Nugatory said:
We know that we’re getting single photons one by one when the dots indicating that a photon has landed on the screen appear one at a time, or our array of photomultiplier tubes triggers one at a time, or the equivalent for whatever other equipment we’re using.
Yes, but note that this is not necessarily the same as...
Nugatory said:
Or in most experiments we know up front that we’ll be getting photons one at a time because we’ve included a single-photon source in our experimental setup. Google will tell you a lot about how these work.
Actually this isn't true for "most" experiments--certainly not for most double slit experiments. Single photon sources--sources that emit Fock states--are hard to set up and control.
As far as the photon impacts are concerned, although for, e.g., a double slit experiment the interference pattern on the screen will be the same for different kinds of photon sources, other things will not be. For example, if the photon source is a laser, or even an ordinary incandescent bulb, the timing of the arrivals of the individual photon impacts on the screen will be random (in more technical language, it will follow a Poisson distribution).
But if the photon source emits Fock states, the individual impacts will occur with the same time interval (to a good approximation) between each, i.e., the timing will
not be random. (This is called "antibunching" in the literature.)
There are still other kinds of sources that can produce the opposite effect--the impacts tend to occur in clumps (called "bunching" in the literature), i.e., when one impact occurs, the probability of another one in a very short time is increased (where it is decreased in antibunching, and doesn't change at all for a Poisson distribution).