Collective phases of identical particles interfering on linear multiports
V. S. Shchesnovich, M. E. O. Bezerra · Physical Review A · 2018
We introduce collective geometric phases of bosons and fermions interfering on a linear unitary multiport, where each phase depends on the internal states of identical particles (i.e., not affected by the multiport) and corresponds to a cycle of the symmetric group. We show that quantum interference of $N$ particles in generic pure internal states, i.e., with no pair being orthogonal, is governed by $(N\ensuremath{-}1)(N\ensuremath{-}2)/2$ independent triad phases (each involving only three particles). The deterministic distinguishability, preventing quantum interference with two or three particles, allows for the genuine $(N\ensuremath{\ge}4)$-particle phase (interference) on a multiport: setting each particle to be deterministically distinguishable from all others except two by their internal states allows for a novel (circle-dance) interference of $N\ensuremath{\ge}4$ particles governed by a collective $N$-particle phase, while simultaneously preventing the $R$-particle interference for $3\ensuremath{\le}R\ensuremath{\le}N\ensuremath{-}1$. The genuine $N$-particle interference manifests the $N\mathrm{th}$-order quantum correlations between identical particles at a multiport output; it does not appear in the marginal probability for a subset of the particles, e.g., it cannot be detected if at least one of the particles is lost. This means that the collective phases are not detectable by the usual ``quantumness'' criteria based on the second-order quantum correlations. The results can be useful for quantum computation, quantum information, and other quantum technologies with single photons.