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Spatial non-cyclic geometric phase in neutron interferometry

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 some of the authors [Hasegawa et al., PRA 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 [Wagh, PRA 59, 1715 (1999)]. The extension to 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. The theoretical treatment comprises the cyclic geometric phase as a special case, which is confirmed by experiment.

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Stefan Filipp, Yuji Hasegawa, Rudolf Loidl, Helmut Rauch. 2004-08-23. Spatial non-cyclic geometric phase in neutron interferometry. https://arxiv.org/abs/quant-ph/0408144

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