Unveiling contextual realities by microscopically entangling a neutron

Abstract

The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. The dramatic progress made by modern probe techniques to uncover the microscopic structure of matter is fundamentally rooted in our control of two defining traits of quantum mechanics: discreteness of physical properties and interference phenomena. Magnetic Resonance Imaging, for instance, exploits the fact that protons have spin and can absorb photons at frequencies that depend on the medium to image the anatomy and physiology of living systems. Scattering techniques, in which photons, electrons, protons or neutrons are used as probes, make use of quantum interference to directly image the spatial position of individual atoms, their magnetic structure, or even unveil their concomitant dynamical correlations. None of these probes have so far exploited a unique characteristic of the quantum world: entanglement. Here we introduce a fundamentally new quantum probe, an entangled neutron beam, where individual neutrons can be entangled in spin, trajectory and energy. Its tunable entanglement length from nanometers to microns and energy differences from peV to neV will enable new 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 era of entangled neutron scattering in matter. Text:A most amazing aspect of quantum reality is the possibility to share information non-locally between two or more spacelike separated subsystems, a "spooky action at a distance", as Einstein liked to call it and Bell epitomized in an inequality 1,2 . The fact that measuring compatible observables does not unveil predetermined physical properties, as pointed out by Kochen and Specker 3,4 , reveals the contextual nature of quantum measurements. Behind all these non-classical statistical correlations is the property of entanglement wherein "the state of the whole is more than the sum of its [constituent] parts'' 5 . Developing novel quantum probes that exploit these correlations as a means for investigating entanglement in matter could lead to novel insight into some of the most interesting materials studied today, such as frustrated magnets hosting quantum spin liquids and unconventional superconductors with strange metallic behavior 6 .

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

“…This matrix will introduce complex phases in the transition amplitudes defined in Eq. (7) and (8). If the incident state is |↑ +|↓ √ 2 ⊗ |a , then this entangler creates a Bell state…”

“…As in the case of the MWP interferometer |ψ f passes through the π 2 spin turner, polarization analyzer, and detector. Similar to previous section, we write the Pauli matrices in terms of projectors 8. This interferometer consists of two RFNSFG entanglers, three commuting neutron optical phase shifters in the three different distinguished subspaces, and a polarization analyzer and neutron detector.…”

“…The neutron interferometric setup we describe below [8] is well-suited for exploring spin dynamics in the most physically-interesting cases of highly-entangled many-body systems, for which there is a need to develop new techniques that can unveil complex emergent behavior. For a quantitative interpretation of entangled neutron scattering one must also develop a scattering theory for entangled neutron beams on entangled systems.…”

Single‐Particle Entanglement

“…However, in this review we deal with intraparticle entanglement and we refer the reader to the cited papers for a discussion of quantum contextuality tests. Violation of BCHSH inequalities by SPE states have been reported for a few types of particles, namely single photons, [14,15,69,70] single neutrons [16][17][18]71] and single atoms. [72,73] Entanglement has been shown between different degrees of freedom of the single particles: spin-momentum and spin-orbital momentum for photons; spin-momentum and spin-energy for neutrons; spin-momentum for atoms.…”

“…[ 7 ] In particular, this variety of possibilities opens up also to the realization of entanglement between different degrees of freedom of a unique particle, such as, for example, the polarization and momentum of a single photon [ 14,15 ] or spin and path of a neutron. [ 16–18 ] This is the so‐called single particle entanglement (SPE) or intraparticle entanglement , to which this review article is dedicated. Contrary to the case of the interparticle entanglement , which involves correlations between two different particles, the intraparticles entangled states are rather easy to produce and possess some robustness properties under decoherence and dephasing.…”