Structured Quantum Projectiles

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 e ects pertaining to
this potential in applications relying on structured quantum waves