Interaction of a propagating guided matter wave with a localized potential

TL;DR

This paper develops a theoretical framework for understanding how guided matter waves interact with localized potentials, analyzing both weak and strong interaction regimes, and suggests experimental methods to control and measure these interactions.

Contribution

It introduces a comprehensive quantum scattering model for guided matter waves interacting with localized potentials, including analytical and non-perturbative approaches, and explores new effects like confinement-induced resonances.

Findings

Analytical output state under Born approximation with Gaussian potential

Validation of approximation through numerical simulations

Identification of confinement-induced resonances in non-perturbative regime

Abstract

We provide a theoretical framework to describe the interaction of a propagating guided matter wave with a localized potential in terms of quantum scattering in a confined environment. We analyze how this scattering correlates the longitudinal and transverse degrees of freedom and work out analytically the output state under the Born approximation using a Gaussian localized potential. In this limit, it is possible to engineer the potential and achieve coherent control of the output channels. The robustness of this approximation is studied by comparing the stationary scattering theory to numerical simulations involving incident wave packets. It remains valid in a domain of weak localized potential that is achievable experimentally. We infer a possible method to determine the longitudinal coherence length of a guided atom laser. Then, we detail the non-perturbative regime of the interaction of the guided matter wave with the localized potential using a coupled channel approach. This approach is worked out explicitly with a square potential. It yields new non-perturbative effects such as the occurrence of confinement-induced resonances. The perspectives opened by this work for experiments are discussed.