Detecting correlation functions of ultracold atoms through Fourier sampling of time-of-flight images

TL;DR

This paper introduces a novel Fourier sampling technique using Raman pulses to reconstruct detailed correlation functions of ultracold atoms from time-of-flight images, enabling advanced analysis of quantum states.

Contribution

It presents a new detection method for ultracold atoms that reconstructs one- and two-particle correlations from experimental data, enhancing quantum state characterization.

Findings

Reconstruction of correlation functions from experimental images.

Application to detect phase separation and exotic orders.

Potential to analyze entanglement and fluctuating orders.

Abstract

We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.