# Solving the quantum many-body problem via correlations measured with a momentum microscope

## TL;DR

This paper demonstrates measuring multi-particle momentum correlations in ultracold helium atoms using a quantum momentum microscope, providing operational insights into the quantum many-body problem and revealing classical inequality violations.

## Contribution

It introduces a method to measure higher-order momentum correlations in a quantum many-body system, advancing understanding of complex quantum phenomena.

## Key findings

- Measured multi-particle momentum correlations up to third order.
- Extracted the pairing field amplitude as a key correlation component.
- Observed a record violation of the classical Cauchy-Schwarz inequality.

## Abstract

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation/annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here we demonstrate this paradigm by measuring multi-particle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system|the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multi-particle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localisation.