Hybrid quantum-classical modeling of quantum dot devices

TL;DR

This paper introduces a hybrid quantum-classical modeling approach combining semiconductor transport theory and quantum mechanics to simulate quantum dot devices, enabling detailed optical and electrical analysis.

Contribution

It develops a new coupled framework using the van Roosbroeck system and Lindblad quantum master equation that respects thermodynamic principles and applies to realistic device geometries.

Findings

Successfully simulates quantum dot single-photon sources

Ensures charge conservation and thermodynamic consistency

Demonstrates feasibility with numerical simulations

Abstract

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non-)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.