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Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

Stefan Filipp·Yuji Hasegawa·Rudolf Loidl·Helmut Rauch
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Abstract

We present a split-beam neutron interferometric experiment to test the non-cyclic 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 severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere.

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Stefan Filipp, Yuji Hasegawa, Rudolf Loidl, Helmut Rauch. 2005-10-17. Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer. https://doi.org/10.1103/physreva.72.021602

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