The atomic damping basis and the collective decay of interacting two-level atoms

TL;DR

This paper introduces an analytical approach to model the evolution of interacting two-level atoms with symmetric dissipation, revealing decay behaviors characterized by super- and sub-radiant exponential terms.

Contribution

It develops an atomic damping basis for solving the master equation, enabling polynomially scalable solutions for symmetric atomic systems with dissipation.

Findings

Decay as a sum of super- and sub-radiant exponential terms

Analytical solutions leveraging system symmetries

Introduction of an atomic damping basis analogous to bosonic damping basis

Abstract

We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: First, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second, we expand the solutions in a basis composed of eigenvectors of the dissipative part of the master equation that models the independent dissipation of the atoms. This atomic damping basis is an atomic analog to the damping basis used for bosonic fields. The solutions show that the system decays as a sum of sub- and super-radiant exponential terms.