Superconductivity, superfluidity and Bose-Einstein condensation (BEC) are many-body phenomena where quantum statistics are crucial and the effect of interactions may be intriguing. Theoretical understanding of superconductivity and condensation in several real-world systems is still a challenge, and superconductivity at room temperature remains a grand goal. We have discovered that superconductivity has a connection to quantum geometry [1-3]. The superfluid weight in a multiband system has a previously unnoticed geometric component, proportional to the quantum metric and Berry curvature. Due to this, superconductivity is possible also in a flat band where individual electrons would not move. We have shown that the geometric contribution is essential in explaining the recent observation of superconductivity in bilayer graphene , and may eventually help realize superconductors at elevated temperatures.
Bose-Einstein condensation has been realized for various particles or quasi-particles, such as atoms, molecules, photons, magnons and semiconductor exciton polaritons. We have recently experimentally realized a new type of condensate: a BEC of hybrids of surface plasmons and light in a nanoparticle array [5,6]. The condensate forms at room temperature and shows ultrafast dynamics. We utilized a special measurement technique, based on formation of the condensate under propagation of the plasmonic excitations, to monitor the sub-picosecond thermalization dynamics of the system. This new platform is ideal for studies of differences and connections between BEC and lasing [7,8], and eventually also studies of topological phenomena due to the easy tunability of the array geometry.
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