Dr. Francesco Di Colandrea

Direct measurement of the quantum geometric tensor

The quantum dynamics of two-band wavepackets is controlled by the quantum geometric tensor. The Berry curvature (the imaginary part of the tensor) accounts for adiabatic trajectories, while the quantum metric (the real part of the tensor) describes non-adiabatic corrections. The quantum metric also features a fundamental geometrical interpretation, expressing the distance between the system eigenstates. It has measurable effects on flat-band superfluidity, exciton Lamb shift, and orbital magnetic susceptibility. We show that, in chiral-symmetric systems, the quantum geometric tensor can be retrieved by measuring the mean chiral displacement of delocalized wavefunctions. Interestingly, an appropriate gauge choice allows linking the tensor to the Berry connection. These findings are experimentally demonstrated in a topological quantum walk of structured light [1]. [1] F. Di Colandrea et al., arXiv: 2401.07946