Quantum coherence in momentum space of light-matter condensates

We show that the use of momentum-space optical interferometry, which avoids any spatial overlap between two parts of a macroscopic quantum state, presents a unique way to study coherence phenomena in polariton condensates. In this way, we address the longstanding question in quantum mechanics: "\emph{Do two components of a condensate, which have never seen each other, possess a definitive phase?}" [P. W. Anderson, \emph{Basic Notions of Condensed Matter Physics} (Benjamin, 1984)]. A positive answer to this question is experimentally obtained here for light-matter condensates, created under precise symmetry conditions, in semiconductor microcavities taking advantage of the direct relation between the angle of emission and the in-plane momentum of polaritons.