Quantum localization of light and non-Markovian photoemission process in photonic crystals

具有较大的折射率周期性调制的人造晶体称为光子晶体，它可以实现光子带隙，即没有辐射本征模的频率范围。由于量子电动力学效应，光学跃迁接近光子带隙频率的原子/分子有望产生光子的量子局域化和相关的非马尔可夫光发射现象。在这项研究中，我们旨在利用稀土原子和染料分子的超辐射来证明这些新的量子电动力学效应。对于大光子带隙光子晶体，基于时域有限差分法和SVE近似的传统分析方法是不适用的，我们开发了一个不需要SVE近似的计算程序。我们发现，在铅笔状激发的情况下，超辐射发射与激发激光束的传播方向相同，因此，一维光子带隙和态的光子密度与非马尔可夫超辐射的行为有关，即使对于二维和三维光子晶体也是如此。我们还研究了量子点作为发射器冷却到极低温度的可能性，以及由于光子晶体的局域模式而使用的异常光子密度态。在此研究过程中，我们取得了GaAs量子点的激光化、耦合双球真空拉比分裂的第一性原理计算、米克尔森干涉仪对单个量子点发射带光谱宽度的精确评估、量子双环电子能级的计算以及它们的光致发光测量等成功成果。

Artificial crystals with a large periodic modulation of their refractive indices, which are called photonic crystals, can realize photonic bandgaps, or frequency ranges in which there is no radiative eigenmode. Those atoms/molecules whose optical transition is close to the frequency of the photonic bandgaps are expected to bring about quantum localization of photons and the relevant non-Markovian photoemission phenomena due to the quantum-electrodynamical effects. In this study, we aimed at the demonstration of these novel quantum-electrodynamical effects by making use of superradiance of rare earth atoms and dye molecules. We developed a code for computation without the slowly-varying-envelope (SVE) approximation for photonic crystals with a large photonic bandgap to which the conventional analysis of based on the finite-difference time-domain method and the SVE approximation is not applicable. We found that the superradiant emission is propagated to the same direction as the excitation laser beam in the case of the pencil-like excitation, and hence, it is the one-dimensional photonic bandgap and photon density of states that are relevant to the behavior of the non-Markovian superradiance even for two- and three-dimensional photonic crystals We examined the superradiance of chelates of rare earth ions With a pulsed dye laser and a streak camera. We also examined the possibility of quantum dots cooled down to an extremely low temperature as an emitter and the usage of the extraordinary photon density of states due to the localized modes of the photonic crystals. On this research process, we obtained successful results such as the lasing of GaAs quantum dots, the first-principle calculation of the vacuum Rabi splitting by coupled bispheres, accurate evaluation of the spectral width of emission bands of single quantum dots by a Mickelson interferometer, calculation of electronic levels of quantum double rings, and their photoluminescence measurements.