Scattering bright solitons: Quantum versus mean-field behavior

Abstract

(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.

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

“…therein). The behaviour of solitary waves is similar in soliton-like regimes; in particular, fast solitary wave collisions with a narrow barrier lead to smooth splitting of an incoming solitary wave into transmitted and reflected solitary waves [108,109,[114][115][116]. This behaviour is analogous to bright solitons in the NLSE scattering from a δ -function potential: it can be analytically demonstrated in such a situation that the incoming bright soliton is split into transmitted and reflected components, each of which consist mainly of a bright soliton, plus a small amount of radiation [114].…”

“…In the following sections we briefly review existing proposals for the necessary coherent beam-splitting of solitary waves, using an internal-state interference protocol [81] (Section 7.2.1) and potential barriers [106][107][108][109] (Section 7.2.2). In Section 7.3 we outline proposals to use interferometry devices based on bright solitary waves for improved sensitivity in the measurement of atom-surface interactions [110].…”

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

“…(7) for the density profile reduces to a cubic algebraic equation for n 1/3 (3π 2 ) 2/3 n 2/3 + r 2 + γ z 2 n = 2μ (11) at r < r TF , and n = 0 at r > r TF , where the TF radius is…”

“…In particular, the use of solitons in matterwave interferometers should help to dramatically increase the accuracy of these devices (see Refs. [8][9][10][11][12] and a recent review [13]). …”

Mean-field analog of the Hong-Ou-Mandel experiment with bright solitons

“…Restricting our consideration (for the present work) to attractive interactions and bright solitary waves, we can note that both one [12] and many [13,14] (as a result of the modulational instability) such waves have been created in 7 Li. More recently, they have also been produced in 85 Rb [15], and furthermore the interactions between them and with barriers have been explored [16][17][18][19] both at the mean-field and at the quantum-mechanical [20,21] level. Very recently experimental signatures have also been reported, both for the case of interactions with barriers [22] and for those between bright solitons with different phases [23].…”