  The tunneling process in a many-body system is a phenomenon which lies at the
very heart of quantum mechanics. It appears in nature in the form of
alpha-decay, fusion and fission in nuclear physics, photoassociation and
photodissociation in biology and chemistry. A detailed theoretical description
of the decay process in these systems is a very cumbersome problem, either
because of very complicated or even unknown interparticle interactions or due
to a large number of constitutent particles. In this work, we theoretically
study the phenomenon of quantum many-body tunneling in a more transparent and
controllable physical system, in an ultracold atomic gas. We analyze a full,
numerically exact many-body solution of the Schr\"odinger equation of a
one-dimensional system with repulsive interactions tunneling to open space. We
show how the emitted particles dissociate or fragment from the trapped and
coherent source of bosons: the overall many-particle decay process is a quantum
interference of single-particle tunneling processes emerging from sources with
different particle numbers taking place simultaneously. The close relation to
atom lasers and ionization processes allows us to unveil the great relevance of
many-body correlations between the emitted and trapped fractions of the
wavefunction in the respective processes.
