Collective Description of Density Matrix of Identical Multi-level Atoms for Superradiance

TL;DR

This paper introduces a collective density matrix description for identical multi-level atoms, enabling efficient simulation of superradiance phenomena by reducing computational complexity from exponential to polynomial growth.

Contribution

It presents a novel method to describe the density matrix collectively, significantly simplifying calculations for large atomic ensembles in superradiance studies.

Findings

Efficient simulation of hundreds of atoms achieved.

Demonstrated conditions for superradiance and superfluorescence.

Reduced computational complexity from exponential to polynomial.

Abstract

A collective description of density matrix is presented for identical multi-level atoms, which are either excited initially, driven coherently or pumped incoherently. The density matrix is defined as expectation value of projection or transition operators in a basis of atom's product states. The identical matrix elements are identified with several integers, which specify uniquely the involved operators. To remove the redundancy, these identical elements are treated as single quantity and the equation for this quantity is dervied by mapping the transition or projection operators to a single vector specified with these integers. As a result, the number of computed elements increases polynomially rather than exponentially with the number of atoms. As an example, we carry out exact simulation of hundreds of two-level atoms and demonstrate the different conditions for observing superradiance and superfluorescence.