Scattering bright solitons: quantum versus mean-field behavior

TL;DR

This paper compares quantum and mean-field descriptions of bright soliton scattering, revealing significant differences at low energies and identifying signatures of quantum superpositions versus classical mixtures.

Contribution

It provides a detailed analysis of quantum versus mean-field behavior in soliton scattering, highlighting quantum superposition signatures and the transition from stepwise to continuous scattering behavior.

Findings

Quantum superpositions can be distinguished from statistical mixtures with harmonic confinement.

GPE soliton splitting is partial and does not produce superpositions.

Transmission and reflection exhibit non-continuous jumps at increased potential strength.

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 non-linear 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 non-continuously. 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.