# Theory of non-Markovian dynamics in resonance fluorescence spectrum

## TL;DR

This paper provides a comprehensive theoretical analysis of non-Markovian effects on the resonance fluorescence spectrum of a driven quantum dot, highlighting how phonon interactions influence spectral features under various conditions.

## Contribution

It introduces an exact solution for dot-phonon coupling in a non-Markovian regime and compares it with Markovian approximations, revealing the impact of phonon bath temperature and detuning.

## Key findings

- Phonon coupling effects vanish at resonant pump.
- Sideband narrowing and asymmetry increase with phonon temperature.
- Exact and Born approximation results coincide for dot-phonon interactions.

## Abstract

We present a detailed theoretical study of non-Markovian dynamics in the fluorescence spectrum of a driven semiconductor quantum dot (QD), embedded in a cavity and coupled to a three-dimensional (3D) acoustic phonon reservoir. In particular, we investigate the effect of pure dephasing on one of the side-peaks of the Mollow-triplet spectrum, expressed in terms of the off-diagonal element of the reduced system operator. The QD is modeled as a two-level system with an excited state representing a single exciton, and ground state represents the absence of an exciton. Coupling to the radiative modes of the cavity is treated within usual Born-Markov approximation, whereas dot-phonon coupling is discussed within non-Markovian regime beyond Born approximation. Using an equation-of-motion technique, the dot-phonon coupling is solved exactly and found that the exact result coincides with that of obtained within Born approximation. Furthermore, a Markov approximation is carried out with respect to the phonon interaction and compared with the non- Markovian lineshape for different values of the phonon bath temperature. We have found that coupling to the phonons vanishes for a resonant pump laser. For a non-resonant pump, we have characterzied the effect of dot-laser detuning and temperature of the phonon bath on the lineshape. The sideband undergoes a distinct narrowing and aquires an asymmetric shape with increasing phonon bath temperature. We have explained this behavior using a dressed-state picture of the QD levels.