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AIP conference proceedings

Nonadditive Mixed State Phases in Neutron Optics

Jürgen Klepp, Stephan Sponar, Stefan Filipp, Matthias Lettner, G. Badurek, Yuji Hasegawa, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 3 citations
Publisher

Abstract

In a neutron polarimetry experiment mixed neutron spin phases are determined. We consider evolutions leading to purely geometric, purely dynamical and combined phases. It is experimentally demonstrated that the sum of the geometric and dynamical phases—both obtained in separate measurements—is not equal to the associated total phase as obtained from a third measurement, unless the system is in a pure state. In this sense, mixed state phases are not additive.

DOI
10.1063/1.3109956

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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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 23, 2002•0 citations
In a neutron polarimetry experiment mixed neutron spin phases are determined. We consider evolutions leading to purely geometric, purely dynamical and combined phases. It is experimentally demonstrated that the sum of the geometric and dynamical phases—both obtained in separate measurements—is not equal to the associated total phase as obtained from a third measurement, unless the system is in a pure state. In this sense, mixed state phases are not additive.
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.
We report robust polarimetric measurements of mixed-state geometric phases. An all-optical setup was used to generate geometric phases with great versatility, thereby extending the scope of analogous methods used in neutron polarimetry. Our method allows us to explore geometric phases generated by unitarily evolving mixed states. These are realized as partially polarized single-photon states whose degree of polarization and normalized Stokes vector can be fixed independently of one another. The geometric phases correspond to both open and closed trajectories in Poincar\'e space. By exploiting the gauge invariance of geometric phases we nullify their dynamical part, thereby making the geometric phase coincide with the total (Pancharatnam) phase, which can be directly addressed by employing standard techniques.
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.