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Tunneling in a many-body system appears as one of the novel implications ofquantum physics, in which particles move in space under an otherwiseclassically-forbidden potential barrier. Here, we theoretically describe thequantum dynamics of the tunneling phenomenon of a few intricate bosonic cloudsin a closed system of a two-dimensional symmetric double-well potential. Weexamine how the inclusion of the transverse direction, orthogonal to thejunction of the double-well, can intervene in the tunneling dynamics of bosonicclouds. We use a well-known many-body numerical method, called themulticonfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHBallows one to obtain accurately the time-dependent many-particle wavefunctionof the bosons which in principle entails all the information of interest aboutthe system under investigation. We analyze the tunneling dynamics by preparingthe initial state of the bosonic clouds in the left well of the double-welleither as the ground, longitudinally or transversely excited, or a vortexstate. We unravel the detailed mechanism of the tunneling process by analyzingthe evolution in time of the survival probability, depletion and fragmentation,and the many-particle position, momentum, and angular-momentum expectationvalues and their variances. As a general rule, all objects lose coherence whiletunneling through the barrier and the states which include transverseexcitations do so faster. Implications are briefly discussed.

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction