Scaling of Superradiant Peak Emission in Spatially Extended Emitter Arrays

TL;DR

This paper derives scaling laws for superradiant peak emission in spatially extended quantum emitter arrays, revealing linear, superlinear, and quadratic scaling depending on array geometry and coupling, using cumulant expansion methods.

Contribution

It introduces general scaling laws for superradiant emission peak rates in extended emitter arrays, addressing computational challenges with a third-order cumulant expansion approach.

Findings

Linear scaling of peak emission in 1D free-space arrays

Superlinear but sub-quadratic scaling in 2D and 3D arrays

Quadratic scaling in waveguide-coupled emitter chains

Abstract

In quantum optics, superradiance is a phenomenon in which a system of $N$ fully excited quantum emitters radiate intense flashes of light during collective decay. However, computing its peak intensity exactly for many spatially separated emitters remains challenging due to the exponential growth of the underlying Hilbert space with system size $N$. Based on third-order cumulant expansion methods, we present general scaling laws for the expononent of the peak emission rate as a function of the emitter number in free-space emitter arrays and arrays coupled to one-dimensional waveguide reservoirs. We find, that for 1D chains in free-space the peak emission rate scales linearly with $N$, while for 2D and 3D arrays with finite emitter spacing it scales superlinearly but sub-quadratically. For emitter chains coupled to waveguide reservoirs we find that the peak emission rate scales quadratically with $N$.