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Physical Review A

Observation of geometric and dynamical phases by neutron interferometry

Brendan E. Allman, Helmut Kaiser, S. A. Werner, Apoorva G. Wagh, Veer Chand Rakhecha, Johann Summhammer

Published Dec 1, 1997• 44 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.4420

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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.

arXiv:quant-ph/0103134•Mar 24, 2001•1 citation
The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, \ensuremath−1/\ensuremath\Elzxh\ensuremath∫H(t)dt,\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,\ensuremath−1/\ensuremath\Elzxh\ensuremath∫H(t)dt, given by the integrated expectation value of the Hamiltonian, and a geometric phase \ensuremathΦG(C){\ensuremath{\Phi}}_{G}(C)\ensuremathΦG​(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.
Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.
Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.
The concept of a Hamiltonian-independent geometric phase which depends only on the path of the evolution in parameter space is well established in a broad spectrum of physical phenomena. Recently it has been extended to the so-called `off-diagonal' geometric phase, which is associated with the off-diagonal matrix elements of the evolution. Here we present a polarized neutron interferometer experiment which for the first time allows an explicit observation and quantitative determination of off-diagonal geometric phase shifts: Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.