Estudio Te\'orico del espectro de emisi\'on para un sistema microcavidad-punto cu\'antico en una aproximaci\'on de campo medio (Theoretical study of emission spectrum for a quantum dot-microcavity system in a mean field approximation)

TL;DR

This paper develops a numerical method using mean field theory and density matrix formalism to calculate the emission spectrum of a quantum dot-microcavity system, accounting for photon leakage and exciton pumping.

Contribution

It introduces a nonlinear mean field master equation for the first time to model the emission spectrum of a quantum dot-microcavity system.

Findings

Derived a numerical expression for emission spectrum calculation.

Validated the model with typical semiconductor micropillar parameters.

Provides a framework for analyzing open quantum systems with photon leakage.

Abstract

En este trabajo, se obtiene una expresi\'on num\'erica para calcular el espectro de emisi\'on de un sistema microcavidad-punto cu\'antico usando una teor\'ia de campo medio en el formalismo de la matriz densidad. El sistema modelado es un micropilar semiconductor que contiene un \'unico punto cu\'antico en el interior de la microcavidad, este sistema presenta p\'erdida de fotones a trav\'es de los espejos de la cavidad y bombeo de excitones al punto cu\'antico. Obtenemos una ecuaci\'on maestra de campo medio no lineal que nos permite calcular el espectro de emisi\'on. In this work, we deduce a numerical expression to calculate the emission spectrum for a quantum dot-microcavity system, using a mean field theory in the density matrix formalism. The open system modeled, is a typical semiconductor micropillar that contains a single quantum dot inside a microcavity, this system presents leakage of photons through cavity mirrors and pumping of excitons to the quantum dot. We obtain a mean field nonlinear master equation that allow us calculate the emission spectrum.