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，可能允许研究经典计算机无法访问的过程，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，可以量身定做强大的“量子模拟器”来探索特定类别的物理问题。结合了驱动和耗散的量子系统就是这样一类问题，它展示了丰富的物理现象，与完全隔离的系统相比，这种现象更难建模，因此需要一个功能强大的量子模拟器。这一博士学位的目的是进一步发展和应用经典的数值方法，以帮助理解具有驱动和耗散的多体量子物理，作为迈向实用的量子模拟器的一步。我们看到的物理系统--那些基于由光和物质组合而成的量子力学对象的物理系统--特别适合作为实现这一目标的平台，因为它们固有的驱动力和耗散性质，高度的可控性和灵活性，以及室温操作的潜力。这些新兴的平台已经显示出拥有大量深刻和新颖的物理，对这些物理的研究不仅可以导致用于技术的新材料的开发，而且还可以让我们进入新的和未被探索的量子力学领域。

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.