Geometric phase in coupled neutron interference loops

Abstract

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

Observation of off-diagonal geometric phases in polarized-neutron-interferometer experiments

“…Besides the interferometric method, the geometric and dynamical phases are more precisely measured with the use of a neutron polarimeter [27]. A neutron interferometer with coupled interference loops was used to create and to measure the spin-independent geometric phase in a sort of double-slit experiment [28].…”

Noncyclic geometric phase due to spatial evolution in a neutron interferometer

“…Rev. A 53, 2486(1996] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys.…”

“…Besides these theoretical work numerous experiments have been performed to verify geometric phases using various types of quantum mechanical systems, e. g. polarized photons [12] or NMR [13]. In addition, neutron interferometry has been established as a particularly suitable tool to study basic principles of quantum mechanics [14,15,16] providing explicit demonstrations [17,18,19,20] and facilitating further studies [21] of geometric phenomena.There is no reason to consider only inherent quantum properties like spin and polarization for the emergence of a geometric phase; equally well one can consider a subspace of the momentum-space of a particle and its geometry. On this issue some authors of the present article performed an experiment to test the spatial geometric phase [17] .…”

“…In addition, neutron interferometry has been established as a particularly suitable tool to study basic principles of quantum mechanics [14,15,16] providing explicit demonstrations [17,18,19,20] and facilitating further studies [21] of geometric phenomena.…”

“…The results are fully consistent with the values predicted by theory, however, there is an ambiguity in the interpretation as pointed out by Wagh [22]. He concludes that in this setup the phase picked up by a state during its evolution is merely a U(1) phase factor stemming from the dynamics of the system and not due to the geometric nature of the subjacent Hilbert space.In this paper we generalize the idea of the experiment in [17] to resolve the ambiguity in the interpretation of this antecedent neutron interferometry experiment. There the geometric phase has been measured for a 2π (cyclic) rotation of the Bloch-vector representing the path state of the neutron.…”