## Particle-wave duality in quantum tunneling of a bright soliton |

Optics Express, Vol. 20, Issue 20, pp. 22675-22682 (2012)

http://dx.doi.org/10.1364/OE.20.022675

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### 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 in the latter *T* always changes smoothly with a wave nature. Here we report a systematic study of the quantum tunneling property for a bright soliton, which behaves as a classical particle (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.

© 2012 OSA

**OCIS Codes**

(020.1335) Atomic and molecular physics : Atom optics

(020.1475) Atomic and molecular physics : Bose-Einstein condensates

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: June 21, 2012

Revised Manuscript: August 17, 2012

Manuscript Accepted: September 4, 2012

Published: September 19, 2012

**Citation**

Ching-Hao Wang, Tzay-Ming Hong, Ray-Kuang Lee, and Daw-Wei Wang, "Particle-wave duality in quantum tunneling of a bright soliton," Opt. Express **20**, 22675-22682 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22675

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