(2012) 'Scattering bright solitons : quantum versus mean-eld behavior. ', Physical review A., 86 (3). 033608.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevA.86.033608Publisher's copyright statement:Reprinted with permission from the American Physical Society: Gertjerenken, Bettina and Billam, Thomas P. and Khaykovich, Lev and Weiss, Christoph (2012) 'Scattering bright solitons : quantum versus mean-eld behavior.', Physical Review A 86 (3): 033608 c 2012 by the 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, modi ed, 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-pro t 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. We investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the quantum behavior are particularly large. On the N -particle quantum level, adding an additional harmonic confinement leads to a simple signature to distinguish quantum superpositions from statistical mixtures. While the nonlinear character of the GPE does not allow quantum superpositions, the splitting of GPE solitons takes place only partially. When the potential strength is increased, the fraction of the soliton which is transmitted or reflected jumps noncontinuously. We explain these jumps via energy conservation and interpret them as indications for quantum superpositions on the N -particle level. On the GPE level, we also investigate the transition from this stepwise behavior to the continuous case.

We investigate numerically the collisions of two distinguishable quantum matter-wave bright solitons in a one-dimensional harmonic trap. We show that such collisions can be used to generate mesoscopic Bell states which can reliably be distinguished from statistical mixtures. Calculation of the relevant s-wave scattering lengths predicts that such states could potentially be realized in quantum-degenerate mixtures of 85 Rb and 133 Cs. In addition to fully quantum simulations for two distinguishable two-particle solitons, we use a mean-field description supplemented by a stochastic treatment of quantum fluctuations in the soliton's center of mass: We demonstrate the validity of this approach by comparison to a mathematically rigorous effective potential treatment of the quantum many-particle problem. Generating quantum entanglement between mesoscopic objects over mesoscopic distances allows exploration of a fascinating "middle-ground" between quantum and classical physics [1,2], and promises significant advances in quantum-enhanced interferometry [3]. The high degree of experimental control offered by quantum-degenerate gases makes them an ideal platform with which to explore such multi-particle entanglement [4,5]. From a fundamental perspective, the creation of maximally-entangled many-particle Bell states in quantum-degenerate gases presents an intriguing proposition. The generation of similar macroscopic Bell states of many photons is an area of current theoretical and experimental research [6,7]. In addition to their inherent fundamental interest, such states are of potential application as a resource in quantum information [7].Previously, the scattering of quantum bright matterwave solitons [8][9][10][11][12][13][14][15][16][17] in quasi-one-dimensional (1D) trapping geometries has been suggested as a way to create mesoscopic entangled states in single-species BoseEinstein condensates (BECs) [13,18,19]. In this Letter we consider a dual-species BEC [20,21] where |A, B (|B, A ) signifies that the BEC A is on the left (right) and the BEC B is on the right (left). In particular, we show that a favorable combination of interand intra-species s-wave scattering lengths means that such states may be realized using 85 Rb and 133 Cs mixtures. We also show that the interference properties of these bright-soliton Bell states distinguish them from statistical mixtures. In contrast to the Bell ground states associated with double-well potentials, our collisionallygenerated Bell states are robust to the presence of asymmetries. While distinguishable solitons are essential to produce Bell states, entanglement generation for solitons of the same species was investigated in [13].For our quasi-1D system, we consider an experimentally motivated harmonic confinement ω = 2πf . Mixtures of ultracold gases can be confined in a common optical trap with the same trap frequencies [24], yieldingwhere m A (m B ) is the atomic mass of species A (B); the interactions g = hf ⊥ a are set by the scattering lengths a and the perpendicular tra...

We argue that a time-periodically driven bosonic Josephson junction supports stable, quasiparticle-like collective response modes which are N-particle analogs of the nonspreading Trojan wave packets known from microwave-driven Rydberg atoms. Similar to their single-particle counterparts, these collective modes, dubbed 'flotons', are well described by a Floquet-Mathieu approximation, and possess a well-defined discrete set of excitations. In contrast to other, 'chaotic' modes of response, the nonheating Trojan modes conform to a mean-field description, and thus may be of particular interest for the more general question under which conditions the reduction of quantum N-particle dynamics to a strongly simplified mean-field evolution is feasible. Our reasoning is supported by phase-space portraits which reveal the degree of correspondence beween the N-particle dynamics und the mean-field picture in an intuitive manner.

In a parameter regime for which the mean-field (Gross-Pitaevskii) dynamics becomes chaotic, mesoscopic quantum superpositions in phase space can occur in a double-well potential which is shaken periodically. For experimentally realistic initial states like the ground state of some 100 atoms, the emergence of mesoscopic quantum superpositions in phase space is investigated numerically. It is shown to be reproducible even if the initial conditions slightly change. While the final state is not a perfect superposition of two distinct phase-states, the superposition is reached an order of magnitude faster than in the case of the collapse and revival phenomenon. Furthermore, a generator of entanglement is identified.

The scattering of bright quantum solitons at barrier potentials in one-dimensional geometries is investigated. Such protocols have been predicted to lead to the creation of nonlocal quantum superpositions. The centre-of-mass motion of these bright matter-wave solitons generated from attractive Bose-Einstein condensates can be analysed with the effective potential approach. An application to the case of two particles being scattered at a delta potential allows analytical calculations not possible for higher particle numbers as well as a comparison with numerical results. Both for the dimer and a soliton with particle numbers on the order of N = 100, we investigate the signatures of the coherent superposition states in an interferometric setup and argue that experimentally an interference pattern would be particularly well observable in the centre-of-mass density. Quantum superposition states of ultra-cold atoms are interesting as input states for matter-wave interferometry as they could improve signal-to-noise ratios. arXiv:1208.4984v1 [cond-mat.quant-gas]