Analytical and numerical studies of periodic superradiance

TL;DR

This paper presents a theoretical model for periodic superradiance in Er:YSO crystals, deriving equations that explain the phenomenon's characteristics and exploring conditions for its occurrence.

Contribution

The study develops a simplified two-variable model capturing the core features of periodic superradiance and analyzes parameter conditions for its realization.

Findings

The model reproduces periodic superradiance behavior.

Actual experimental parameters are outside the ideal parameter region.

Variable field decay rate can explain observed periodic superradiance.

Abstract

We conduct a theoretical study to understand the periodic superradiance observed in an Er:YSO crystal. First, we construct a model based on the Maxwell-Bloch equations for a reduced level system, a pair of superradiance states and a population reservoir state. Analysis of the eigenvalues of the linearized differential equations shows that periodic superradiance can be realized only for certain parameters. We also derive two-variable equations consisting of the coherence and population difference between the two superradiance states, which contain the essential feature of the periodic superradiance. The two-variable equations clarify a mathematical structure of this periodic phenomenon and give analytical forms of the period, pulse duration, and number of emitted photons. Our model successfully reproduces the periodic behavior, but the actual experimental parameters are found to be outside the parameter region for the periodic superradiance. This result implies that some other mechanism(s) is required. As one example, assuming that the field decay rate varies with the electric field, the periodic superradiance can be reproduced even under the actual experimental condition.