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New Journal of Physics

High-efficiency manipulations of triply entangled states in neutron polarimetry

Stephan Sponar, Jürgen Klepp, Katharina Durstberger-Rennhofer, Claus Schmitzer, Hannes Bartosik, Hermann Geppert, M Both, G. Badurek, Yuji Hasegawa

Published May 24, 2012• 9 citations
Publisher

Abstract

Entanglement occupies a peculiar position in quantum mechanics (QM). It occurs in quantum systems that consist of space-like separated parts or—more generally—in systems whose observables belong to disjoint Hilbert spaces. The latter is the case with single-neutron systems. Here, we report on a neutron polarimetric experiment, where a triply entangled Greenberger–Horne–Zeilinger state is exploited. The entanglement of spin, momentum and total energy degree of freedom is generated utilizing a suitable combination of radio-frequency and static magnetic fields. An average deviation of expectation values from theory—ideal circumstances—of 0.016(1) confirms the predictions of QM with high accuracy, demonstrating the high-efficiency manipulation of the entangled single-neutron system.

DOI
10.1088/1367-2630/14/5/053032

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Entanglement occupies a peculiar position in quantum mechanics (QM). It occurs in quantum systems that consist of space-like separated parts or—more generally—in systems whose observables belong to disjoint Hilbert spaces. The latter is the case with single-neutron systems. Here, we report on a neutron polarimetric experiment, where a triply entangled Greenberger–Horne–Zeilinger state is exploited. The entanglement of spin, momentum and total energy degree of freedom is generated utilizing a suitable combination of radio-frequency and static magnetic fields. An average deviation of expectation values from theory—ideal circumstances—of 0.016(1) confirms the predictions of QM with high accuracy, demonstrating the high-efficiency manipulation of the entangled single-neutron system.
Entanglement is a remarkable peculiarity in quantum mechanics. It occurs in quantum systems that consist of space-like separated parts, or in systems whose observables belong to disjoint Hilbert spaces. The latter is the case in single-neutron systems. Entangled states are renowned for exhibiting non-classical correlations between observables of individual sub-systems. In a perfect Si-crystal interferometer experiment entanglement between three degrees of freedom in a single-neutron system is created. The prepared entanglement of spin, path and energy is induced by interaction with an oscillating magnetic field. The generated Greenberger-Horne-Zeilinger (GHZ) state is analyzed with an inequality derived by Mermin, yielding a value M = 2.558(4) 2, which exhibits a clear violation of the classical assumption. In addition observation of a GHZ entanglement, consisting of spin, momentum and total energy, in a neutron polarimetric experiment is presented. Here the advantages of neutron polarimetry, such as high contrast or insensitivity to ambient disturbances, are utilized resulting in final value of M = 3.936(2) 2.
Entanglement between degrees of freedom, namely between the spin, path and (total) energy degrees of freedom, for single neutrons is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated relative phases of two-level quantum subsystems. An inequality derived by Mermin was applied to analyze the generated GHZ-like state: we determined the four expectation values and finally obtained [Formula: see text]. This demonstrates the violation of a Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, exhibits a clear inconsistency between noncontextual assumptions and quantum mechanics and confirms quantum contextuality.
Entanglement between degrees of freedom, namely between the spin, path, and (total) energy degrees of freedom, in a single-neutron system is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger (GHZ)--like state and coherently manipulated relative phases of two-level quantum subsystems. An equality derived by Mermin was applied to analyze the generated GHZ-like state: We determined the four expectation values and finally obtained $M=2.558\ifmmode\pm\else\textpm\fi{}0.004\ensuremath{\leqslant}\ensuremath{\llap{\not\;}}2$. This demonstrates a violation of Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, clearly contradicts the noncontextual assumption and confirms quantum contextuality.
A neutron interferometer experiment which clearly demonstrates the violation of a Bell-like inequality is reported. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single particle. The total wave function of spin-1/2 neutron is described in a tensor product Hilbert space. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow experimental verification of the violation of a Bell-like inequality. Manipulation of the wave function in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! The violation of the Bell-like inequality is discussed in terms of quantum contextuality and an entanglement-induced correlation.
We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single-particle. The spin-{\small 1/2} property of neutrons are utilized. The total wave function of the neutron is described in a tensor product Hilbert space. A Bell-like inequality is derived not by a non-locality but by a contextuality. Joint measurements of the spinor and the path properties lead to the violation of a Bell-like inequality. Manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space. A discussion is given on the quantum contextuality and an entanglement-induced correlation in our experiment.