Manifestation of the quantum metric in chiral lattice systems

Recent years have seen a surge in research on the role of quantum geometry in condensed matter physics. For instance, the Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields due to an obstruction in space associated with a magnetic flux. A similar effect can be observed in solid-state systems, where the topology of the Berry connection can influence electron dynamics. These are paradigmatic examples of how the dynamics can be affected by the system's geometry. Here, we show that in chiral-symmetric processes the quantum metric has a measurable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk and demonstrates an effect that can be attributed directly to the geometry of the state space. Advanced materials are characterized by complex mathematical properties such as the topology and geometry of quantum states. This work demonstrates that in some systems, the evolution of a particle's spatial distribution is a direct measure of these properties: the relative displacement in two sublattices is found to be given by the quantum metric.