Observing the quantum statistics of distant ions

Modern advances in single-particle control have led to remarkable demonstrations of quantum indistinguishability. However, this property is difficult to show for trapped ions, as their mutual repulsion makes it challenging to perform atomic Hong-Ou-Mandel experiments. To this end, we present a new method of atom interferometry using a low-entropy quantum rotor. We use a specialized surface-electrode Paul trap which confines a freely rotating two-ion Coulomb crystal. By preparing the crystal in a superposition of angular momentum, we realize corotating ion pairs with slightly different angular velocity. Eventually, the ions interfere with themselves, but after one branch of their two-particle wavefunction has been physically exchanged. At this time, we observe an interferometric signal which reveals the ions' quantum statistics. This work shows that it is possible to engineer a system over which non-overlapping particles can impose their quantum statistics.