Vibrational self-induced transparency and phonon squeezing

It is shown that the phenomenon of self-induced transparency can occur when a coherently excited propagating phonon mode has a frequency that is equal to the difference between the frequencies of two flat phonon branches. The nonlinear coupling is due to cubic anharmonicity. Using a quantum kinetic- type approach, the Maxwell-Bloch equations are derived for such systems. In cluding third-order correlations in this approach, the intrinsic damping of parametrically excited two-phonon oscillations is investigated, that lead to phonon squeezing. In addition, we analyze the resonant interaction of a coherently driven phonon mode with one flat branch of the phonon dispersion relation.