Condensed Matter Theory

Bettina Gertjerenken Scattering bright solitons: Quantum versus mean-field behavior

Author(s): Bettina Gertjerenken, Thomas P. Billam, Lev Khaykovich, Christoph Weiss

Scattering bright solitons: Quantum versus mean-field behavior

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Article: Phys. Rev. A 86, 033608 (2012), American Physical Society

Keywords: Schrodinger-cat states, quantum matter-wave solitons, bright solitons, effective potential approach, beyond-mean-field behavior

PACS: 03.75.Gg, 03.75.Lm, 34.50.Cx, 03.65.Sq

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.

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