Phonon Echo from Multi-Level Systems and Many-Body Interactions in Low-Temperature Glasses

TL;DR

This paper extends the two-level-system model to multi-level systems in low-temperature glasses, demonstrating that phonon echoes persist with many-body interactions, and analyzing how thermal fluctuations cause dephasing and echo decay.

Contribution

It introduces a multi-level-system framework with many-body interactions to explain phonon echoes in glasses, advancing beyond the traditional two-level-system model.

Findings

Phonon echoes persist in multi-level systems with many-body interactions.

Many-body interactions enhance the echo signal through nonlinear eigen-energies.

Thermal fluctuations lead to dephasing and decay of the echo amplitude.

Abstract

At low temperatures, glasses exhibit distinctive properties compared to crystalline solids. A notable example is the phonon echo, a phenomenon that motivated the two-level-system (TLS) model. This model has successfully explained many universal anomalies in glasses. Here, we extend the TLS framework to a multi-level system and show that phonon echoes persist when nonlinear energy structures and disorder are included. By incorporating virtual phonon exchange, we introduce many-body interactions between these multi-level systems, leading to nonlinear eigen-energies that enhance the echo signal. Meanwhile, finite-temperature thermal fluctuations cause dephasing, resulting in a decay of echo amplitude over time. The analytical and numerical results are consistent across semi-classical and quantum regimes. Our work validates the multi-level-system model and underscores the role of many-body interactions in low-temperature glassy dynamics.