On the early-time behavior of quantum subharmonic generation

TL;DR

This paper explains the early-time behavior of quantum subharmonic generation, revealing that nonlinearities similar to those in positronium Bose-Einstein condensates are common in various coupled quantum oscillator systems.

Contribution

It introduces a quantum oscillator model to explain the nonlinear growth rate observed in positronium BEC, showing such nonlinearities are widespread in coupled quantum systems.

Findings

Growth rate proportional to square root of density

Nonlinearities are common in coupled quantum oscillators

Model explains early-time quantum subharmonic behavior

Abstract

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.