Single-site- and single-atom-resolved measurement of correlation functions

TL;DR

This paper discusses recent advances in in-situ fluorescence imaging of ultracold atoms in optical lattices, enabling single-site and single-atom resolution to directly measure local and non-local correlation functions in many-body quantum systems.

Contribution

It introduces a method for in-situ detection of correlation functions at the single-particle level, allowing comprehensive analysis of quantum phases without long-range order.

Findings

Single-site and single-atom-resolved images obtained in a single experimental run

Direct measurement of arbitrary correlation functions between lattice sites

Ability to characterize quantum phases with non-local correlations

Abstract

Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments whereas in cold-gases systems, time-of-flight and in-situ absorption imaging are the standard observation techniques. However, none of these methods allow the in-situ detection of spatially resolved correlation functions at the single-particle level. Here we give a more detailed account of recent advances in the detection of correlation functions using in-situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.