Noise Correlations in low-dimensional systems of ultracold atoms

TL;DR

This paper establishes theoretical relations between order parameter correlations and noise correlations in ultracold atomic systems, revealing their sensitivity to various quantum fluctuations and pairing phenomena in low-dimensional regimes.

Contribution

It derives a unified framework linking noise correlations to order parameters in both bosonic and fermionic low-dimensional systems, including temperature effects.

Findings

Noise correlations distinguish spin, charge, and pairing in 1D Fermi systems.

Sharp peaks in noise correlations indicate pairing in bosonic condensates.

Temperature enhances noise correlation peaks in low-temperature regimes.

Abstract

We derive relations between standard order parameter correlations and the noise correlations in time of flight images, which are valid for systems with long range order as well as low dimensional systems with algebraic decay of correlations. Both Bosonic and Fermionic systems are considered. For one dimensional Fermi systems we show that the noise correlations are equally sensitive to spin, charge and pairing correlations and may be used to distinguish between fluctuations in the different channels. This is in contrast to linear response experiments, such as Bragg spectroscopy, which are only sensitive to fluctuations in the particle-hole channel (spin or charge). For Bosonic systems we find a sharp peak in the noise correlation at opposite momenta that signals pairing correlations in the depletion cloud. In a condensate with true long range order, this peak is a delta function and we can use Bogoliubov theory to study its temperature dependence. Interestingly we find that it is enhanced with temperature in the low temperature limit. In one dimensional condensates with only quasi-long range (i.e. power-law) order the peak in the noise correlations also broadens to a power-law singularity.