Multi-Quantum Dark Solitons in One-Dimensional Bose Gas

TL;DR

This paper explores the quantum-classical correspondence in a one-dimensional Bose gas, demonstrating that quantum dark solitons exhibit classical-like properties such as stability and predictable collisions.

Contribution

It introduces quantum states corresponding to multi-dark solitons in a 1D Bose gas and analyzes their dynamics using exact methods, revealing classical soliton behaviors in quantum systems.

Findings

Quantum dark solitons show classical-like stability.

Quantum soliton collisions result in position shifts.

Density profiles exhibit localized solitary waves.

Abstract

Quantum and classical integrable systems share common mathematical structures, and the phenomena appearing in them are interrelated. Solitons, which universally appear in classical integrable systems, also appear in quantum integrable systems. Here, we consider quantum-classical correspondence in a one-dimensional Bose gas with repulsive delta-function interaction and present quantum states corresponding to multi-dark solitons. Using an exact method, we compute the time evolution of the density profile in the multi-quantum dark soliton states. Localized solitary waves that behave like classical dark solitons are observed in the density profile. We observe collisions of quantum dark solitons and show that they exhibit the properties of classical solitons: stability against scatterings and position shifts due to interactions.