Wannier Function Formalism for Defects in Periodic Materials for Microlaser Resonator and Cavity QED-Applications

光子晶体中的缺陷结构在微激光谐振器和腔量子电动力学(腔QED)中有很好的应用前景，例如，可以抑制缺陷中具有光子带隙内跃迁频率的原子的自发辐射，形成光子-原子束缚态。由于必须同时捕捉寄主晶体的周期性和缺陷的短尺度结构，对这类缺陷中的光子态密度和动力学的理论描述受到了阻碍。在标准的Bloch或平面波展开(PWE)方法中，这意味着使用非常大的基函数集。在本项目中，将发展一种基于Wannier函数展开的光子晶体微激光谐振器和腔QED中的动力学过程的有效形式，它允许使用相对较小的基函数集。特别是，所谓的Bloch相位优化问题将使用一种有效的遗传算法来处理。这一理论将应用于光子晶体微激光器的动力学和利用格林函数技术的腔QED中。我们希望与R1(Daniel Haertle，Karsten Buse)、R3(Arno Rauschenbeutel)和W1(Dieter Meschede，Wolfgang Alt)项目产生刺激的互动。

Defect structures in photonic crystals are promising for applications as microlaser resonators and in cavity quantum electrodynamics (cavity QED) where, for example, the spontaneous emission from an atom in the defect with a transition frequency inside a photonic bandgap can be suppressed and photon-atom bound states can be formed. The theoretical description of the photonic density of states and of the dynamics in such defects has been hampered by the necessity of simultaneously capturing the periodicity of the host crystal and the short-scale structure of the defect. In the standard Bloch or plane wave expansion (PWE) methods this implies using extraordinarily large sets of basis functions. In the present project an efficient formalism for the dynamical processes in photonic crystal microlaser resonators and cavity QED, based on a Wannier function expansion, will be developed, which allows using a relatively small set of basis functions. In particular, the so-called Bloch phase-optimization problem will be treated using an efficient genetic algorithm. The formalism will be applied to the dynamics in photonic crystal microlasers and in cavity QED using Green's function techniques. We expect stimulating interactions with the Projects R1 (Daniel Haertle, Karsten Buse), R3 (Arno Rauschenbeutel), and W1 (Dieter Meschede, Wolfgang Alt).