Quantum optical and nonlinear optical properties of semiconductors and semiconductor heterostructures in photonic crystals

光子晶体是介质材料在光波长尺度上的周期性排列，光子晶体中的光子色散关系从根本上影响着光物质的相互作用。例如，通过降低相应光谱区域中的态的光子密度，激发态的辐射寿命可以在几个数量级上变化。光和物质之间的有效耦合强度也可以通过改变光子态密度来调节。直接带隙半导体异质结为研究光-物质相互作用的可能性提供了特别有趣的材料系统，这既有基本的原因，也有实际的原因。它们即使在室温下也表现出很强的激子共振，设计良好的光电子器件的量子效率受到自发辐射的限制，而且它们可以以几乎分子的精度生长。在这个项目中，我们想从理论上研究半导体与半导体异质结构和光子晶体之间的相互作用。我们的方法的基础是半导体发光方程，它是完全量子化光场的半导体Bloch方程的推广。光场的量子化对于理解强的光-物质耦合是至关重要的，因为光子晶体中的自发发射率特别是被改变的。我们特别感兴趣的是光发射特性、激光和脉冲传输效应，以及量子光学效应，如激子的辐射寿命、激子和光场统计。

Tayloring the photonic dispersion relation in "photonic crystals", a periodic arrangement of dielectric materials on the length scale of the optical wavelength, influences the lightmatter interaction fundamentally. The radiative life time of an excited state, for instance, can be varied over several orders of magnitude by reducing the photonic density of states in the corresponding spectral region. Also the effective coupling strength between light and matter can be tuned by altering the photonic density of states. Direct-gap semiconductor heterostructures provide particularly interesting material systems to study the possibilities of manipulating the light-matter interaction for both fundamental and practical reasons. They exhibit strong excitonic resonances even at room temperature, the quantum efficiency of well-designed opto-electronic devices is limited by spontaneous emission and they can be grown with almost molecular precision. Within this project, we want to theoretically study the interaction between semiconductors and semiconductor heterostructures and photonic crystals. The basis of our approach are the semiconductor luminescence equations, which are an extension of the semiconductor Bloch equations for a fully quantized light field. The quantization of the light field is crucial to understand the strong light-matter coupling, since the spontaneous emission rate, in particular, is modified in photonic crystals. We are especially interested in light emission properties, lasing and pulse propagation effects, as well as quantum optical effects like the radiative life of excitons and the excitonic and light field statistics.