  Strongly interacting many-body system of bosons exhibiting the quantum carpet
pattern is investigated exactly by using Gaudin solutions. We show that this
highly coherent design usually present in noninteracting, single-body scenarios
gets destroyed by weak-to-moderate interatomic interactions in an ultracold
bosonic gas trapped in a box potential. However, it becomes revived in a very
strongly interacting regime, when the system undergoes fermionization. We track
the whole single- to many-body crossover, providing an analysis of de- and
rephasing present in the system.
