Structured Quantum Projectiles

TL;DR

This paper derives analytical expressions for structured matter waves in linear potentials, revealing their classical trajectories and phase profiles, which simplifies quantum effects analysis in matter wave interferometry.

Contribution

It provides a general analytical framework for understanding structured matter waves under linear potentials, unifying their behavior regardless of wave structure.

Findings

Center of mass follows classical parabolic trajectory

Wave phase profile can be analytically determined

Results applicable to all structured matter waves

Abstract

Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an electric charge. Matter waves, thus, can experience alterations in their wave-like features while propagating through uniform fields to which a linear potential can be attributed. Here, we derive analytical expressions for structured matter waves subjected to linear potentials. We show that the center of mass of corresponding to these wavefunctions follows the classical parabolic trajectory attributed to this potential and also provide the additional phase profile acquired by the wave upon propagation. Furthermore, we find that these features are identical for any structured wave, thus significantly simplifying the action of quantum effects pertaining to this potential in applications relying on structured quantum waves.