# Simulation technique of quantum optical emission process from multiple two-level atoms based on classical numerical method

## TL;DR

This paper introduces a classical numerical method based on finite-difference time-domain simulations to analyze quantum optical emission processes from multiple two-level atoms, capturing atom-field and atom-atom interactions.

## Contribution

The paper presents a novel classical numerical approach to simulate quantum optical emission phenomena, including superradiance and subradiance, from multiple atoms in various environments.

## Key findings

- Successfully simulated spontaneous emission in vacuum.
- Demonstrated emission enhancement due to atom-cavity interactions.
- Showed suppression of emission via destructive dipole-dipole interactions.

## Abstract

In this paper, we report a numerical method for analyzing optical radiation from a two-level atom. The proposed method can consistently consider the optical emission and absorption process of an atom, and also the interaction between atoms through their interaction with a radiation field. The numerical model is based on a damping oscillator description of a dipole current, which is a classical model of atomic transition and is implemented with a finite-difference time-domain method. Using the method, we successfully simulate the spontaneous emission phenomena in a vacuum, where the interaction between an atom and a radiated field plays an important role. We also simulate the radiation from an atom embedded in a photonic crystal (PhC) cavity. As a result, an atom-cavity field interaction is sucessfuly incorporated in the simulation, and the enhancement of the optical emission rate of an excited atom is explained. The method considers the effect of the interaction between atoms through the radiated field. We simulate the optical emission process of the multiple atoms and show that an enhancement of the emission rate can occur owing to the an atom-atom interaction (superradiance)(R. H. Dicke, Phys. Rev. {\bf 93}, 99[1954]). We also show that the emission rate is suppressed by the effect of the destructive dipole-dipole interaction under an out-of-phase excitation condition (subradiance).