A microwave tone at 7.684 GHz and power -130 dBm coherent with a cavity corresponds to about 3 intracavity photons. How can I get 3 photons from this power level at this frequency?
from the frequency and Planck's constant you can calculated the energy of 3 photons. From this energy and the power you can calculate the length of the cavity. (The given power traverses the cross-section of the cavity.)
Joerg Fricke is nearly right. The 3 photon tells you how much energy is stored in the cavity. Together with the power level that tells you the Q of the cavity, but you can't tell the length or area of the cavity from this, I think. Presumably the author knows the Q of the cavity so can tell the stored energy from the input power, and that is equivalent to 3 photons.
Oops, perhaps I misunderstood the scenario: If the cavity is illuminated by radiation of -130 dBm and contains 3 photons on average, then I completely agree with Malcolm White , of course.
My answer refers to a lossless cavity containing 3 photons (somehow injected in the past).
I'm not sure either Joerg Fricke but dBm I think has to refer to power, not energy. Power would have units of photons per second so there is something else that needs to be known to get the number of photons. Q links power with energy and frequency which I think fits the bill.
I've noticed that you usually know what you are talking about.
Many thanks for the compliment, Malcolm White , which I'm glad to hand back enhanced and wholeheartly.
And now I see where my assumptions went wrong: I thought indeed about photons per seconds passing an (imaginary) plane. But taking the reflected photons into account the sum total is 0, of course, (standing wave) so one would not talk of power.
The last straw I could cling to: The cavity forms an annular wave guide, with all photons propagating in the same direction. ;-)
Thank you both for helping me work through this. I got as far as E=3hf but then I could not relate it to power. Can you kindly elaborate on how Q ties power and energy?