Can a single photon source be set up in a way that we know the time when each photon is emitted?
It seems to me that it ought to be impossible to determine the time. If it were possible, then in principle one might be able to work out which slit a photon went through (in the double slit experiment) via a time-of-flight of experiment where the source is asymmetrically placed. But we know any attempt to do so should destroy the fringe pattern.
There is something as the coherence length that should make it impossible. The difference of path length must be lower than the coherence length, which in turn is linked to the time span of emission. In other words, even if the time of emission can be known, its uncertainty is too large for deciding which slit has been passed through, in a setup where interference remains possible.
Curiously, a single photon passes trough both slits.
This is what causes interference patterns when many individual photons are sent one at a time.
This statistical behavior doesn't depend on when photons are emitted.
Such an interesting question - as in radioactive decay, predicting the exact instant of individual emission is elusive, but a conclusive theoretical explanation as to why it is so is not entirely straightforward
@Chris. I agree that with radioactive decay you cannot know the time of an individual decay event as it is spontaneous. Similarly for photons that are generated by spontaneous emission, you cannot know the the time of each emission event.
So my question really boils down to these two things:
a) Are single photon sources always by spontaneous emission only, or can they stimulated in a timed way?
b) After a single photon leaves its source is there some kind of weak measurement that can be made to record the time it passes by?
....if the answers to either are "yes", it could be interesting as it could be a trick to violate what we know about the the double-slit experiment. But at the end of the day the trick might not work as uncertainties in the measurements will probably swamp everything. But I thought it was interesting to at least think about it :-)
One of the issues Derek is that we would have to more fully understand how 'spontaneousness' works here:
is it related to some resonance trigger (which we would have to understand further), is it related to Heisenberg's uncertainty playing a role within the trigger mechanism, do virtual particles play a role, etc.: To understand point a) we must better understand what spontaneity really is, and hence how it may differentiate from other, non-spontaneous event triggers.
To enable emission, the resonant quantum of energy must be released after it's been absorbed (and an electron has shot up to a higher orbit) - how to trigger that release at a given point in time does not seem at all trivial ....It might be , or more likely not, feasible
As for b) - any measurement you'd undertake here, however 'weak', would still always interfere with the photon, so it seems that the answer to b) has to definitely be no....
Correct me if I am wrong but doesn't this ( i.e. determining the time of each emission event) violate the Heisenberg Uncertainty Principle in Quantum Mechanics?
It really would depend on the actual emission mechanism Issam, it's not quite as straightforward as it looks.
I have a vague suspicion that the instant of individual photon (or radioactive) emission is triggered in part by the unpredictable effect of local virtual particles (arising from the quantum vacuum "foam"). This could be quite interesting because we do not know the statistics of the distribution of attributes of virtual particles (distribution of virtual mass, of time span of existence ...), and conceivably there could be a way to infer such statistics indirectly from their effect, e.g. from the half-life of radioactive elements and other decay rates , if a credible mechanism were found.
Virtual 'quantum foam' particles lead to a slew of quite measurable effects (such as the tunnel effect, or the Casimir effect, for instance), and I wouldn't be surprised if they were involved in the emission triggering mechanism. If such were the case, then the macroscopic statistical laws of photon emission and radioactive decay would indeed be much like what we experience.
Subject for a thesis,perhaps.
If a and b are true, we have a time of emission with an uncertainty dt. The photon must hit the screen with a time difference smaller than dt between the two paths in order to interfere with itself. Then we must have an uncertainy on the time of flight smaller than dt to be able to know which slit, which is impossible.
That reasoning is equivalent to the one with the coherence length, my previous answer. It isn't an issue of Heisenberg uncertainty or technical feasibility, only that QM is consistent.
Since lasers can be made from single quantum dots, I could imagine that a stimulated single photon emitter is a possibility.
As far as I understand it, the photon emitted by stimulation inherits the propertues of the stimulating photon. So you know the time of emission if you know the time of stimulation. the better known the time of stimulation, the sharper was the corresponding light wave packet. So you could have taken the original packet right away. therefore i don't think you gain anything here.
There is however an interesting alternative, maybe. I do not recall the source, I believe it's from the German Physical Society journal quite a few years ago (probably reporting on this experiment shortly after it appeared in PRL, Science or nature or so).
There it was shown, that light scattering off an atom can be used to monitor the absorption of light of this same atom (if light scattering is different in the two states). therefore one might be able to capture that moment, when the atom emits as the onset or stopping moment of light scattering. How good/fast this can be achieved - I don't know.
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