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We unravel the out-of-equilibrium quantum dynamics of a few interactingbosonic clouds in a two-dimensional asymmetric double-well potential at theresonant tunneling scenario. At the single-particle level of resonanttunneling, particles tunnel under the barrier from, typically, the ground-statein the left well to an excited state in the right well, i.e., states ofdifferent shapes and properties are coupled when their one-particle energiescoincide. In two spatial dimensions, two types of resonant tunneling processesare possible, to which we refer to as longitudinal and transversal resonanttunneling. Longitudinal resonant tunneling implies that the state in the rightwell is longitudinally-excited with respect to the state in the left well,whereas transversal resonant tunneling implies that the former istransversely-excited with respect to the latter. We show that interactionbetween bosons makes resonant tunneling phenomena in two spatial dimensionsprofoundly rich, and analyze these phenomena in terms of the loss of coherenceof the junction and development of fragmentation, and coupling betweentransverse and longitudinal degrees-of-freedom and excitations. To this end, adetailed analysis of the tunneling dynamics is performed by exploring the timeevolution of a few physical quantities, namely, the survival probability,occupation numbers of the reduced one-particle density matrix, and themany-particle position, momentum, and angular-momentum variances. In general,we display the impact of the transversal and longitudinal degrees-of-freedom inthe many-boson tunneling dynamics at the resonant tunneling scenarios.

Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction: Mean-field and many-body dynamics