No abstract

The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spinpolarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable. The longitudinal Goos-Hänchen shift is well known for photons. It was Sir Isaac Newton [1] who suggested a beam of light, specularly reflected at a glass-vacuum surface, first penetrates into the vacuum and then is attracted back toward the glass surface. The result is a shift of the incident ray over some distance along the surface of the interface as shown in Fig. 1. F. Goos and H. Hänchen were the first to observe such a shift experimentally [2,3]. Since then, this shift for electromagnetic waves have been subject of further studies [4,5], including also transverse shifts, known as the Imbert-Fedorov shift [6]. Because of the particlewave duality, as advocated by quantum mechanics, such a shift should also be observable for particles reflecting from a potential well. As a neutron possesses a magnetic moment, the neutron wave function is represented by a spinor, consisting of an up-spin wave function and a down-spin wave function. The Goos-Hänchen shift for an up-spin wave function is different from the one for a down-spin wave function due to the difference in potential well for the spin up and down wave functions. The difference in these shifts results in a different polarization after reflection from the mirror with respect to the polarization before reflection.For neutrons, experimental possibilities have been discussed [7,8] previously, but to the best of the authors' knowledge, these experiments have not been performed. The measurements described by Pleshanov [9] are indirect measurements of the shift, determining the effect on the reflectivity, similar as the ones described by Toperverg [10]. Experimentally, to observe this change in polarization requires a high neutron flux instrument with excellent control and characterization of the neutron spin polarization. The development of the spin-echo neutron reflectometer OffSpec [11,12] at ISIS second target station enables measurement of the difference in Goos-Hänchen shift via the direct and unambiguous measurement of the polarization change during reflection.The practical importance of the shift for neutrons is for the design of neutron waveguides as discussed by Rohwedder [13] similar to Pillon [14] and it can also be used to study the co...

The total dynamic structure factor S(k,co) measured by neutron scattering on a mixture of 80% He and 20% Ne at 39.3 K and total number density 15.1 nm" 3 shows clear side peaks or shoulders at frequencies ck (with c the velocity of sound) in agreement with the predicted existence of a fast sound mode in mixtures, due to oscillations in the light component alone. 61.20.Lc Recent molecular-dynamics simulations on two-fluid mixtures 1 ' 2 representative for, respectively, 80% lithium and 20% lead and 80% helium and 20% neon have shown that in the partial dynamic structure factor S\\(k,co) of the light component (1) clear side peaks occur at frequencies co^cQs l) (k) for wave numbers k in the neutron scattering regime. Such side peaks at co^cos (k) are absent in the partial dynamic structure factor Siiik.oo) of the heavy component (2), however. Furthermore, o)s ]) (k) is clearly larger than ck, with c the velocity of sound of the fluid mixture.These results for S\\ (k,(o) and S22^k,co), with k in the neutron scattering regime, are fundamentally different from those predicted by hydrodynamics, valid for k -• 0. For, when k -> 0, side peaks then occur both in S\\ (k,co) and Snik.co) at the same locations (o=ck, which are caused by a single sound mode of the fluid mixture, in which both the light and heavy particles contribute to the sound propagation. In fact, c is determined by the dynamic properties of both constituents of the mixture, where, in particular, the large mass mi of the heavy particles reduces c as compared to the sound velocity c\ of an equivalent fluid of light particles alone.Thus, in the neutron scattering regime, the side peaks in S\\ (k,co) are attributed to a so-called "fast sound" mode, l that is, an eigenmode of the fluid mixture which propagates mainly through the light component alone since the particles of the heavy component (2) are too massive to follow the "fast" oscillations of the light particles. Therefore, in the neutron scattering regime, (Os l) (k) s =c\k with c\ (> c) the sound velocity of the light component.These observations from molecular-dynamics simulations are supported by theoretical calculations for binary mixtures of hard spheres on the basis of the revised Enskog theory. 3 Campa and Cohen also find that S\\(k,co) shows side peaks (or, rather, side wings) at co-cos (k), which are absent in S2i (k,(o) and that a>s l \k) =c\k with c i > c.The side peaks in S\\(k,eo) will also appear in the total dynamic structure factor S(k,co), relevant for neutron scattering, since the contribution S22^k,co) to S(k,co) is narrower than Sn(k,co), due to the large mass ratio m 2 /m\. l~3 The effect will be most pronounced when mi/mx is very large, since £22(k,co) becomes increasingly narrower than S\\(k,co), while furthermore the fast sound frequency ct)s l) (k) will be increasingly larger than the hydrodynamic sound dispersion ck, for increasing 1712! m\.However, actual neutron scattering experiments on disparate ...

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 .

No abstract