Axion, photon-pair mixing in models of axion dark matter

Abstract: A system of light axions comprising a classical axion field, one candidate for dark matter, has an instability that would rapidly mix in photon pairs in a coherent fashion if the system were initially seeded by some tiny amount of such mixing. We develop equations that contain the mixing and at the same time incorporate enough quantum mechanics to eliminate the need for seeds. Extending to many modes brings many interesting issues to the fore. For example, the argument of the inevitable logarithmic factor in the mixing time becomes reduced by many orders of magnitude; concerns concerning red-shifts are laid to rest, as are those related to lumpiness of the original axion state. We further see that even the fully developed states of the electromagnetic field are completely non-classical in our solutions.