GEOMETRIC PHASE IN COUPLED NEUTRON INTERFERENCE LOOPS

A geometric phase factor is derived for a split-beam experiment as an example of cyclic evolutions. Poincare sphere descriptions for the spl it-beam experiment show its geometric property. We observe this geomet ric phase with a two-loop neutron interferometer, where a reference be am can be added to the beam from one interference loop. The combinatio n of phase shifters and partial absorbers permitted the compensation o f the dynamical phase and measurement of the geometric phase. All the experimental results show complete agreement with our theoretical trea tment. We discuss a situation where a geometric phase exists even when the dynamical phase becomes zero.