Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion

TL;DR

This paper studies the quantum reflection of dark solitons encountering reflectionless barriers and position-dependent dispersion, revealing a sharp transition at a critical speed and resonant scattering phenomena.

Contribution

It provides analytical and numerical analysis of the critical speed for quantum reflection of dark solitons, including new expressions derived from variational methods.

Findings

Quantum reflection occurs with a sharp transition at a critical speed.

Analytical expressions for the critical speed are derived and validated.

Resonant scattering occurs at the critical speed, linked to trapped modes.

Abstract

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, a time-independent, and a time-dependent variational calculations. It is then shown that resonant scattering occurs at the critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multi-soliton ejection regime is avoided.