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arXiv:1908.09823 · Nature Communications

Unveiling contextual realities by microscopically entangling a neutron

Jiazhou Shen, Stephen J. Kuhn, Robert M. Dalgliesh, V.O. de Haan, Niels Geerits, Abu Ashik Irfan, Fankang Li, Shufan Lu, Steven R. Parnell, Jeroen Plomp, A.A. van Well, Adam L. Washington, David V. Baxter, Gerardo Ortíz, William Michael Snow, R. Pynn

Published Feb 18, 2020• 38 citations
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Abstract

The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. Here we introduce an unconventional quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. The spatial separation of trajectories from nanometers to microns and energy differences from peV to neV will enable investigations of microscopic magnetic correlations in systems with strongly entangled phases, such as those believed to emerge in unconventional superconductors. We develop an interferometer to prove entanglement of these distinguishable properties of the neutron beam by observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities in the same experimental setup. Our work opens a pathway to a future of entangled neutron scattering in matter.

DOI
10.1038/s41467-020-14741-y

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The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. Here we introduce an unconventional quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. The spatial separation of trajectories from nanometers to microns and energy differences from peV to neV will enable investigations of microscopic magnetic correlations in systems with strongly entangled phases, such as those believed to emerge in unconventional superconductors. We develop an interferometer to prove entanglement of these distinguishable properties of the neutron beam by observing clear violations of both Clauser-Horne-Shimony-Holt and Mermin contextuality inequalities in the same experimental setup. Our work opens a pathway to a future of entangled neutron scattering in matter.
The development of direct probes of entanglement is integral to the rapidly expanding field of complex quantum materials.Here we test the robustness of entangled neutrons as a quantum probe by measuring the Clauser-Horne-Shimony-Holt contextuality witness while varying the beam properties.Specifically, we show that the mode entanglement of the spin and path subsystems of individual neutrons prepared in two different experiments using two different apparatuses persists even after varying the entanglement length, coherence length, and neutron energy difference of the paths.The two independent apparatuses acting as entangler-disentangler pairs are static-field magnetic Wollaston prisms and resonance-field radio-frequency flippers.Our results show that the spatial and energy properties of the neutron beam may be significantly altered without reducing the contextuality witness value below the Tsirelson bound, meaning that maximum entanglement is preserved.We also show that two paths may be considered distinguishable even when the path states significantly overlap.Therefore, we have shown that our experimental results are consistent with the distinguishable subsystem assumption down to a separation of less than 100 nm, proving entanglement and the contextual nature of reality on short length scales.This work is the key step in the realization of the modular, robust technique of entangled neutron scattering, which can extract entanglement information from a sample without the knowledge of the microscopic sample Hamiltonian: only semiquantitative knowledge of the correlation lengths of the relevant degrees of freedom and the timescales of the characteristic dynamics is required.
Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena. Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle systems shows that quantum correlations are to some extent more demanding than classical ones. In this case entanglement between external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden variable theories can be rejected by arguments based on the Kochen-Specker theorem.
We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe, Nature (London) 409, 791 (2001)10.1038/35057215] and single neutrons [Y. Hasegawa, Nature (London) 425, 45 (2003)10.1038/nature01881] based on violations of Clauser-Horne-Shimony-Holt-like inequalities.
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.
Abstract We develop an entangled-probe scattering theory, including quantum detection, that extends the scope of standard scattering approaches. We argue that these probes may be revolutionary in studying entangled matter such as unconventional phases of strongly correlated systems. Our presentation focuses on a neutron beam probe that is mode-entangled in spin and path as is experimentally realized by Shen et al (2020 Nat. Commun. 11 930), although similar ideas also apply to photon probes. We generalize the traditional van Hove theory (van Hove 1954 Phys. Rev. 95 249) whereby the magnetic response is written as a properly-crafted combination of two-point correlation functions. Tuning the probe’s entanglement length allows us to interrogate spatial scales of interest by analyzing interference patterns in the differential cross-section. Remarkably, for a spin dimer target we find that the typical Young-like interference pattern observed if the target state is un-entangled gets quantum erased when that state becomes maximally entangled.