Scattering bright solitons: Quantum versus mean-field behavior

Gertjerenken, Bettina; Billam, Thomas P.; Khaykovich, Lev; Weiss, Christoph

doi:10.1103/physreva.86.033608

Scattering bright solitons: Quantum versus mean-field behavior

Gertjerenken, Bettina; Billam, Thomas P.; Khaykovich, Lev; Weiss, Christoph

Authors

Bettina Gertjerenken

Thomas P. Billam

Lev Khaykovich

Christoph Weiss

Abstract

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.

Citation

Gertjerenken, B., Billam, T. P., Khaykovich, L., & Weiss, C. (2012). Scattering bright solitons: Quantum versus mean-field behavior. Physical Review A, 86(3), Article 033608. https://doi.org/10.1103/physreva.86.033608

Journal Article Type	Article
Publication Date	Sep 7, 2012
Deposit Date	Jul 23, 2014
Publicly Available Date	Oct 15, 2014
Journal	Physical Review A
Print ISSN	1050-2947
Electronic ISSN	1094-1622
Publisher	American Physical Society
Peer Reviewed	Peer Reviewed
Volume	86
Issue	3
Article Number	033608
DOI	https://doi.org/10.1103/physreva.86.033608

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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-field behavior.', Physical Review A 86 (3): 033608 © 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, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.