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Physical Review Letters

Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry

Apoorva G. Wagh, Veer Chand Rakhecha, Johann Summhammer, G. Badurek, Harald Weinfurter, Brendan E. Allman, Helmut Kaiser, K. Hamacher, D. L. Jacobson, S. Werner

Published Feb 3, 1997• 88 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.78.755

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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.

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Physical Review Letters•Jun 12, 1967•89 citations
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.
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.
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 neutron polarimetric textbook experiment is performed to demonstrate the noncommutation properties of the Pauli spin operator. The polarization of the transmitted neutron beam depends upon the sequential order of two successive spin-flip devices with mutually inclined precession axes. Furthermore, an interpretation of the observed results is presented in terms of an intrinsic phase shift between two interfering mutually orthogonal spin states, which in a sequence of two successive spinor transformations stores particular information about the intermediate state. This phase shift is discussed with respect to its geometrical and dynamical components, and its formal connection with the noncommuting properties of Pauli spin operators is explicitly shown.
Experimental detection of geometric phase effects is based on interferometry techniques. The observation of a nonadiabatic geometric phase in nuclear magnetic resonance has been reported by D. Suter, K. T. Mueller, and A. Pines (1988, Phys. Rev. Lett., 60, 1218). A rigorous interpretation of their results is presented here. The experiment exploits the concept of fictitious spin-1/2 subsystems embedded in a spin system of higher order. A relevant expression for the geometric phase is derived here using the Euler rotation representation for the SU(2) group. In order to correlate the experimental data to the geometric phase, a decomposition of the density matrix in a basis of pure states is used and the isomorphism between the cyclic evolution of pure states and mixed states is constructed. Rigorous treatment of the dynamic phase, along with technical aspects of the experiment, shows that the observed echo shift is related directly to the geometric phase, in agreement with Suter et al. The observed geometric phase is classified as a frame-related phase.