Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices

TL;DR

This paper demonstrates how to extract particle current distributions and Hall responses from quantum simulation snapshots, enabling detailed analysis of quantum lattice models and their transport properties in experiments.

Contribution

It introduces a method to compute local particle currents and Hall responses directly from snapshot data in quantum simulators, bridging theory and experimental measurements.

Findings

Full probability distribution of local currents can be obtained from snapshots.

Hall polarization and voltage can be accurately computed from snapshot data.

Method applicable to current quantum-gas experiments with flux ladders.

Abstract

Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by means of projective measurements. A central goal of theoretical efforts must be to predict the exact same quantities that can be measured in experiments. Here, we report on the snapshot based calculation of particle currents in quantum lattice models with a conserved number of particles. It is shown how the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data. Moreover, we investigate the Hall response of interacting bosonic flux ladders, exploiting snapshots drawn from matrix-product states. Flux ladders are minimal lattice models, which enable microscopic studies of the Hall response in correlated quantum phases and they are successfully realized in current quantum-gas experiments. Using a specific pattern of unitary two-site transformations, it is shown that the Hall polarization and the Hall voltage can be faithfully computed from the snapshots obtained in experimentally feasible quench and finite-bias simulations.