Steady-state Hall response and quantum geometry of driven-dissipative lattices

TL;DR

This paper investigates how the quantum geometric tensor influences the steady state of driven-dissipative bosonic lattices, enabling the mapping of quantum geometry through Hall response measurements.

Contribution

It introduces a method to measure the full quantum geometric tensor in flat bands via steady-state Hall response in driven-dissipative lattices.

Findings

Quantum Hall response depends on all components of the quantum geometric tensor.

Steady-state Hall response can map out the quantum geometric tensor in momentum space.

Numerical demonstration on the Lieb lattice shows feasibility of measurement.

Abstract

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 wave function in the presence of an external potential gradient depends on all the components of the quantum geometric tensor. Looking at this steady-state Hall response, one can map out the full quantum geometric tensor of a sufficiently flat band in momentum space using a driving field localized in momentum space. We use the two-dimensional Lieb lattice as an example and numerically demonstrate how to measure the quantum geometric tensor.