# Quantum kinetic equations for the ultrafast spin dynamics of excitons in diluted magnetic semiconductor quantum wells after optical excitation

## TL;DR

This paper derives quantum kinetic equations to describe ultrafast exciton spin dynamics in diluted magnetic semiconductor quantum wells, capturing non-Markovian effects and predicting complex spin decay behaviors after optical excitation.

## Contribution

It introduces a comprehensive quantum kinetic model including various interactions and arbitrary excitation pulses, extending previous theories by explicitly treating non-Markovian effects.

## Key findings

- Non-Markovian spin decay with initial rate halved compared to Markovian predictions
- Prediction of a non-monotonic spin polarization decay with an overshoot of up to 10%
- Quantum kinetic simulations show significant deviations from Markovian behavior in narrow quantum wells

## Abstract

Quantum kinetic equations of motion for the description of the exciton spin dynamics in II-VI diluted magnetic semiconductor quantum wells with laser driving are derived. The model includes the magnetic as well as the nonmagnetic carrier-impurity interaction, the Coulomb interaction, Zeeman terms, and the light-matter coupling, allowing for an explicit treatment of arbitrary excitation pulses. Based on a dynamics-controlled truncation scheme, contributions to the equations of motion up to second order in the generating laser field are taken into account. The correlations between the carrier and the impurity subsystems are treated within the framework of a correlation expansion. For vanishing magnetic field, the Markov limit of the quantum kinetic equations formulated in the exciton basis agrees with existing theories based on Fermi's golden rule. For narrow quantum wells excited at the $1s$ exciton resonance, numerical quantum kinetic simulations reveal pronounced deviations from the Markovian behavior. In particular, the spin decays initially with approximately half the Markovian rate and a non-monotonic decay in the form of an overshoot of up to $10\,\%$ of the initial spin polarization is predicted.