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arXiv:1404.3512 · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment

Improvement of the polarized neutron interferometer setup demonstrating violation of a Bell-like inequality

Hermann Geppert, Tobias Denkmayr, Stephan Sponar, Hartmut Lemmel, Yuji Hasegawa

Published Jul 7, 2014• 25 citations
arXivHTMLPDF

Abstract

For precise measurements with polarised neutrons high efficient spin-manipulation is required. We developed several neutron optical elements suitable for a new sophisticated setup, i.e., DC spin-turners and Larmor-accelerators which diminish thermal disturbances and depolarisation considerably. The gain in performance is exploited demonstrating violation of a Bell-like inequality for a spin-path entangled single-neutron state. The obtained value of S=2.365(13), which is much higher than previous measurements by neutron interferometry, is 28σ above the limit of S=2 predicted by contextual hidden variable theories. The new setup is more flexible referring to state preparation and analysis, therefore new, more precise measurements can be carried out.

DOI
10.1016/j.nima.2014.06.080

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For precise measurements with polarised neutrons high efficient spin-manipulation is required. We developed several neutron optical elements suitable for a new sophisticated setup, i.e., DC spin-turners and Larmor-accelerators which diminish thermal disturbances and depolarisation considerably. The gain in performance is exploited demonstrating violation of a Bell-like inequality for a spin-path entangled single-neutron state. The obtained value of S=2.365(13), which is much higher than previous measurements by neutron interferometry, is 28σ above the limit of S=2 predicted by contextual hidden variable theories. The new setup is more flexible referring to state preparation and analysis, therefore new, more precise measurements can be carried out.
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.
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.
Neutron optical experiments are presented, which exhibit quantum contextual phenomena. Entanglement is achieved not between particles, but between degrees of freedom, in this case, for a single‐particle. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow an experimental verification of the violation of a Bell‐like inequality. Our experiments manifest the fact that manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! Next, we report another experiment which exhibits other peculiarity of quantum contextuality, e.g., originally intended to show a Kochen‐Specker‐like phenomenon. We have introduced inequalities for quantitative analysis of the experiments. The value obtained in the experiments clearly showed violations of prediction by non‐contextual theory. Finally, we have accomplished a tomographic determination of entangled quantum state in single‐neutrons. There, characteristics of the Bell‐sate are confirmed: four poles for the real part of the density matrix are clearly seen.
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
There are two powerful arguments against the possibility of extending quantum mechanics (QM) into a more fundamental theory yielding a deterministic description of nature. One is the experimental violation of Bell inequalities, which discards local hidden‐variable theories as a possible extension to QM. The other is the Kochen‐Specker (KS) theorem, which stresses the incompatibility of QM with a larger class of hidden‐variable theories, known as noncontextual hidden‐variable theories. We performed experiments with neutron interferometer, which exploits spin‐path entanglements in single neutrons. A Bell‐like state is generated to demonstrate a violation of the Bell‐like inequality and phenomena in accordance with KS theorem: both experiments study quantum contextuality and show clear evidence of the incompatibility of noncontextual hidden variable theories with QM. The value S = 2.202±0.007≰2 is obtained in the new measurement of the Bell‐like inequality, which shows a larger violation than the previous measurement. For the study of KS theorem, the obtained violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.