Recovering quantum correlations in optical lattices from interaction quenches

TL;DR

This paper introduces a method to recover local coherent currents in optical lattice quantum simulations by analyzing density responses to quenches, enabling the study of quantum correlations and entanglement.

Contribution

It develops a data analysis technique using semi-definite optimization to reconstruct the full covariance matrix, including off-diagonal coherent current terms, from density measurements.

Findings

Successfully reconstructs coherent currents from density data.

Provides a lower bound on entanglement at finite temperature.

Enables studying quantum correlations beyond classical limits.

Abstract

Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this work, we show how to achieve that by measuring densities that are altered in response to quenches to non-interacting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunnelling currents and atom number dynamics, allowing to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semi-definite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about non-commuting observables allows to lower bound entanglement at finite temperature which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities.