#### Condensed Matter Theory

### Bettina Gertjerenken et.al.: Scattering bright solitons: Quantum versus mean-field behavior

**Author(s)**:**Bettina Gertjerenken, Thomas P. Billam, Lev Khaykovich, Christoph Weiss****Title**:**Date of Upload**: 2012-10-05
**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**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.
**URL: http://www.physik.uni-oldenburg.de/condmat/Papers/p_ScatBrightSol2012.pdf (text/plain)****URL: http://arxiv.org/abs/1208.2941 (text/plain)**

**Scattering bright solitons: Quantum versus mean-field behavior**

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