Exact Quantum Dynamics of a Bosonic Josephson Junction

Sakmann, Kaspar; Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.

doi:10.1103/physrevlett.103.220601

Cited by 176 publications

(226 citation statements)

References 26 publications

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“…More recently, the potential of the MCTDH method for the treatment of systems of indistinguishable particles, either fermions or bosons, has been realized as well, and many applications can be counted nowadays in such new directions. [21][22][23][24][25][26][27] Although the equations of motion (EOM) remain the same in such cases, the symmetry properties of the wavefunction and the often two-body nature of the interactions have led to the appearance of dedicated programs that specifically and efficiently deal with such cases. [28][29][30] In general, the solution of the time-dependent Schrödinger equation in a direct-product basis of 1D a) Electronic mail: oriol.vendrell@cfel.de.…”

Section: Introductionmentioning

confidence: 99%

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Vendrell¹,

Meyer

2011

The Journal of Chemical Physics

360

388

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The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is discussed and a fully general implementation for any number of layers based on the recursive ML-MCTDH algorithm given by Manthe [J. Chem. Phys. 128, 164116 (2008)] is presented. The method is applied first to a generalized Henon-Heiles (HH) Hamiltonian. For 6D HH the overhead of ML-MCTDH makes the method slower than MCTDH, but for 18D HH ML-MCTDH starts to be competitive. We report as well 1458D simulations of the HH Hamiltonian using a seven-layer scheme. The photoabsorption spectrum of pyrazine computed with the 24D Hamiltonian of Raab et al. [J. Chem. Phys. 110, 936 (1999)] provides a realistic molecular test case for the method. Quick and small ML-MCTDH calculations needing a fraction of the time and resources of reference MCTDH calculations provide already spectra with all the correct features. Accepting slightly larger deviations, the calculation can be accelerated to take only 7 min. When pushing the method toward convergence, results of similar quality than the best available MCTDH benchmark, which is based on a wavepacket with 4.6 × 10 7 time-dependent coefficients, are obtained with a much more compact wavefunction consisting of only 4.5 × 10 5 coefficients and requiring a shorter computation time.

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Section: Introductionmentioning

confidence: 99%

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Vendrell¹,

Meyer

2011

The Journal of Chemical Physics

360

388

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“…In order to investigate the differences between mean-field dynamics and quantum dynamics on the N -particle level in more detail, a BEC in a double-well potential is an ideal system [5,17,[33][34][35][36][37][38][39][40][41][42]. While differences between mean-field dynamics and N -particle quantum dynamics have been observed for small BECs [33,35], it would be tempting to assume that Eq.…”

Section: Introductionmentioning

confidence: 99%

Beyond-mean-field behavior of large Bose-Einstein condensates in double-well potentials

Gertjerenken

Weiß

2013

Phys. Rev. A

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(2013) 'Beyond-mean-eld behavior of large Bose-Einstein condensates in double-well potentials. ', Physical review A., 88 (3). 033608.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevA.88.033608Publisher's copyright statement:Reprinted with permission from the American Physical Society: Gertjerenken, Bettina and Weiss, Christoph (2013) 'Beyond-mean-eld behavior of large Bose-Einstein condensates in double-well potentials.', Physical review A., 88 (3). 033608. c 2013 American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. For the dynamics of Bose-Einstein condensates (BECs), differences between mean-field (Gross-Pitaevskii) physics and N -particle quantum physics often disappear if the BEC becomes larger and larger. In particular, the time scale for which both dynamics agree should thus become larger if the particle number increases. For BECs in a double-well potential, we find both examples for which this is the case and examples for which differences remain even for huge BECs on experimentally realistic short time scales. By using a combination of numerical and analytical methods, we show that the differences remain visible on the level of expectation values even beyond the largest possible numbers realized experimentally for BECs with ultracold atoms.

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“…The MCTDHB method has been shown to produce accurate many-body solutions in various applications [19,[40][41][42][43][44], and is well documented in the literature [45,46]. Until recently, MCTDHB has been applied to one-dimensional systems.…”

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confidence: 99%

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

et al. 2014

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A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate for the first time the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed by a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs. [4][5][6]. While three-dimensional trapped BECs have been extensively studied since their discovery, the static and time-dependent properties of their two-dimensional counterparts are comparatively less explored.One of the most popular scenarios studied with ultracold bosonic atoms, both experimentally and theoretically, is the splitting of a BEC by a central barrier into two spatially-disjoint clouds, e.g., Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. It is a common practice that in order to produce a fragmented BEC in the splitting process, the ground state must be fragmented. This renders high barriers and strong interaction strengths necessary. Previous works dealt with splitting of a BEC in one or three spatial dimensions. To the best of our knowledge, splitting of a BEC in two spatial dimensions has not been explored experimentally or theoretically on the many-body level.In the present work we investigate theoretically, on an accurate many-body level, the physics of splitting a twodimensional (2D) BEC. A natural approach is to exploit the 2D symmetry of the system. We thus split a circular BEC by a radial potential barrier, see Fig. 1a for an illustration. This would lead to two concentric clouds, unlike the above-discussed common way of splitting a BEC and, as we shall see below, enrich the physics of BEC splitting.By analyzing the many-body time-independent and time-dependent wavefunctions of the system, we construct both static and dynamic phase diagrams of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We therefore demonstrate the dynamical fragmentation of a BEC, despite its ground state being fully condensed. The results imply that a large manifold of fragmented excited states can significantly impact the dynamics of 2D BECs.We consider a repulsive BEC with N = 100 bosons in the 2D circular trap shown in Fig. 1a. Throughout this work dimensionless units are used, such that the single-particle kinetic-energy operator readsT (r) = − 1 2 ∇ 2 r [22]. The explicit form of the one-body potential is given by V (r) = V trap (r) + V barrier (r). Here V trap (r) = {200e −(r−rc) 4 /2 , r ≤ r c = 9; 200, r > r c } is a flat trap which has the shape of "a crater" and V barrier (r) = 200e ...

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Exact Quantum Dynamics of a Bosonic Josephson Junction

Cited by 176 publications

References 26 publications

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine

Beyond-mean-field behavior of large Bose-Einstein condensates in double-well potentials

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

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