Particle-wave duality in quantum tunneling of a bright soliton
  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. 
Ching-Hao Wang, Tzay-Ming Hong, Ray-Kuang Lee, and Daw-Wei Wang
cond-mat.quant-gas quant-ph