The primary focus of this project was to explore the impact of topology and quantum geometry in diverse bosonic systems, including ultracold atoms in optical lattices and photonic systems. A Bose-Hubbard model was investigated in weakly interacting regimes, and Bose-Einstein condensates in flat band systems were analyzed using Bogoliubov theory, where mean-field interactions play a crucial role in dictating the condensate momentum, which can differ from non-flat band systems. The research demonstrated that the speed of sound and excitation fraction in flat band condensates are connected to orbital-independent generalization of the quantum metric, which reduces to the usual quantum metric (Fubini-Study metric) and the Hilbert-Schmidt quantum distance only in special cases. Further investigation focused on the superfluid properties of a many-body bosonic system in 1D, specifically a Bose-Hubbard model on a two-leg ladder (Creutz ladder) with two flat bands. The research provided insights into the different behaviors of the single-particle quantum metric (defined in momentum space) and the many-body quantum metric (defined in the twisted-boundary condition space) with regards to the Drude response. This work showed that the many-body quantum metric tends to decrease an upper bound of the superfluid weight, whereas prior studies associated the single-particle quantum metric with an increase in superfluid weight and extended our understanding of many-body topological and quantum geometrical effects in bosonic lattices.
In addition, the project applied topological and quantum geometrical concepts to a specific bosonic system, namely a lattice of nanoparticles arrays hosting plasmonic modes. In such plasmonic lattices, the project studied how topological modes known as bound states in the continuum (BICs) are affected by non-Hermitian losses and geometry of the system. Collaborating closely with experiments in my host institution, the research theoretically predicted and experimentally demonstrated a lasing mode topological transition with various topological charges, emphasizing the significance of light polarization winding in plasmonic modes.
The project's results were effectively disseminated through a diverse array of channels, reaching both the scientific community and the general public. These dissemination efforts included presentations at conferences, seminars, and the publication of scientific papers. Notably, the research yielded successful publications in peer-reviewed journals during the project, with additional preprints submitted for peer review, showcasing the wide reach of the research findings. Moreover, the researcher actively engaged in outreach activities to popularize their work on topological matter. Through talks, posters, and seminars, they fostered scientific exchange and promoted awareness and understanding of their research in topological matter, both within the scientific community and among the broader public. These efforts not only contributed to the advancement of scientific knowledge but also played a crucial role in disseminating important scientific insights to a wider audience.
