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Selected applications of the MCTDHB

  • Generic quantum many-body dynamics of trapped strongly repulsive Bose systems with finite/long range interactions (movie 1, 2D); (movie 2, 2D); (movie 3, 3D); (movie 4, 3D).
    Evolutions of a two-hump two-fold fragmented initial state in 2D and 3D induced by a sudden displacement of the trap along with a simultaneous quench of the inter-particle repulsion (computed with MCTDHB). Strong decrease of the interaction leads to `over-a-barrier' dynamics (movies 1 and 3), whereas moderate increase of the interaction leads to `under-a-barrier' dynamics (movies 2 and 4). The concept of interaction-induced time-dependent barriers, used to explain the two generic dynamical regimes, is visualized in 2D (movies 1 and 2). For more details, see:
    Generic regimes of quantum many-body dynamics of trapped bosonic systems with strong repulsive interactions, O. I. Streltsova, O. E. Alon, L. S. Cederbaum, A. I. Streltsov, arXiv:1312.6174v1 [cond-mat.quant-gas].

  • Build-up of correlations and wave chaos in a BEC expanding in a 1D periodic potential (movie).
    A weakly interacting BEC is prepared in the ground state of a 1D harmonic potential. The potential is then switched off and the BEC is allowed to expand in a shallow periodic potential. The movie shows the two-particle normalized correlation function g(2)(x1,x2,x1,x2,t) as well as the (scaled) density of the second natural orbital as a function of time (computed with MCTDHB). The BEC is initially almost perfectly coherent. Deviations from g(2)=1 emerge at about t=3t0. This onset of depletion and loss of coherence on the many-body level is in close correspondence with the onset of wave chaos in the Gross-Pitaevskii equation, that is, the onset of exponential separation in Hilbert space of two nearby condensate wave functions. For more details, see:
    Wave chaos as signature for depletion of a Bose-Einstein condensate, I. Brezinová, A. U. J. Lode, A. I. Streltsov, O. E. Alon, L. S. Cederbaum, and J. Burgdörfer, Phys. Rev. A 86, 013603 (2012), arXiv:1202.5869.

  • Few-boson decay-by-tunneling and fragmentation (movie 1); (movie 2).
    Two weakly interacting bosons are prepared in an harmonic trap. When the trap is made open such that the bosons can tunnel out, the initially-coherent two-boson system becomes fragmented. The fragmentation manifests itself with the emergence of a pronounced two-peak structure in momentum space (computed with MCTDHB, see movie 1) and the correlation function |g(x'1,x1,t)|2 differing from 1 (computed with MCTDHB, see movie 2). The corresponding Gross-Pitaevskii dynamics, where the system remains coherent at all times, exhibits a single-peak structure in momentum space and has |g(x'1,x1,t)|2=1 (not shown). For more details, see:
    Mechanism of Tunneling in Interacting Open Ultracold Few-Boson Systems, A. U. J. Lode, A. I. Streltsov, O. E. Alon, L. S. Cederbaum, arXiv:1005.0093v1 [cond-mat.quant-gas].

  • Exact many-body dynamics of a bosonic Josephson junction (movie).
    In a bosonic Josephson junction the density tunnels from one side of the junction to the other. The repulsive interaction between the particles can lead to an effect known as self-trapping, a large increase in the time needed for the bosons to tunnel through the potential barrier from a certain (repulsive) interaction strength onwards. Here we compare the bosonic Josephson junction dynamics of 100 bosons based on two approaches: the numerically exact solution of the time-dependent many-body Schrödinger equation obtained using the MCTDHB algorithm, and the respective result based on the Bose-Hubbard model. The self-trapping effect can be seen in both results, but the exact dynamics is very different from that of the Bose-Hubbard model. Shown is the density of the condensate. For more details, see:
    Exact quantum dynamics of a bosonic Josephson junction, K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. Lett. 103, 220601 (2009), arXiv:0905.0902.

  • Fragmenton formation (movie).
    Formation of a dynamically-stable fragmented object termed Fragmenton in 1D attractive Bose gases. Given a ground-state bright soliton, making the interaction suddenly more attractive (here by a factor of four) leads to the breakup of the bright soliton into two sub-clouds, signifying the birth of the Fragmenton. The phenomenon is seen on the many-body level (computed with MCTDHB), whereas on the Gross-Pitaevskii mean-field level, which assumes all bosons to remain coherent at all times, it does not occur. For more details, see:
    Formation and Dynamics of Many-Boson Fragmented States in One-Dimensional Attractive Ultracold Gases, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. Lett. 100, 130401 (2008), arXiv:0711.2778.