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Maximum-entropy method applied to the many-particle hierarchy problem in quantum-dot-microcavity systems

最大熵方法应用于量子点微腔系统中的多粒子层次问题

基本信息

批准号：
327790415
负责人：
Professor Dr. Jan Wiersig
金额：
--
依托单位：
Abteilung Theorie der kondensierten Materie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/327790415?language=en
关键词：
Maximum entropy method applied many

项目摘要

The study of light-matter interaction in semiconductor quantum dots embedded into optical microcavities is a topical research field in condensed matter physics with many potential applications, such as ultra-low threshold micro- and nanolasers, single-photon sources, and sources of entangled photon pairs. The theoretical description of such driven-dissipative quantum many-particle systems in terms of the reduced density operator is, however, only feasible for small or highly symmetric systems. Approaches based on equations of motion of relevant expectation values are numerically much more efficient, but require to truncate the many-particle hierarchy at a suitable level and therefore only provide a subset of moments instead of the full statistics. In this project, we propose to apply the maximum entropy method, which was originally introduced in equilibrium statistical mechanics, to the many-particle hierarchy problem of non-equilibrium systems in two different ways. The first method still uses the results of conventional equations-of-motion approaches and allows to approximately determine the full statistics und substatistics such as the photon statistics of a microcavity laser. The second method goes much further by replacing the equations-of-motion approaches for stationary non-equilibrium problems by a novel scheme which has three important advantages: (i) it does not require any factorization scheme to truncate the many-particle hierarchy, (ii) avoids the numerical integration of equations of motion, and (iii) gives access to the full statistics. The purpose of the project is to study in detail both methods with focus on semiconductor quantum-dot microcavity systems. Once completed, we expect not only to have developed an highly efficient scheme to solve driven-dissipative quantum many-particle problems, but also to have gained a deeper understanding of the many-particle hierarchy and its truncation.

嵌入光学微腔中的半导体量子点中的光-物质相互作用研究是凝聚态物理学中的一个热门研究领域，具有许多潜在的应用，例如超低阈值微和纳米激光器，单光子源和纠缠光子对源。然而，这种驱动耗散量子多粒子系统的约化密度算符的理论描述只适用于小的或高度对称的系统。基于相关期望值的运动方程的方法在数值上要有效得多，但需要在适当的水平上截断多粒子层次，因此只提供一个子集的时刻，而不是完整的统计。在这个项目中，我们提出了应用最大熵方法，这是最初引入平衡统计力学，以两种不同的方式来解决非平衡系统的多粒子层次问题。第一种方法仍然使用传统的运动方程方法的结果，并允许近似地确定完整的统计和子统计，如微腔激光器的光子统计。第二种方法走得更远，用一种新的方案取代了静止非平衡问题的运动方程方法，该方案具有三个重要优点：（i）它不需要任何因子分解方案来截断多粒子层次，（ii）避免了运动方程的数值积分，以及（iii）提供了完整的统计数据。该项目的目的是详细研究这两种方法，重点是半导体量子点微腔系统。一旦完成，我们期望不仅开发出一个高效的方案来解决驱动耗散量子多粒子问题，而且还获得了更深入的了解多粒子层次及其截断。