Observation of geometric and dynamical phases by neutron interferometry

The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $-1/ħ\int H\left(t\right)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\Phi }_G\mathrm{}\left(C\right)\mathrm{}$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of π radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.