  Quantum tunneling remains unexplored in many regimes of many-body quantum
physics, including the effect of quantum phase transitions on tunneling
dynamics. In general, the quantum phase is a statement about the ground state
and has no relation to far-from-equilibrium dynamics. Although tunneling is a
highly dynamical process involving many excited states, we find that the
quantum phase of the Bose-Hubbard model determines phase-dependent tunneling
outcomes for the quantum tunneling escape, or quasi-bound problem. Superfluid
and Mott insulator correlations lead to a new quantum tunneling rate, the
quantum fluctuation rate. This rate shows surprising and highly dynamical
features, such as oscillatory interference between trapped and escaped atoms
and a completely different macroscopic quantum tunneling behavior for
superfluid and Mott insulator phases. In the superfluid phase we find that
escape dynamics are wave-like and coherent, leading to interference patterns in
the density with a rapid decay process which is non-exponential. Quantum
entropy production peaks when about half the atoms have escaped. In the Mott
phase, despite stronger repulsive interactions, tunneling is significantly
slowed by the presence of a Mott gap, creating an effective extra barrier to
overcome. Only one atom can tunnel at a time, yet the decay process is nearly
linear, completely defying the single-particle exponential model. Moreover,
quantum entropy peaks when only about one quarter of the atoms have escaped.
These and many other such effects go beyond the usual notions of
single-particle quantum tunneling, quantum statistical effects on tunneling,
and well-known semi-classical approaches from WKB to instanton theory. These
results thus open up a new regime of exploration of far-from-equilibrium
dynamics for quantum simulators and quantum dynamics.
