Controlling and manipulating quantum matter is a fast-growing research topic that could revolutionise technology and influence many aspects of our daily life. A promising step in this direction is to use topological concepts to tune physical properties of matter and to exploit novel phenomena useful to build new physical devices. In the last decade, topology have been extensively studied in the context of quantum many-body systems, a revolution that has led to the discovery of the topological insulators. Similarly, the Fubini-Study metric has just begun to show its physical meaning and role played in some quantum phenomena, but a lot more remains to be investigated. In this Action, I will study how topological and geometrical effects emerge in the physics of bosons in lattices. I will first address the geometrical contribution in the dynamics of two-body bound states, and then I shall identify conditions for enhancing inter-particle interactions on a full many-body system. I will apply these findings on photonic lattice systems and investigate how non-trivial quantum geometry and topology can lead to novel lasing phenomena. The nature of the work, being based on a combination of expertise, will have a strong interdisciplinary character. The research will be done at Aalto University in the Quantum Dynamics group led by Academy Professor Päivi Törmä, with the unique and exciting opportunity for me to work on the theory in a side by side collaboration with the experimentalists of the group. The expected impact of this research will advance our understanding of the topological properties of bosons in lattices, towards the exploration of geometrically-induced ultrafast lasers and strongly correlated topological fluids of light.
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