Sampling methods to describe superradiance in large ensembles of quantum emitters

TL;DR

This paper compares and improves two sampling methods for calculating photon correlations in large quantum emitter ensembles, enabling better analysis of superradiance phenomena.

Contribution

It introduces and benchmarks two approximate sampling methods with offset corrections for large emitter arrays, expanding the tools for studying superradiance.

Findings

The methods provide bounds for $g^{(2)}(t,0)$ in large ensembles.

Offset corrections significantly improve prediction accuracy.

The optimal method depends on the number of emitters.

Abstract

Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function $g^{(2)}(t,\tau)$, which describes the photon statistics of emitted radiation. However, the critical task of determining $g^{(2)}(t,\tau)$ becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for $g^{(2)}(t,0)$. We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.