On the Theory of Parametric Resonance in the Optical Region

O. S. Vasiutinskii, N. A. Dovator, R. A. Zhitnikov

Kihwan Kim, Heung‐Ryoul Noh, Wonho Jhe

L. Yu. Nad’kin, P. I. Khadzhi, K. D. Lyakhomskaya

The pump-probe method of studying of the optical properties of a semiconductor in the exciton region of a spectrum is considered theoretically taking into account the exciton–photon and elastic exciton–exciton interactions. It is shown that the concentration of excitons, and the susceptibility of the medium are mainly determined by the detuning from the exciton resonance and the magnitude of the pump field. The values of the parameters corresponding to the observed parametric resonance are obtained and the dynamic analysis of the found solutions is carried out.

Pavel A Apanasevich, V. A. Khodovoǐ

Alexander A. Zabolotskii

Roxane Thériault, George Zahariade

We study a system of two quadratically-coupled harmonic oscillators, prepared respectively in the ground state and in a coherent state. This toy model can describe for instance the dynamics of one mode of a quantum field evolving in a harmonically-oscillating classical background. In such situations, it is well-known that, depending on the background oscillation amplitude and coupling strength, the system may exhibit parametric resonance. Using the Feynman-Vernon influence functional, we analyze the interplay between parametric resonance and quantum entanglement by perturbatively computing the purity of the mixed state resulting from tracing over one of the oscillators. We find a runaway behavior of the quantum entanglement between the two oscillators, as well as a rapid breakdown of the validity of perturbation theory, in regions of parametric instability. This provides a quantitative confirmation of various statements in the literature and is highly relevant to questions pertaining to the validity of the semiclassical approximation in coupled quantum-classical systems.