Towards Microscopic Understanding of the Phonon Bottleneck

TL;DR

This paper investigates the phonon bottleneck in spin relaxation, revealing that traditional kinetic models are invalid due to narrow phonon distributions, and proposes a dynamical approach to better understand the phenomenon.

Contribution

It introduces a new dynamical model incorporating spin-phonon correlations to accurately describe the phonon bottleneck effect.

Findings

Identifies the failure of the Pauli master equation in narrow phonon distributions.

Develops a dynamical system capturing the phonon-bottleneck plateau and spectral gap.

Highlights limitations in modeling phonon lineshape accurately.

Abstract

The problem of the phonon bottleneck in the relaxation of two-level systems (spins) to a narrow group of resonant phonons via emission-absorption processes is investigated from the first principles. It is shown that the kinetic approach based on the Pauli master equation is invalid because of the narrow distribution of the phonons exchanging their energy with the spins. This results in a long-memory effect that can be best taken into account by introducing an additional dynamical variable corresponding to the nondiagonal matrix elements responsible for spin-phonon correlation. The resulting system of dynamical equations describes the phonon-bottleneck plateau in the spin excitation, as well as a gap in the spin-phonon spectrum for any finite concentration of spins. On the other hand, it does not accurately render the lineshape of emitted phonons and still needs improving.