Spatial noise correlations of a chain of ultracold fermions - A numerical study

TL;DR

This numerical study demonstrates that noise correlations in ultracold fermionic systems reveal detailed many-body correlations, serving as a universal probe for characterizing quantum states in optical lattices.

Contribution

The paper shows that noise correlations contain complete information about system correlations and reveal structures beyond bosonization predictions, using DMRG in the extended Hubbard model.

Findings

Noise correlations reflect full many-body correlations.

Sum rules ensure nonsingular structures in noise data.

Noise correlations outperform bosonization in revealing order.

Abstract

We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the shot noise contains full information on the correlations present in the system. We point out the importance of the sum rules fulfilled by the noise correlations and show that they yield nonsingular structures beyond the predictions of bosonization approaches. Noise correlations can thus serve as a universal probe of order and can be used to characterize the many-body states of cold atoms in optical lattices.