Theoretical tools for atom laser beam propagation

TL;DR

This paper develops a theoretical framework for modeling atom laser beam propagation, adapting optical methods to quantum matter waves, and applies it to analyze recent experimental results.

Contribution

It introduces a set of optical-inspired tools for atom laser propagation, including integral equations, approximations, and the ABCD matrix formalism, for the first time in this context.

Findings

Derived a propagation integral equation for atom lasers.

Applied optical approximations to atom laser propagation.

Analyzed a recent experiment using the developed tools.

Abstract

We present a theoretical model for the propagation of non self-interacting atom laser beams. We start from a general propagation integral equation, and we use the same approximations as in photon optics to derive tools to calculate the atom laser beam propagation. We discuss the approximations that allow to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the ABCD matrices formalism and the beam quality factor. As an example, we apply these tools to analyse the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].