Mapping out the quantum geometry of driven-dissipative lattices

Tomoki Ozawa

Published 2017-08-01Version 1

We study the effects of the quantum geometric tensor, i.e. the Berry curvature and the Fubini-Study metric, on the steady state of driven-dissipative bosonic lattices. We show that the quantum-Hall type response of the steady-state wavefunction in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. When the band is sufficiently flat, we can map out the full quantum geometric tensor in momentum space by measuring the center-of-mass of the steady-state wavefunction with a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an example and numerically demonstrate how our method works.