# Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions

## TL;DR

This paper analytically derives higher-order momentum correlation functions for three entangled ultracold fermions in a trap, advancing matter-wave interferometry and quantum state characterization beyond standard methods.

## Contribution

It introduces a novel methodology for calculating third- and second-order momentum correlations in tripartite entangled fermionic states, surpassing Wick's factorization approach.

## Key findings

- Derived explicit third- and second-order momentum correlations for GHZ and W states.
- Demonstrated potential for matter-wave interference studies with trapped massive particles.
- Extended the scope of quantum-optics interferometry to ultracold fermionic systems.

## Abstract

Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W- and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order and second-order spin-resolved and spin-unresolved momentum correlations, aiming at matter-wave interference investigations with trapped massive particles in analogy with, and having the potential for expanding the scope of, recent three-photon quantum-optics interferometry.