Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-onedimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schrödinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F , the coherence by means of the visibility α of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and α to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.

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“…(16), (18), and (20)], we can evaluate the coherence visibility (28) in the three regimes U/J → −∞, U/J → +∞, and U → 0. In the first case, Eq.…”

Section: Coherence and Entanglement At Zero Temperaturementioning

confidence: 99%

Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schrödinger cat states to separable Fock states

et al. 2011

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“…[13,14]). In general, situations with important quantum correlations, where a mean-field approach is no longer adequate, are in the focus of current research, e.g., many-particle entanglement [15], the experimental realization * b.gertjerenken@uni-oldenburg.de of entangled squeezed states [16], mesoscopic quantum superpositions [17][18][19][20][21], and mean-field chaos [22,23]. In order to estimate time scales on which the mean-field dynamics still agrees with N -particle quantum dynamics, classical-field methods can be used to approximate the quantum dynamics by averaging over mean-field solutions [24][25][26][27][28][29][30][31][32], thus mimicking quantum uncertainties that disappear in the mean-field limit (2) but will always be present for finite particle numbers.…”

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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“…2 (c, d). Such a failure or breakdown of the mean-field theory due to rapid decoherence has long been noticed in literature [28][29][30][31]. In Ref.…”

Section: Example Of Triple-well Modelmentioning

confidence: 94%

Ehrenfest breakdown of the mean-field dynamics of Bose gases

Han

2016

Phys. Rev. A

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The mean-field dynamics of a Bose gas is shown to break down at time τ h = (c1/γ) ln N where γ is the Lyapunov exponent of the mean-field theory, N is the number of bosons, and c1 is a systemdependent constant. The breakdown time τ h is essentially the Ehrenfest time that characterizes the breakdown of the correspondence between classical and quantum dynamics. This breakdown can be well described by a quantum fidelity defined for one-particle reduced density matrices. Our results are obtained with the formalism in particle-number phase space and are illustrated with a triple-well model. The logarithmic quantum-classical correspondence time may be verified experimentally with Bose-Einstein condensates.

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Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos

Cited by 14 publications

References 58 publications

Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schrödinger cat states to separable Fock states

Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schrödinger cat states to separable Fock states

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

Ehrenfest breakdown of the mean-field dynamics of Bose gases

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