Exploring matter wave scattering by means of the phase diagram

¹ Department of Applied Science, National Taitung University - Taitung 95092, Taiwan
² Institute of Photonics Technologies, National Tsing Hua University - Hsinchu 30013, Taiwan
³ Physics Division, National Center for Theoretical Sciences - Hsinchu 30013, Taiwan
⁴ Department of Physics, National Tsing Hua University - Hsinchu 30013, Taiwan

Received: 21 August 2018
Accepted: 25 October 2018

Abstract

For matter wave scattering from passive quantum obstacles, based on probability conservation we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering probabilities. In the phase diagram, we can not only have the physical bounds on scattering coefficients for all channels, but also indicate the probability competitions among absorption, extinction, and scattering cross-sections. With the 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. Two sets of realizable semiconductor materials and geometry are proposed for the desired probability distribution. Our results provide a guideline in designing quantum scatterers with controlling and sensing matter waves.