This project aims to develop new theories of quantum matter by investigating the connection between microscopic few-particle correlations and macroscopic quantum phenomena. There is a pressing need for such a novel approach, due to the growing class of strongly correlated quantum systems that defy a conventional explanation. A key innovation is the use of the clean and tuneable cold-atom system, where microscopic properties are precisely known, allowing new spectral techniques to be directly verified. A greater understanding of quantum correlations will advance a range of fields including condensed matter physics, and could potentially underpin a new generation of quantum devices where energy can be efficiently stored and rapidly extracted.