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Quantum tunneling remains unexplored in many regimes of many-body quantumphysics, including the effect of quantum phase transitions on tunnelingdynamics. In general, the quantum phase is a statement about the ground stateand has no relation to far-from-equilibrium dynamics. Although tunneling is ahighly dynamical process involving many excited states, we find that thequantum phase of the Bose-Hubbard model determines phase-dependent tunnelingoutcomes for the quantum tunneling escape, or quasi-bound problem. Superfluidand Mott insulator correlations lead to a new quantum tunneling rate, thequantum fluctuation rate. This rate shows surprising and highly dynamicalfeatures, such as oscillatory interference between trapped and escaped atomsand a completely different macroscopic quantum tunneling behavior forsuperfluid and Mott insulator phases. In the superfluid phase we find thatescape dynamics are wave-like and coherent, leading to interference patterns inthe density with a rapid decay process which is non-exponential. Quantumentropy production peaks when about half the atoms have escaped. In the Mottphase, despite stronger repulsive interactions, tunneling is significantlyslowed by the presence of a Mott gap, creating an effective extra barrier toovercome. Only one atom can tunnel at a time, yet the decay process is nearlylinear, 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 ofsingle-particle quantum tunneling, quantum statistical effects on tunneling,and well-known semi-classical approaches from WKB to instanton theory. Theseresults thus open up a new regime of exploration of far-from-equilibriumdynamics for quantum simulators and quantum dynamics.

Quantum Phases and Correlations Drive the Dynamics of Macroscopic Quantum Tunneling Escape in Quantum Simulators