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Physical Review A

Geometric phase in coupled neutron interference loops

Yuji Hasegawa, Michael Zawisky, H. Rauch, A. Ioffe

Published Apr 1, 1996• 40 citations
Publisher

Abstract

A geometric phase factor is derived for a split-beam experiment as an example of cyclic evolutions. Poincar\'e 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. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2486

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arXiv:quant-ph/0103134•Mar 24, 2001•1 citation
A geometric phase factor is derived for a split-beam experiment as an example of cyclic evolutions. Poincar'e 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. \textcopyright{} 1996 The American Physical Society.
Neutron interferometer experiments have served as elegant demonstrations of the foundations of quantum mechanics. We show here two interferometer-experiments: one is the demonstration of a geometric phase in a split-beam experiment and the other is the measurement of off-diagonal geometric phase acquired in an evolution of a 1/2-spin system. The former was accomplished with the use of a two-loop neutron interferometer, where a reference beam can be added to the beam from one interference ioop. The combination of phase shifters and partial absorbers permitted the compensation of the dynamical phase and measurement of the geometric phase. The latter is investigated by means of a polarized neutron interferometer. Final counts with and without the polarization analysis enabled us to observe both the off-diagonal and diagonal geometric phases in two detectors. All experimental results show complete agreement with theoretical treatments.
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 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. 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.
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.
The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.
The wave function of a quantum system may acquire an additional phase factor (the geometric phase), when its parameters undergo a cyclic change. An optical manifestation of the geometric phase is the change in the phase of a light wave produced when its state of polarization is taken around a circuit on the Poincare sphere. This phase change can be verified by interferometric measurements. We describe an interferometer in which the two beams traverse the same path in opposite directions, so that their optical paths are always equal, and the phase difference between them is varied by operating on the geometric phase. Measurements made with this interferometer, at a light level at which the probability of more than one photon being present simultaneously in the interferometer was negligibly small, confirmed that the interference effects observed due to the geometric phase persist down to the single photon level.