Readout of multi-level quantum geometry from electronic transport

TL;DR

This paper proposes a new measurement protocol to directly probe the quantum geometric tensor in electronic transport systems using weak and resonant parameter modulations, revealing geometric and topological features.

Contribution

It introduces a novel method for measuring the local quantum geometric tensor in transport systems, bridging a gap in experimental capabilities.

Findings

The protocol enables direct measurement of the QGT from conductance changes.

It allows simultaneous access to geometric and topological properties.

The approach is applicable to a broad class of transport-based quantum systems.

Abstract

The quantum geometric tensor (QGT) of a quantum system in a given parameter space captures both the geometry of the state manifold and the topology of the system. While the local QGT elements have been successfully measured in various platforms, the challenge of detecting them in electronic transport systems - such as tunnel or molecular junctions - has yet to be resolved. To fill this gap, we propose a measurement protocol based on weak and resonant parameter modulations, and theoretically demonstrate how the local QGT in such systems can be directly probed from changes of the tunnel conductance. This approach enables the measurement of both geometrical and topological features of quantum states in a broad class of transport-based quantum systems.