Nonlinear Regime of the Three Wave Interaction

The three-wave interaction describes energy-momentum transfer between three resonant waves in the quantum regime as well as acting as a finite-degree-of-freedom approximation of the classical three-wave interaction in certain circumstances. Using the quantum field theoretic quantization scheme, recently used to model the interaction on a quantum computer, we build on work describing the quantum three-wave instability near the classical fixed point to show how the finite-dimensional quantum three-wave interaction can capture both the classical orbit shape and its period. We also numerically compare the long-time quantum/classical correspondence far from the fixed point dynamics, where the systems have been shown to become harmonic.