Observation of Off-Diagonal Geometric Phases in Polarized-Neutron-Interferometer Experiments

The concept of a Hamiltonian-independent geometric phase which depends only on the path of the evolution in parameter space is well established in a broad spectrum of physical phenomena. Recently it has been extended to the so-called `off-diagonal' geometric phase, which is associated with the off-diagonal matrix elements of the evolution. Here we present a polarized neutron interferometer experiment which for the first time allows an explicit observation and quantitative determination of off-diagonal geometric phase shifts: Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.