Coherent networks of polariton condensates in microcavities

The study of interacting many-element systems is as vital for our understanding of complex organisms, as it is important for the modelling of disease spreading in pandemics, and is a key element in the search for materials with novel properties. The presence of nonlinearities and interaction time-lags critically influences the dynamics and complicates control over these systems. Moreover, complexity in network structures rapidly scales with a larger number of elements and increasing degrees of freedom, often making them computationally intractable. Artificially engineered networks, on the other hand, can be used for the simulation and study of interacting systems, and pave the way for novel and unconventional computing paradigms. The implementation of these schemes is being explored in various fields such as electronics, photonics and quantum systems. In particular, lattices of polariton condensates in optical microcavities present a promising platform for the realisation of coupled network structures. Microcavity polaritons are light-weight bosonic quasi-particles formed by the strong coupling of cavity photons and quantum well excitons. Their hybrid light-matter character facilitates macroscopically accessible quantum degenerate states (condensates) at elevated temperatures. Large optical malleability, picosecond-timescale dynamics, and strong intrinsic nonlinearities highlight the potential of polariton lattices for future technological applications. The work presented in this PhD thesis investigates the interactions of coupled polariton condensates, and shows substantial advancements in both, the engineering and the manipulation of optically generated condensate lattices. In particular, the introduction of a laser feedback scheme for condensate density stabilisation makes it possible to accurately build macroscopic lattices of tuneable size and network architecture. The nonlinear dynamics and synchronisation phenomena of coupled condensates are explored in various coupling topologies, ranging from simply-connected structures to one- and two-dimensional periodic systems. Shaping of the polariton potential landscape by using spatially patterned lasers opens up an all-optical method of controlling couplings, interaction time-lags, and coherence properties in condensate lattices. The results and methods presented support the realisation of an ultra-fast delay-coupled nonlinear oscillator network, with precise control over individual couplings