Dynamics of macroscopic tunneling in elongated 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 photo-synthesis [4]. Macroscopic quantum tunneling (MQT), the aggregate tunneling behavior of a quantum many-body 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 mean-field or semiclassical observation of quantum escape has been made in Toronto [11]. However, with the rise of entanglement as a key perspective on quantum many-body 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, 14-17] 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 en-tanglement 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 semi-classical 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 qua-sibound atoms falls to 1/e of its initial valu...

Energetically constrained co-tunneling of cold atoms

“…The other motivation for studying the under-barrier tunneling of the bound pair is the problems of many-particle tunneling in correlated systems [7,8] and macroscopic tunneling of a Bose-Einstein condensate of cold atoms [9][10][11][12]. In particular, the recent paper [12] analyzes numerically the under-barrier tunneling of a bright soliton consisting of N 1 condensed atoms.…”

Entangled Dynamics in Macroscopic Quantum Tunneling of Bose-Einstein Condensates

“…The NLS approach already establishes non-smooth timeevolution of a quasibound state in the form of "blips" or bursts of condensate [27], although mean-field theory sometimes gives incorrect predictions in this regard; we demonstrate that the burst predictions are correct. Beyond mean-field, semiclassical, and instanton approaches, two time-evolving many-body studies have been performed recently.…”

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

“…Matterwave transmission and/or reflection has been investigated for ultracold atoms coherently interacting with optical lattices [14][15][16], double-well potentials [17], and silicon surfaces [18,19], and also under driving and dissipative processes [20]. Previous theoretical studies into the transmission properties of condensates with interatomic interactions through potential barriers have investigated the emergence of blips [21], the lifetime and stability of quasibound states in a potential well [22], and the transmission time [23].…”