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arXiv:1309.4253 · Physical Review A

Controlling the velocities and the number of emitted particles in the tunneling to open space dynamics

Axel U. J. Lode, Shachar Klaiman, Ofir E. Alon, Alexej I. Streltsov, L. S. Cederbaum

Published May 19, 2014• 24 citations
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Abstract

A scheme to control the many-boson tunneling process from a trap through a potential barrier to open space is devised and demonstrated. The number of ejected particles and their velocities can be controlled by two parameters, the threshold of the potential and the interparticle interaction. Employing a recently developed efficient many-body method, results for two, three, and one hundred interacting bosons in one spatial dimension can be computed numerically exactly, solving thereby an intricate problem of general interest. It is shown that the control scheme devised for the many-boson tunneling process performs very well for the dynamics of the momentum density, the correlations, and the coherence, as well as for the number of particles remaining in the trap. To interpret the many-body tunneling process, a transparent model assembling the many-body process from single-particle emission processes is derived. Analysis of the energetics of available decay channels together with the numerical results rules out the situation of two (or more) bosons tunneling together to open space. The present investigation generalizes the findings reported by us [Proc. Natl. Acad. Sci. USA 109, 13521 (2012)] for many-boson tunneling to open space in the absence of a threshold.

DOI
10.1103/physreva.89.053620

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A scheme to control the many-boson tunneling process from a trap through a potential barrier to open space is devised and demonstrated. The number of ejected particles and their velocities can be controlled by two parameters, the threshold of the potential and the interparticle interaction. Employing a recently developed efficient many-body method, results for two, three, and one hundred interacting bosons in one spatial dimension can be computed numerically exactly, solving thereby an intricate problem of general interest. It is shown that the control scheme devised for the many-boson tunneling process performs very well for the dynamics of the momentum density, the correlations, and the coherence, as well as for the number of particles remaining in the trap. To interpret the many-body tunneling process, a transparent model assembling the many-body process from single-particle emission processes is derived. Analysis of the energetics of available decay channels together with the numerical results rules out the situation of two (or more) bosons tunneling together to open space. The present investigation generalizes the findings reported by us [Proc. Natl. Acad. Sci. USA 109, 13521 (2012)] for many-boson tunneling to open space in the absence of a threshold.
The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of α-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: The overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wave function in the respective processes.
The dynamical properties of a one-dimensional system of two and three bosons escaping from an open potential well are studied in terms of the momentum distributions of particles. In the case of a two-boson system, it is shown that the single- and two-particle momentum distributions undergo a specific transition as the interaction strength is tuned through the point where tunneling switches from the pair tunneling to the sequential one. Characteristic features in the momentum spectra can be used to quantitatively determine the participation of specific decay processes. A corresponding analysis is also performed for the three-boson system, showing a scheme for generalizations to higher particle numbers. For completeness, the time-dependent Tan contact of the system is also examined and its dynamics is found to undergo a similar transition. The results provide insight into the dynamics of decaying few-body systems and offer potential interest for experimental research.
The dynamics of a few ultracold bosons tunneling from a one-dimensional potential well into an open space is studied. In such a system several decay channels can be distinguished, each corresponding to a different number of bosons escaping simultaneously. We show that as the interparticle interaction strength is changed, the system undergoes transitions between distinct regimes characterized by the dominance of different decay channels. These transitions are reflected in the behavior of the decay rate of the system, which is measurable experimentally. By means of a simple theoretical description, we show that the transitions occur at the points where a new decay channel becomes energetically viable. The results provide insight into the behavior of decaying few-body systems and may have potential interest for experiments.
The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant, and scattering states are included on an equal footing and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.
The dynamics of bosons in curved geometries have recently attracted significant interest in quantum many-body physics. Leveraging recent experimental advances in tailored trapping landscapes, we investigate the quantum transport of weakly interacting bosons in two-dimensional bent trapping potentials, showing that geometry alone can serve as a precise control knob for tunneling dynamics. Using time-adaptive many-body simulations, complemented by mean-field analysis and exact diagonalization, we analyze both static and dynamical properties of bosons confined in the bent potential. We reveal how bending an initially straight channel induces a transition from density localization to delocalization and drives the buildup of correlations in the ground state. In the dynamics, the bend acts as a tunable barrier that enables controllable tunneling: weak curvature allows coherent tunneling across the bend, while a stronger bend suppresses transport and enhances self-trapping. The tunneling rate can be precisely tuned by geometric parameters, establishing bent traps as versatile platforms for geometry-controlled quantum transport.
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.