Alexander Pimenov (WIAS), Markus Kantner (WIAS, core support)
01.01.2019 – 31.12.2020
The second quantum revolution aims to bring quantum communication and information processing to real world applications, and semiconductor quantum dots (QDs) were identified as ideal optically active elements for the emerging quantum technologies as they can be directly integrated into semiconductor-based photonic resonators. However, simple electrically driven quantum light emitting diodes have severe limitations as they do not allow for resonant excitation and intrinsically suffer from charge noise. A promising solution to this problem are nanolasers (see Fig. 1a), which employ only a few QDs as gain medium, embedded in a high quality optical micro-resonator with spatial dimensions down to the diffraction limit. This tremendous size reduction takes the concept of lasing to a completely new regime, where the light-matter interaction is dominated by cavity quantum electrodynamic (cQED) effects. In this respect, nanolasers operate on the exciting crossroad between quantum light emitters and conventional diode lasers. The exploitation of cQED effects facilitates thresholdless lasing (see Fig. 1b), increased modulation speed and significantly reduced energy consumption (“green photonics”). Beyond their usage in nanophotonic circuits, nanolasers are promising candidates for optical interconnects in data centers and supercomputers.
The mathematical modeling of nanolasers is a complex multi-physics problem, which requires a fully quantum mechanical description of the light-matter interaction in the optically active region. We employ a comprehensive hybrid quantum-classical modeling approach, which includes aspects of semi-classical transport theory in semiconductors, electromagnetic field theory and cQED in second quantization for the coupled QD-photon system. Mathematically, this involves systems of nonlinear partial differential equations (electronic transport, heat transport), complex non-Hermitian eigenvalue problems (optical fields in microcavities, Schrödinger–Poisson problem for QD electronics) and operator evolution equations for the quantum statistical operator describing the open quantum system (Lindblad master equation, Jaynes–Cummings model). Our comprehensive modeling framework allows for investigation of the device characteristics under stationary, pulsed and noisy (stochastic) injection conditions.
For the numerical simulation of the nanolasers we employ tools such as state-of-the-art solvers for nonlinear transport problems (finite volumes Scharfetter–Gummel method) and coupled cluster expansion techniques for the solution of the quantum optical problem. Other possibilities to truncate the huge dimensionality of the underlying Hilbert space include tensor network methods. Finally, we perform further simplifications within our framework, and study the dynamics of the reduced systems of differential equations to gain qualitative insights on the novel regimes of operation arising due to the extreme size of these lasers.
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