  In homogeneous universes the propagation of quantum fields gives rise to pair
creation of quanta with opposite momenta. When computing expectation values of
operators, the correlations between these quanta are averaged out and no
space-time structure is obtained. In this article, by an appropriate use of
wave packets, we reveal the space-time structure of these correlations. We show
that every pair emerges from vacuum configurations which are torn apart so as
to give rise to two semi-classical currents: that carried by the particle and
that of its `partner'. The partner's current lives behind the Hubble horizon
centered around the particle. Hence any measurement performed within a Hubble
patch would correspond to an uncorrelated density matrix, as for Hawking
radiation. However, when inflation stops, the Hubble radius grows and
eventually encompasses the partner. When this is realized the coherence is
recovered within a patch. Our analysis applies to rare pair creation events as
well as to cases leading to arbitrary high occupation numbers. Hence it might
be applied to primordial gravitational waves which evolve into highly squeezed
states.
