Dynamics of Macroscopic Quantum Tunneling from Superfluid to Mott Insulating Regimes

In 1928 quantum tunneling was discovered to explain alpha decay, and in 2002 the Mott-Superfluid quantum phase transition was experimentally observed. How would the transition between a Superfluid and Mott insulator alter the tunneling dynamics of a many-body system? Specifically, we study bosons in a quasi one-dimensional meta-stable trap, modeled by the Bose-Hubbard Hamiltonian, using matrix product state methods which grant access to many-body observables, and compare to mean-field, which fails for strong interactions. We quantify how the barrier and interaction energies can amplify or reduce number fluctuations by an order of magnitude. Bond entropy is found to maximize when nearly half of the atoms have escaped in a Superfluid, while Mott-dominated interactions result in a maximum when only one quarter of the atoms have escaped. Mott-dominated dynamics also produce strong, long-range, and off-diagonal correlations. We find significantly different time scales in observables, i.e., when bond entropy and fluctuations maximize. Periodic fluctuations in time derivatives are found for several observables, scaling with the size of the meta-stable trap, Finally, preliminary results suggest that interaction energies can alter the escape velocity of atoms.