task that may mean anything - cook a soup or deliver a rover to Mars. All these things are states of a physical system, even classically. The procedures to achieve them of course depend on the physical system but with enough tools and interactions, it can always be done in principle. | |
| Aug 18, 2012 at 19:58 | comment | added | Luboš Motl | OK, just shoot the particle into the box using a double-slit-like gadget where the kinetic energy is ready for the first level in the first arm, and accelerated to the 5th level in the second arm. Let the electrons in the two arms interfere before they're trapped in the box. The relative size of the slits will determine the ratio of the normalizations of the two amplitudes, fine adjustments of the arms' length will adjust the relative phase. If I can't shoot the particles inside, e.g. because you want the particle to be inside the box, you would have to tell me what I can do to manipulate it. | |
| Aug 18, 2012 at 19:53 | comment | added | Revo | But this does not answer how to superimpose experimentally 2 eigenstates or more of the particle in a box Hamiltonian. | |
| Aug 18, 2012 at 18:48 | history | answered | Luboš Motl | CC BY-SA 3.0 |