Parametric Interaction of VLF and ELF Waves in the Ionosphere

In this Chapter we analyze a non-linear parametric interaction between Very Low Frequency (VLF) and Extremely Low Frequency (ELF) waves in the ionosphere. We demonstrate that nonlinear parametric coupling between quasi-electrostatic Lower Oblique Resonance (LOR) and ELF waves significantly contributes to the VLF electromagnetic whistler wave spectrum. Analytical and numerical results are compared with experimental data obtained during active space experiments and satellite data. These data clearly show that presence of VLF waves in the region of plasmasphere boundary layer, where there are no injected due to substorm/storm activity energetic electrons with energies of tens keV can strongly affect the radiation belt boundary.

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators

We analytically and numerically show that the Hillery-Zubairy’s entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.