Polariton and circuit QED lattices: solid-state platforms for quantum simulations of correlated and topological states

量子模拟--一个量子系统被另一个量子系统模拟--是现代量子技术的支柱之一，有可能允许研究经典计算机无法实现的过程，甚至是自然界中不存在的过程。与理论上允许实现任何量子力学动力学过程的通用量子计算机相比，强大的“量子模拟器”可以量身定制，以探测特定类别的物理问题。量子系统结合了驱动和耗散的组合-能量被泵入系统并允许分散到周围环境中的过程-就是这样一类问题，表现出丰富的物理现象，与完全隔离的系统相比，更难以建模，因此需要功能量子模拟器的存在。这个博士学位的目的是进一步发展和应用经典数值方法，以帮助理解具有驱动和耗散的多体量子物理学，作为实用量子模拟器的实际实现的一步。我们所研究的物理系统--那些基于量子力学物体，由光和物质的组合构成的系统--由于其固有的驱动耗散性质、高度的可控性和灵活性以及室温操作的潜力，特别适合作为实现这一目标的平台。这些新兴的平台已经被证明承载了大量深刻而新颖的物理学，对这些物理学的研究不仅可以导致新材料在技术上的发展，而且还可以让我们进入量子力学的新领域。

Quantum simulation-where one quantum system is emulated by another quantum system-is one of the pillars of modern quantum technologies, potentially allowing for the study of processes inaccessible to a classical computer, and even processes that do not occur in nature. In contrast to a universal quantum computer that theoretically allows for the implementation of any quantum mechanical dynamical process, powerful "quantum simulators" can be tailor-made to probe a specific class of physics problems. Quantum systems incorporating a combination of drive and dissipation- processes where energy is pumped into the system and allowed to disperse into the surrounding environment-is one such class of problems, exhibiting rich physical phenomena that is substantially more difficult to model compared to a perfectly isolated system, thus necessitating the existence of a functional quantum simulator. The aim of this PhD is to further develop and apply classical numerical methods to aid in the understanding of many-body quantum physics with drive and dissipation, as a step toward the practical realisation of useful quantum simulator. The physical systems we look at-those based on quantum mechanical objects constructed form a combination of light and matter-are particularly suited as platforms for this goal, due to their inherent drivendissipative nature, high degree of controllability and flexibility, and potential for room temperature operation. These emergent platforms have shown to host a great deal of profound and novel physics, the study of which could not only lead to the development of new materials for use in technology, but could also allow us to enter new and unexplored realms of quantum mechanics.