Manifestation of quantum chaos in second-harmonic generation

•Report of a solid evidence for the appearance of a Poisson-GOE transition, due to combination effect of the driving field and nonlinearity coupling.•Prediction of the steady-state regime for both weak enough nonlinearity and low intensities of the electric field.•Finding a critical point (ϵc,κc) for which the participation ratio and so the level of delocalization become maximized.

Second-harmonic generation as a frequency doubling process is ubiquitous in modern optical systems. The present study explores prospects of the stability region of second-harmonic generation in a medium coupled to a bosonic bath. We show that a stability-instability transition due to the combined action of driving field and nonlinearity coupling is seen. We report a reliable evidence confirming the appearance of the chaos in second-harmonic generation under suitable conditions. By tracing direct signatures of chaos in the quantum mechanics, adjacent-spectral-spacing-ratio (ASSR) distribution and participation ratio, we also find a critical point (ϵc,κc)=(2.8,1.1) for which a pronounced delocalized regime is seen. To verify the existence of chaotic behavior we also turn our attention on long-range correlation statistics.