Measuring the single-particle density matrix for fermions and hard-core bosons in an optical lattice

TL;DR

This paper proposes a scheme to measure off-diagonal elements of the single-particle density matrix in optical lattice experiments with ultracold atoms, enabling new insights into quantum many-body systems.

Contribution

The authors introduce a novel protocol to access off-diagonal density matrix elements for fermions and hard-core bosons in optical lattices, expanding measurement capabilities.

Findings

Scheme is feasible with current quantum-gas microscope technology.

Protocol accurately measures off-diagonal density matrix elements.

Potential to enhance understanding of quantum correlations in lattice systems.

Abstract

Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off-diagonal in the occupation basis. Here, we propose a scheme to access these basic quantities both for fermions as well as hard-core bosons and investigate its accuracy and feasibility. The scheme relies on the engineering of a large effective tunnel coupling between distant lattice sites and a protocol that is based on measuring site occupations after two subsequent quenches.