Even-Odd Correlation Functions on an Optical Lattice

TL;DR

This paper analyzes how parity correlations in quantum gas microscopes reveal many-body states, providing analytic results for various models and comparing their strength to density correlations.

Contribution

It offers the first analytic calculations of parity correlation functions for multiple models in quantum gases, enhancing understanding of site-resolved imaging data.

Findings

Parity correlations are generally weaker than density correlations.

Parity correlations contain similar information about many-body states.

Analytic expressions are derived for noninteracting bosons, large U Bose-Hubbard, and noninteracting fermions.

Abstract

We study how different many body states appear in a quantum gas microscope, such as the one developed at Harvard [Bakr et al. Nature 462, 74 (2009)], where the site-resolved parity of the atom number is imaged. We calculate the spatial correlations of the microscope images, corresponding to the correlation function of the parity of the number of atoms at each site. We produce analytic results for a number of well-known models: noninteracting bosons, the large U Bose-Hubbard model, and noninteracting fermions. We find that these parity correlations tend to be less strong than density-density correlations, but they carry similar information.