Towards the end of the following video https://www.youtube.com/watch?v=GzbKb59my3U the double slit experiment is executed with 'single' photons and it is shown how the interference pattern emerges as the aggregation of registrations of single photons behind the slit.
How slow can this experiment be done and still show the interference pattern?
In other words: at what interval between photons reaching the detector will the interference pattern not be visible any more in the detection data? us? ns? seconds? years?
Is this effect dependent on the interval at all? If so how?
Answer
Fundamentally, you can slow down double-slit experiments as much as you like but a version of the Heisenberg principle will not allow you to put definite "gaps" between the detection events or to be sure to produce a photon on demand, at the right frequency etc. It is commonly stated that the particle must be interacting with itself in a double slit experiment, but when you take a look exactly at these uncertainties of the sparseness of particles in the beam along with the fact that there is no clear picture of the single-particle interaction, you have to take the textbook story about "particle self-interaction" with a grain of salt.
However, as technology progresses we actually have working single-photon sources which are commonly used in both science (quantum optics) and even industry (development of imaging devices).
As mentioned, these sources cannot surpass a certain amount of indeterminism. The quantum picture of a continuous beam of photons as a stationary wave-function is only replaced by a picture of separate gaussian-like pulses in the wave function into which a single photon might or might not squeeze in. But you might actually squeeze two photons into the pulse. Or three, or none. The design of a single-photon device is such that the probability of such events is minimized but it is there and the minimization comes at cost of another uncertainty in the produced photon. I.e., when you get down to it, all the quantum weirdness stays in it's full extent even for single-photon devices.
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