Diffraction of particles in free fall

TL;DR

This paper analyzes quantum particle diffraction during free fall through a diffractive screen, deriving explicit solutions for single and double slits, and discusses implications for testing the equivalence principle with various quantum systems.

Contribution

It provides explicit solutions for quantum diffraction patterns in free fall and introduces a quasi-time parameter affecting the patterns, with implications for precision tests of the equivalence principle.

Findings

Diffraction patterns depend on a quasi-time related to classical parameters.

Transverse diffraction effects are governed by the ratio m/ħ.

Proposes experimental realizations with ultracold neutrons, BECs, and molecular beams.

Abstract

The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasi-time $\tau$ given by a function of the coordinate along the propagation axis in a classical combination $z_0-t^2 F/m$, while the diffraction effects along transverse axes are due solely to $m/\hbar$. The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultra cold neutrons, Bose-Einstein condensates and molecular beams are proposed.