How an interacting many-body system tunnels through a potential barrier to open space.

Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Heidelberg, Germany.
Proceedings of the National Academy of Sciences (Impact Factor: 9.81). 08/2012; 109(34):13521-5. DOI: 10.1073/pnas.1201345109
Source: PubMed

ABSTRACT 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.

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    ABSTRACT: We derive a general linear-response many-body theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented Bose-Einstein condensates (BECs). To obtain the linear-response equations we linearize the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method, which provides a self-consistent description of many-boson systems in terms of orbitals and a state vector (configurations), and is in principle numerically-exact. The derived linear-response many-body theory, which we term LR-MCTDHB, is applicable to systems with interaction potentials of general form. From the numerical implementation of the LR-MCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubov-de Gennes (BdG) equations. The derived theory is first applied to study BECs in a one-dimensional harmonic potential. The LR-MCTDHB method contains the BdG excitations and, also, predicts a plethora of additional many-body excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow one-dimensional double-well potential. We find with LR-MCTDHB low-lying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LR-MCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.
    Physical Review A 07/2013; 88(2). · 2.99 Impact Factor
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    ABSTRACT: Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use different time-dependent processes to destabilize the systems -- a sudden displacement of the trap is accompanied by a sudden quench of the strength of the inter-particle repulsion. A rather moderate non-violent evolution of the density in the first "topology-preserved" scenario is contrasted with a highly-non-equilibrium dynamics characterizing an explosive changes of the density profiles in the second scenario. The many-body physics behind is identified and interpreted in terms of self-induced time-dependent barriers governing the respective under- and over-a-barrier dynamical evolutions. The universality of the discovered scenarios is explicitly confirmed in 1D, 2D and 3D many-body computations in (a)symmetric traps and repulsive finite/long range inter-particle interaction potentials of different shapes. Implications are briefly discussed.
    Physical Review A 12/2013; 89(6). · 2.99 Impact Factor
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    ABSTRACT: A unified view on linear response of interacting systems utilizing multicongurational time-dependent Hartree methods is presented. The cases of one-particle and two-particle response operators for identical particles and up to all-system response operators for distinguishable degrees-of-freedom are considered. The working equations for systems of identical bosons (LR-MCTDHB) and identical fermions (LR-MCTDHF), as well for systems of distinguishable particles (LR-MCTDH) are explicitly derived. These linear-response theories provide numerically-exact excitation energies and system's properties, when numerical convergence is achieved in the calculations.
    The Journal of Chemical Physics 09/2013; 140(3). · 3.12 Impact Factor

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