Bhowmik Anal, Haldar Sudip Kumar, Alon Ofir E
Department of Mathematics, University of Haifa, Haifa, 3498838, Israel.
Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa, 3498838, Israel.
Sci Rep. 2020 Dec 8;10(1):21476. doi: 10.1038/s41598-020-78173-w.
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.
在多体系统中，隧穿现象似乎是量子物理学的新奇现象之一，其中粒子在一个原本经典情况下禁止的势垒下在空间中移动。在此，我们从理论上描述了二维对称双阱势封闭系统中几个复杂玻色子云隧穿现象的量子动力学。我们研究了与双阱交界处正交的横向方向如何干预玻色子云的隧穿动力学。我们使用一种著名的多体数值方法，即玻色子的多组态含时哈特里（MCTDHB）方法。MCTDHB 能让我们精确获得玻色子的含时多粒子波函数，原则上该波函数包含了所研究系统所有感兴趣的信息。我们通过将双阱左阱中玻色子云的初始态制备为基态、纵向或横向激发态或涡旋态来分析隧穿动力学。我们通过分析存活概率、耗尽和碎片化以及多粒子位置、动量和角动量期望值及其方差随时间的演化，揭示了隧穿过程的详细机制。一般来说，所有物体在隧穿势垒时都会失去相干性，并且包含横向激发的态失去相干性的速度更快。特别是对于后一种态，我们表明即使横向方向看似冻结，二维玻色子约瑟夫森结中仍会出现显著的多体动力学。我们简要讨论了其意义。
