# Revealing quantum statistics with a pair of distant atoms

## TL;DR

This paper proposes methods to directly measure the quantum statistics of two distant identical particles, such as atoms or ions, by examining their wave function symmetry, even when they are spatially separated.

## Contribution

It introduces two protocols for revealing the bosonic or fermionic nature of distant particles through direct wave function symmetry measurement.

## Key findings

- Protocols successfully distinguish bosons from fermions.
- Methods applicable to trapped atoms or ions.
- Quantum statistics can be probed without particle interaction energy.

## Abstract

Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions.