  A few years ago Avetissian {\it et al.} \cite{Avetissian2014,Avetissian2015}
discovered that the exponential growth rate of the stimulated annihilation
photons from a singlet positronium Bose-Einstein condensate should be
proportional to the square root of the positronium number density, not to the
number density itself. In order to elucidate this surprising result obtained
via a field-theoretical analysis, we point out that the basic physics involved
is the same as that of resonant subharmonic transitions between two quantum
oscillators. Using this model, we show that nonlinearities of the type
discovered by Avetissian {\it et al.} are not unique to positronium and in fact
will be encountered in a wide range of systems that can be modeled as
nonlinearly coupled quantum oscillators.
