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arXiv:1912.10282 · Physical Review A

Operator analysis of contextuality-witness measurements for multimode-entangled single-neutron interferometry

Shufan Lu, Abu Ashik Irfan, Jiazhou Shen, Stephen J. Kuhn, William Michael Snow, David V. Baxter, R. Pynn, Gerardo Ortíz

Published Apr 16, 2020• 19 citations
arXivHTMLPDF

Abstract

We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic-field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutron state space is approximated by a finite tensor product of distinguishable subsystems. We design entangled-neutron interferometers to measure entanglement witnesses for the Clauser, Horne, Shimony, and Holt and Mermin inequalities, and compare the theoretical predictions with recent experimental results. We present the generalization of these expressions to $n$ entangled distinguishable subsystems, which could become relevant in the future if it becomes possible to add neutron orbital angular momentum to the experimentally accessible list of entangled modes. We view this paper as a necessary first step towards a theoretical description of entangled neutron scattering from strongly entangled matter, and we explain why it should be possible to formulate a useful generalization of the usual Van Hove linear-response theory for this case. We also briefly describe some other scientific extensions and applications which can benefit from interferometric measurements using the types of single-neutron multimode entanglement described by this analysis.

DOI
10.1103/physreva.101.042318

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We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic-field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutron state space is approximated by a finite tensor product of distinguishable subsystems. We design entangled-neutron interferometers to measure entanglement witnesses for the Clauser, Horne, Shimony, and Holt and Mermin inequalities, and compare the theoretical predictions with recent experimental results. We present the generalization of these expressions to nnn entangled distinguishable subsystems, which could become relevant in the future if it becomes possible to add neutron orbital angular momentum to the experimentally accessible list of entangled modes. We view this paper as a necessary first step towards a theoretical description of entangled neutron scattering from strongly entangled matter, and we explain why it should be possible to formulate a useful generalization of the usual Van Hove linear-response theory for this case. We also briefly describe some other scientific extensions and applications which can benefit from interferometric measurements using the types of single-neutron multimode entanglement described by this analysis.
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.
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.
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.
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.
An entangled state of a two-particle system is a quantum state that cannot be separated, meaning it cannot be written as the product of states of the individual particles. One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary for such a violation. However, there are other, easier-to-perform measurements that determine whether or not a system is entangled. An operator that corresponds to such a measurement is referred to as an entanglement witness. Here, we present the theory of witness operators and an undergraduate experiment that measures entanglement witnesses for the joint polarization state of two photons. We are able to produce states for which the expectation value of a witness operator is entangled by more than 300 standard deviations. In order to further examine the performance of these witness operators, we present a simple way to generate states that closely approximate Werner states, which have a controllable degree of entanglement.