Pancharatnam geometric phase originating from successive partial projections

Abstract

The spin of a polarized neutron beam subjected to a partial projection in another direction, traces a geodesic arc in the 2-sphere ray space. We delineate the geometric phase resulting from two successive partial projections on a general quantal state and derive the direction and strength of the third partial projection that would close the geodesic triangle. The constraint for the three successive partial projections to be identically equivalent to a net spin rotation regardless of the initial state, is derived.