  Quantum coherence is a fundamental characteristic to distinguish quantum
systems from their classical counterparts. Though quantum coherence persists in
isolated non-interacting systems, interactions inevitably lead to decoherence,
which is in general believed to cause the lost of quantum correlations. Here,
we show that, accompanying to the single-particle decoherence, interactions
build up quantum correlations on the two-, three-, and multi-particle levels.
Using the quantitative solutions of the quantum dynamics of a condensate
occupying two modes, such as two bands of an optical lattice, we find out that
such dynamically emergent multi-particle correlations not only reveal how
interactions control the quantum coherence of a many-body system in a highly
intriguing means, but also evince the rise of exotic fragmented condensates,
which are difficult to access at the ground state. We further develop a generic
interferometry that can be used in experiments to measure high order
correlation functions directly.
