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

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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.