I remember way back , when proton decay was considered seriously ,
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron.The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. There is currently no experimental evidence that proton decay occurs.
The time frame is similar to the building of the first laser which was an exciting development bringing theory into practice:
The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow.
I was suddenly struck by thinking of the whole world sitting on a population inverted quantum state.
Here is a table of the possible decay modes:
What if a single proton decay started the stimulated emission process? A charged meson lives long enough to meet other protons .
At the time, discussing with a theoretician, I was satisfied that the small value of the Heisenberg constant saves us from sitting on a bomb :). ( or being the proof that proton does not decay) .
Searching I found this article:
The feasibility of obtaining stimulated emission of both zero and finite mass particles from nuclei is considered, and the limitations imposed on the relevant nuclear parameters determined.
Note the date , 1974, close to the peak interest on the lasing process at the time. Unfortunately one needs a library or to pay for it in order to read the details.
You ask:
Could it possibly work for composite bosons like mesons and He-4? Which elementary bosons other than photons could undergo stimulated emission?
"Undergo" is the wrong verb. "induce" is what you mean. It is the states with the inverted population that emit/undergo-stimulated-emission.