Impact of the phonon environment on the nonlinear quantum-dot-cavity QED. I. Path-integral approach

TL;DR

This paper investigates how the phonon environment affects the nonlinear optical dynamics of a quantum dot-cavity system in the strong coupling regime, using a novel path integral approach that captures non-Markovian effects and phonon-induced modifications.

Contribution

It introduces a semi-analytic path integral method for analyzing nonlinear QD-cavity QED, including higher-order nonlinearities and quantum correlations, accounting for phonon effects.

Findings

Phonon environment significantly influences quantum dot-cavity dynamics.

Exact solutions reveal non-Markovian effects and spectral asymmetry.

Analytic approximations are valid at low temperatures and weak coupling.

Abstract

We demonstrate a strong influence of the phonon environment on the coherent dynamics of the quantum dot (QD)-cavity system in the quantum strong coupling regime. This regime is implemented in the nonlinear QD-cavity QED and can be reliably measured by heterodyne spectral interferometry. We present a semi-analytic asymptotically exact path integral-based approach to the nonlinear optical response of this system, which includes two key ingredients: Trotter's decomposition and linked-cluster expansion. Applied to the four-wave-mixing optical polarization, this approach provides access to different excitation and measurement channels, as well as to higher-order optical nonlinearities and quantum correlators. Furthermore, it allows us to extract useful analytic approximations and analyze the nonlinear optical response in terms of quantum transitions between phonon-dressed states of the anharmonic Jaynes-Cummings (JC) ladder. Being well described by these approximations at low temperatures and small exciton-cavity coupling, the exact solution deviates from them for stronger couplings and higher temperatures, demonstrating remarkable non-Markovian effects, spectral asymmetry, and strong phonon renormalization of the JC ladder.