Light Propagation and Paired Superradiance in Coherent Medium

Abstract

The problem of light propagation of frequency corresponding to half of the energy difference between a metastable excited state and the ground state of atoms is examined, and solved for coherent medium by analytic means. We demonstrate that the non-linear system of Maxwell-Bloch equation for the effective model of the $\Lambda-$type three levels is integrable in the mathematical sense. Analytic solutions thus obtained describe pulse splitting accompanied by compression, indicating a kind of non-linear instability of propagating pulses. The instability is eventually terminated by coherent two photon emission (called paired superradiance or PSR in short). These results are displayed by numerical outputs for visual understanding, as well. It is further shown that the integrable system allows a new class of soliton solutions. Solitons, implying the phenomenon of seff-induced transparancy at non-resonant frequencies, are stable against PSR. One of our goals of the present work is construction of a calculable theoretical framework for PSR rates associated with a trigger pulse propagation, which is achieved by combining analytic results with perturbative methods. PSR photon spectrum and its rate $\propto$(target number density)$^2$, along with their time structure, are clarified this way. These results may open a new path for interesting technological applications such as quantum entanglement and for solving the remaining problems of the still mysterious neutrino. Some basic strategy for realistic experiments of PSR detection and soliton production is also outlined.