Yes it depends on the frequency ( as a representation, f per unit time ) and the Planck length x the speed of light - not long , not long at all

I don't know if it is a well posed problem....

Stefano has good reasons to have doubts, and here is the answer.

The rigorous terminology in QM is not a "photon" in the sense of a particle being at some time at a certain position. QM speaks of wave-packets. Now, assume that we just opened the aperture of the source. If the source emits wave-packets of length L (more exactly of coherence-length L) the time at which we can obtain a detection is undetermined, the indetermination Δt = L/c. That is quivalent to saying that the detection may be obtained at any place in the wave-packet, i.e. the uncertainty in position is L.

Many thanks for the answers. Most of these seem to be from a purely theoretical perspective. However I was more curious about the practical side of single-photon emitters like quantum dots and other such sources. For example is there a way to detect the instant of emission by monitoring current fluctuations in the bias circuit of a single-photon source? Has anyone tried such a method or anything similar?

Another example would be the entanglement method where two entangled photons are sent in different directions with one of the entangled photons sent to a detector. The time of release of the other photon could then be known using the path length (limited by uncertainty in the detector) since they are both generated at the same instant. Does anyone have experience with this method and its accuracy?

Chris,

It won't help. The indetermination in the emisxion time of a down-conversion pair is of the same order of magnitude as the coherence time of a down-conversion photon.

You can't beat a law of QM with another law of QM.

@Sofia, Thanks for the answer, agree with this but maybe the question was misunderstood because I mentioned about path length. However this is not really needed. What I really need is the emission time of the second photon (the one what is not detected and allowed to go free). Even if the time of the down-conversion event cannot be predicted this is not really needed. With entangled photons, the detection of one of the photons also means the other photon is present at the same instant of time but what is the uncertainty in detection and the uncertainty between them.

To put it another way consider the following experiment:

Two entangled photons are separated and sent to separate detectors linked to a timer. Whichever detector fires first starts the timer. Firing the other detector stops the timer then sends the time data to a computer and also resets the timer, ready for another event.

Then the question becomes what will be the maximum reading on the timer after multiple events using our current state of the art detectors. (Will it be in ms, ns, ps, fs,...)

Thanks.

@Chris Deep,

I understand. This is, what we call, pair-coherence time. It was measured by Raymond Chiao. It is defined as the time-interval along which the down-conversion pair of photons interferes with itself. As far as I remember, the order of magnitude is the same as the coherence time of each one of the photons. Conceptually, it's has a totally different physical meaningwe don't speak of the idler intergering with the idler and the signal with the signal, but of the pair interfering with itself as a whole.

Please note that your requirement "maximum reading" is not a good requirement. You should better ask about the most probable reading, as neither the wave-packet of a photon has sharp boundaries, neither the statistics of pair-coherence intervals, obtained after repeating many times the experiment, would display a fixed limits of the reading you are interested in.

For measuring the pair-coherence time, Chiao did a simple experiment of 2-particle interference. I don't have the article under my eyes, it is a very old article. If it is urgent to you, tell me and I'll look for it.

Many thanks, this the type of thing I was looking for. If you have some further references or even some titles and author names that would be very helpful.

I think the paper you might be referring to is " Observation of a quantum eraser A revival of coherence in a two-photon interference "? It looks very interesting.

I have also found something very similar to the type of experiment I was thinking of been done back in the 1980s. However instead of my elaborate scheme they have used 4th order interference. This eliminates the path length problems. They have found the answer to be around 100fs experimentally using equipment from 1980s but theoretically predicted it should be around 1fs (1um) for down-converted UV light.

Reference below:

Article Measurement of Subpicosecond Time Intervals Between Two Phot...

This to me is quite a remarkable result as it means that the detection of one of the photons means that there are certain positions (in time and space) that the second photon can never exist (to within 100fs).