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arXiv:quant-ph/0103134

Comment on ``Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry"

Rajendra Bhandari

Published Mar 24, 2001• 1 citation
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Abstract

We analyse a recently reported neutron interference experiment to measure a geometric phase and attempt to bring out the inadequacy of the ``phase modulo 2π" approach to the geometric phase. A modified neutron interferometer experiment to observe 2nπphase changes of topological origin resulting from closed circuits around singularities in the parameter space of the experiment is proposed.

DOI
10.48550/arxiv.quant-ph/0103134

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We analyse a recently reported neutron interference experiment to measure a geometric phase and attempt to bring out the inadequacy of the ``phase modulo 2π" approach to the geometric phase. A modified neutron interferometer experiment to observe 2nπphase changes of topological origin resulting from closed circuits around singularities in the parameter space of the experiment is proposed.
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.
We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of \ensuremath{\pi} radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.
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.
A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for phase difference between two different pure states to the case of mixed states in quantum mechanics is analyzed and the existence of phase singularities in the parameter space of an interference experiment with particles in mixed states pointed out. In the vicinity of such singular points the phase changes sharply and precisely at these points it becomes undefined. A closed circuit in the parameter space around such points results in a measurable phase shift equal to 2nπ, where n is an integer. Such effects have earlier been observed in interference experiments with pure polarization states of light, a system isomorphic to the spin-1/2 system in quantum mechanics. Implications of phase singularities for the interpretation of experiments with partially polarized and unpolarized neutrons are discussed. New kinds of topological phases involving variables representing decoherence (depolarization) of pure states are predicted and experiments to verify them suggested.
In this paper, we review how neutron–mirror-neutron mixing can induce a geometric phase for ordinary neutrons and how this phase can be accessed with a two-arm interferometer. By choosing different magnetic fields and suitable arm lengths, the dynamical phase difference can be canceled, so that the observed phase is directly related to the mixing. We summarize the main formulas and discuss representative regions of the neutron–mirror-neutron parameter space that can be explored with cold-neutron interferometry [A. Capolupo, G. Pisacane, A. Quaranta and F. Romeo, Phys. Dark Univ. 46 (2024) 101688].
A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].