Entangled Dynamics in Macroscopic Quantum Tunneling of Bose-Einstein Condensates

Abstract

Tunneling of a quasibound state is a non-smooth process in the entangled many-body case. Using time-evolving block decimation, we show that repulsive (attractive) interactions speed up (slow down) tunneling, which occurs in bursts. While the escape time scales exponentially with small interactions, the maximization time of the von Neumann entanglement entropy between the remaining quasibound and escaped atoms scales quadratically. Stronger interactions require higher order corrections. Entanglement entropy is maximized when about half the atoms have escaped.Tunneling is one of the most pervasive concepts in quantum mechanics and is essential to contexts as diverse as α-decay of nuclei [1], vacuum states in quantum cosmology [2] and chromodynamics [3], and photosynthesis [4]. Macroscopic quantum tunneling (MQT), the aggregate tunneling behavior of a quantum manybody wavefunction, has been demonstrated in many condensed matter systems [5,6] and is one of the remarkable features of Bose-Einstein Condensates (BECs), ranging from Landau-Zener tunneling in tilted optical lattices [7] to the AC and DC Josephson effects in double wells [8,9], as well as their quantum entangled generalizations [10]. The original vision of quantum tunneling was in fact the quantum escape or quasibound problem by Gurney and Condon in 1929 [1], and recently the first meanfield or semiclassical observation of quantum escape has been made in Toronto [11]. However, with the rise of entanglement as a key perspective on quantum manybody physics, the advent of powerful entangled dynamics matrix-product-state (MPS) methods [12,13], and the possibility of observing the moment-to-moment time evolution of quasibound tunneling dynamics directly in the laboratory [11,[14][15][16][17] it is the right time to revisit quantum escape. In this Letter, we take advantage of the powerful new toolset for quantum many-body simulations [13, 18] to show that the many-body quantum tunneling problem differs in key respects from our expectations from semiclassical and other well-established approaches to tunneling.Specifically, we use time-evolving block decimation (TEBD) to follow lowly entangled matrix product states [12,19] for the quantum escape of a quasibound ultracold Bose gas initially confined behind a potential barrier. Our use of a Bose-Hubbard Hamiltonian [20] can be viewed either as a discretization scheme or as an explicitly enforced optical lattice used to control the tunneling dynamics. Unlike instanton and semiclassical approaches, we are able to follow the von Neumann entanglement entropy, number fluctuations, quantum depletion, and other quantum many-body aspects of time evolution of the many-body wavefunction. Such measures clarify when semiclassical approaches are and are not applicable. They also show that hiding in the semiclassical averaged picture are other many-body features with radically different scalings: the escape time t esc , i.e., the time at which the average number of remaining quasibound atoms falls to 1/e of its initial value, ...

Beating effects of vector solitons in Bose-Einstein condensates

“…On the other hand, one can produce the initial density distribution and phase for beating solitons in BEC systems through the well-developed density and phase modulation techniques [6,[13][14][15]27]. The beating period would be measured directly in real experiments [30]. Then the beating period T = 2π ∆ , where ∆ denotes the energy eigenvalue difference in some certain quantum wells.…”

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

“…Figure 3(d) clearly shows that the system can be taken to longer lattices without growth in entanglement. This implies that the system can be effectively simulated with matrix product state methods, though full local dimension is required for convergence, and likely to be an issue for other driven and/or highly oscillatory dynamics [39].…”

Asymmetric Tunneling of Bose-Einstein Condensates

“…This is especially true given recent experimental advances in Bose-Einstein condensates (BEC's), enabling researchers to directly observe the tunneling of complex systems for the first time [6,16,17]. In addition, extensive computational research has been done with BEC tunneling, both using mean-field [18][19][20][21][22][23][24] and many-body [25][26][27][28] theories.…”