Geometric phase through spatial potential engineering

TL;DR

This paper introduces a spatial analog of Berry's phase for particles in a 2D landscape, enabling geometric phase manipulation through potential engineering, which is robust against potential landscape details.

Contribution

It presents a novel spatial approach to geometric phase manipulation, replacing temporal modulation with potential modulation along the particle's transverse direction.

Findings

Demonstrates non-abelian phase shifts via potential engineering

Provides theoretical derivation of the spatial geometric phase

Includes practical examples of the effect

Abstract

We propose a spatial analog of the Berry's phase mechanism for the coherent manipulation of states of non-relativistic massive particles moving in a two-dimensional landscape. In our construction the temporal modulation of the system Hamiltonian is replaced by a modulation of the confining potential along the transverse direction of the particle propagation. By properly tuning the model parameters the resulting scattering input-output relations exhibit a Wilczek-Zee non-abelian phase shift contribution that is intrinsically geometrical, hence insensitive to the specific details of the potential landscape. A theoretical derivation of the effect is provided together with practical examples.