Effects of the transverse direction on the many-body tunneling dynamics

Tunneling in a many-particle system appears as one of the novel implications of quantum physics. Here, we theoretically investigate the tunneling dynamics of a few intricate bosonic clouds in a two-dimensional symmetric double-well potential. We unravel how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds by employing a well-known many-body numerical method, the multiconfigurational time-dependent Hartree for bosons (MCTDHB), which incorporates quantum correlations exhaustively. We analyze the tunneling dynamics by preparing the initial state of the bosonic clouds in the left well of the double-well either as the ground, longitudinally or transversely excited, or a vortex state. We examine the detailed mechanism of the tunneling process by analyzing the evolution in time of the survival probability, depletion and fragmentation, and the many-particle position, momentum, and angular-momentum expectation values and their variances. As a general rule, all objects lose coherence while tunneling through the barrier and the states which include transverse excitations do so faster. In particular for the later states, we show that even when the transverse direction is practically frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs.