Cooperative decay of an ensemble of atoms in a one-dimensional chain with a single excitation

TL;DR

This paper introduces a new expression for the cooperative decay rate in a one-dimensional atomic chain, elucidating superradiance and subradiance phenomena without complex eigenvalue calculations, and explores how decay rates scale with chain length.

Contribution

It provides a novel, simplified formula for cooperative decay rates in 1D atomic chains, connecting interference effects to the imaginary part of an effective Hamiltonian.

Findings

Subradiant decay rate approaches zero for infinite chains.

Decay rate decreases as 1/N for finite chains.

Derived approximate expression depending on lattice constant and atom number.

Abstract

We propose a new expression of the cooperative decay rate of a one-dimensional chain of N two-level atoms in the single-excitation configuration. From it, the interference nature of superradiance and subradiance arises naturally, without the need of solving the eigenvalue problem of the atom-atom interaction Green function. The cooperative decay rate can be interpreted as the imaginary part of the expectation value of the effective non-Hermitian Hamiltonian of the system, evaluated over a generalized Dicke state of N atoms in the single-excitation manifold. Whereas the subradiant decay rate is zero for an infinite chain, it decreases as 1/N for a finite chain. A simple approximated expression for the cooperative decay rate is obtained as a function of the lattice constant d and the atomic number N. The results are obtained first for the scalar model and then extended to the vectorial light model, assuming all the dipoles aligned.