Observing indistinguishability of mutually separated particles

The quantum statistics theorem states that the wavefunction of two indistinguishable particles must be symmetrized. As a result, the phase acquired upon exchanging the particles is restricted to either 0 or π. Although this theorem has profound implications for the structure of nature—most notably for the stability of atoms and nuclei—its consequences are typically observed only indirectly, for example through the Pauli exclusion principle. Moreover, the bosonic or fermionic character of indistinguishable particles usually becomes relevant only at atomic scales or when their wavefunctions significantly overlap.

In contrast, ions confined in an ion trap are always separated by several micrometers due to their mutual Coulomb repulsion. This macroscopic separation naturally invites the interpretation of the ions as distinguishable particles. In this context, I will examine the conditions under which the wavefunction of two trapped ions must nevertheless be symmetrized. Specifically, I discuss experiments that directly reveal a well-defined exchange phase by interfering a two-ion string with itself after a π rotation.