Direct probing the quantum geometric tensor for bosonic collective excitations

Abstract: The quantum geometric tensor (QGT), whose real and imaginary parts define the quantum metric and Berry curvature, encodes the intrinsic geometry of quantum states. While electronic QGT has been directly observed and linked to various phenomena like electron-phonon coupling, its bosonic analogue remains both theoretically and experimentally unexplored. We demonstrate that the dynamical structure factor directly encodes the full QGT throughout the Brillouin zone, establishing it as a sensitive probe of both quantum metric and Berry curvature. Applying this framework, we uncover clear geometric signatures in a twofold quadruple Weyl phonon in BaPtGe and the node-line magnon in Gd. Our results establish a general, direct route to measuring quantum geometry in bosonic systems, a crucial step toward elucidating its impact on condensed matter phenomena.