Particle-wave duality in quantum tunneling of a bright soliton

TL;DR

This paper investigates the quantum tunneling behavior of bright solitons in ultracold atoms, revealing a transition from particle-like to wave-like properties and highlighting the role of localized bound states in inelastic collisions.

Contribution

It provides a systematic analysis of bright soliton tunneling, demonstrating the interplay of classical and quantum features and emphasizing the importance of bound states in nonlinear quantum transport.

Findings

Tunneling transmission coefficient shows a finite discontinuity in the intermediate velocity regime.

Localized bound states are crucial for understanding inelastic collisions of bright solitons.

The behavior transitions from particle-like to wave-like as incident velocity varies.

Abstract

One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient ($T$) as a function in incident velocity between one (complete penetration) and zero (complete reflection), while the later always changes smoothly as a wave nature. Here we report a systematic study of the quantum tunneling property for a bright soliton in ultracold atoms, which behaves as a classical particle (matter wave) in the limit of small (large) incident velocity. In the intermediate regime, the classical and quantum properties are combined via a finite (but not full) discontinuity in the tunneling transmission coefficient. We demonstrate that the formation of a localized bound state is essential to describe such inelastic collisions, showing a nontrivial nonlinear effect on the quantum transportation of a bright soliton.