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

Abstract

Tunneling in a many-body system appears as one of the novel implications of quantum physics, in which particles move in space under an otherwise classically-forbidden potential barrier. Here, we theoretically describe the quantum dynamics of the tunneling phenomenon of a few intricate bosonic clouds in a closed system of a two-dimensional symmetric double-well potential. We examine how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds. We use a well-known many-body numerical method, called the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHB allows one to obtain accurately the time-dependent many-particle wavefunction of the bosons which in principle entails all the information of interest about the system under investigation. 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 unravel 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 seemingly frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs. Implications are briefly discussed.

Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction

“…It is noted that as the considered interparticle interaction in the dynamics is weak, the preparation of the initial state in the relaxation process either with noninteracting bosons or with does not affect the dynamical behavior of the properties discussed in this work. The consistency of preparation of the initial state is documented in the supplemental materials of 29 . The natural units are employed throughout this work.…”

“…Unconventional orbital superfluidity in the P - and F -bands of a bipartite optical square lattice was achieved in 27 , 28 . Recently, we explored the tunneling dynamics of ultracold bosons in a symmetric double-well potential where the atomic motion lies in the ground as well as excited bands 29 . Dynamics and quantum optimal control of different complex atomic quantum systems and the transition from the ground to complicated excited states have been investigated in anharmonic trap or in optical lattices 30 – 32 .…”

“…In order to investigate the tunneling dynamics in the longitudinal resonant scenario, we consider two different structures of bosonic clouds, i.e., the ground and transversely excited ( y -excited) states. Although, the ground state has a one-dimensional analog, but to create a transversely excited state, one requires at least a 2D geometry 29 . Therefore, to investigate the effect of the longitudinal resonant tunneling on the very basic state which includes transverse excitations is of fundamental interest.…”

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

“…[ 44 , 48 , 49 ] and an exploration of the competition of long-ranged dipolar interactions and artificial magnetic fields for two-dimensional ultracold atoms. Another direction of physical interest is the dynamics of two-dimensional bosonic Josephson junctions [ 99 ] subject to gauge fields and the resulting tunneling of (phantom) vortices or the emergence of quantum turbulence [ 100 ] via entropy production [ 101 ], which, in turn, as we have shown above, could result from the presence of artificial gauge fields.…”

Josephson effect at finite temperature along the BCS-BEC crossover

“…In each case, the theoretical results appear to systematically overestimate the experimental values of the critical current, although the discrepancy decreases for increasing V 0 /E t F . This discrepancy may (at least partly) originate from the nontrivial geometrical shape of the experimental barrier transverse to the current flow, whose details are not taken into account in the present calculations but could affect the flow of the supercurrent and lead to a lost of coherence [58]. Although these kinds of geometrical effects could possibly be introduced within the LPDA approach, their consideration is beyond the scope of this work.…”