State space geometry of a double-loop interferometer

The phase of a quantum state comprises information about the geometry of the state space. For example, in a magnetic field the spin state of a neutron traces out a particular path in its spherical shaped state space and the geometric phase acquired during this evolution reflects the curvature of this sphere. But the geometric phase is not only restricted to the spinor wave function, also the path of the neutron in an interferometer gives rise to a non trivial momentum state space and consequently to a geometric phase. Experimental results for a non-cyclic evolution are presented that are in agreement with theoretical predictions derived purely from geometrical considerations. By obeying a parallel transport condition dynamical contributions could largely be avoided and the measured phase is of geometric nature.