AMaSiS 2018 Workshop: Abstracts

Hybrid quantum-classical modeling of quantum dot based single-photon emitting diodes

Markus Kantner, Markus Mittnenzweig, and Thomas Koprucki

Weierstrass Institute for Applied Analysis and Stochastics, Berlin

Semiconductor quantum optics is on the leap from the lab to real world applications. The currently unfolding “second quantum revolution” aims at the development of novel quantum technologies that exploit inherent quantum mechanical phenomena like entanglement and quantum superposition for communication and information processing tasks. Many applications, such as eavesdropping-secure encryption methods and optical quantum computers, rely on efficient quantum light sources that can emit single photons or entangled photon pairs on demand. Semiconductor quantum dots (QDs) have been identified as an ideal optically active element for such devices as they can be directly integrated into complex semiconductor structures and photonic resonators. While semi-classical transport theory can be employed to investigate and optimize the current injection into single-photon emitting diodes [1], it does (of course) not describe any quantum optical features such as, e.g., the correlation statistics of the photons emitted by the device. On the step from basic research to new technologies, device engineers will need simulation tools that combine classical device physics with cavity quantum electrodynamics, to support the development of novel quantum light sources.

As a step on this route, we introduce a new hybrid quantum-classical modeling approach [2], that self-consistently couples van Roosbroeck’s semi-classical drift-diffusion equations with a Markovian quantum master equation in Lindblad form. In detail, the model equations read

$-\nabla \cdot \epsilon \nabla \varphi$ $=q\left(p-n+C+Q\left(\rho \right)\right),$ (1)

${\partial }_{t}n-{\displaystyle \frac{1}{q}}\nabla \cdot {𝐣}_n$ $=-R-S_n(n,p,\varphi ,\rho ),$ (2)

${\partial }_{t}p+{\displaystyle \frac{1}{q}}\nabla \cdot {𝐣}_p$ $=-R-S_p(n,p,\varphi ,\rho ),$ (3)

${\partial }_t\rho$ $=-{\displaystyle \frac{i}{\mathrm{\hslash }}}[H,\rho ]+𝒟(n,p,\varphi )\rho ,$ (4)

where the transport and recombination dynamics of the continuum electrons and holes are described by the continuity Eqs. (2)–(3). The Lindblad master equation (4) models the evolution of the coupled QD-photon system. The coupling between both subsystems is mediated by the scattering rates $S_{n/p}$, electrostatic interaction (Poisson’s Eq. (1)) and the dissipation superoperator $𝒟(n,p,\varphi )\rho$, which is a functional of the state of the macroscopic environment of the QD.

The hybrid system (1)–(4) is shown to be consistent with fundamental principles of (non)equilibrium thermodynamics – in particular it obeys the second law of thermodynamics. The approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single QD in the stationary and pulsed operation regime.

Acknowledgments: This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) within the CRC 787 Semiconductor Nanophotonics under grant B4.