  The universal forms of quantum density and phase correlations after an
interaction quench are found for dilute 1d, 2d, and 3d condensates. A
Bogoliubov approach in a local density aproximation is used. We obtain compact
expressions for the most visible effects. Our results show how loss of phase
coherence and antibunching are built up after the quench by quantum
fluctuations. We demonstrate further that the density correlations can be
observed even with imaging resolution much worse than healing length. This
indicates that the direct measurement of counterpropagating atom pairs in situ
in a continuum system is realistic. The conditions in contemporary 1d
experiments are especially favorable for the correlation wave observations.
