Random Nonlinear Infinite-Level-System Model for Amorphous Solid Phonon Echo and Saturation Phenomena

TL;DR

This paper generalizes the tunneling-two-level-system model to an infinite-level-system with randomness and nonlinearity, demonstrating phonon echo as stimulated emission and explaining saturation phenomena in amorphous solids.

Contribution

It introduces a novel infinite-level-system model with randomness and nonlinearity, providing theoretical proofs for phonon echo as stimulated emission and the conditions for saturation.

Findings

Phonon echo is a stimulated emission process.

Quantum nonlinearity enables saturation phenomena.

Randomness and nonlinearity are essential for echo and saturation.

Abstract

The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness and nonlinearity, we prove that phonon echo is a stimulated emission process. The classical infinite-level-system (taking $\hbar\to 0$ limit) cannot find saturation effect, while quantum infinite-level-system can find it with certain nonlinearity assumed. We also prove that without randomness or nonlinearity neither phonon echo nor saturation exists in arbitrary infinite-level-system.