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Noncyclic geometric phase due to spatial evolution in a neutron interferometer

2005; American Physical Society; Volume: 72; Issue: 2 Linguagem: Inglês

10.1103/physreva.72.021602

1538-4446

Stefan Filipp, Yuji Hasegawa, Rudolf Loidl, Helmut Rauch,

Quantum Mechanics and Applications

We present a split-beam neutron interferometric experiment to test the noncyclic geometric phase tied to the spatial evolution of the system: The subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer, and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys 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 with severe criticism from Wagh [Phys. Rev A 59, 1715 (1999)]. The extension to a noncyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the noncyclic geometric phase in terms of paths on the Bloch-sphere.