Exploring matter wave scattering by means of the phase diagram

TL;DR

This paper introduces a phase diagram framework for analyzing matter wave scattering from quantum obstacles, enabling the design of scatterers with tailored directional scattering properties and minimal scattering in specific directions.

Contribution

It proposes a novel phase diagram approach to explore and control matter wave scattering patterns, including conditions for zero scattering directions.

Findings

Phase diagram maps physical bounds of scattering coefficients.

Interference between channels can steer scattering distribution.

Conditions for quantum scatterers with minimal or zero scattering are identified.

Abstract

For matter wave scattering from passive quantum obstacles, we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering patterns. In the phase diagram, we can not only have the physical bounds on scattering coefficients for all channels, but also indicate the competitions among absorption, extinction, and scattering cross sessions. With help of this phase diagram, we discuss different scenarios to steer scattering probability distribution, through the interference between $s$- and $p$-channels. In particular, we reveal the required conditions to implement a quantum scatterer, i.e., a quantum dot in semiconductor matrix, with a minimum (or zero) value in the scattering probability toward any direction. Our results provide a guideline in designing quantum scatterers with controlling and sensing matter waves.