Noise Correlations in one-dimensional systems of ultra-cold fermions

TL;DR

This paper demonstrates how noise correlations in time of flight images can reveal subtle many-body correlations, such as pairing and density waves, in one-dimensional ultra-cold fermionic systems using Bosonization.

Contribution

It introduces a method to identify and extract pairing and density wave correlations from noise in time of flight images of 1D ultra-cold fermions, linking singularities to Luttinger parameters.

Findings

Noise correlations reveal pairing and density wave orders.

Power law singularities depend on Luttinger parameters.

Technique provides a way to measure correlations experimentally.

Abstract

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using Bosonization, we study such noise correlations in generic one dimensional systems of ultra cold fermions. Specifically, we show how pairing as well as spin and charge density wave correlations may be identified and extracted from the time of flight images. These incipient orders manifest themselves as power law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.