  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.

Quantum Physics;Mesoscale and Nanoscale Physics