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We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases of the Fourier components of a periodic structure can be fully recovered by deliberately choosing a probe wavelength of the diffracting radiation much smaller than the lattice constant. In the course of the demonstration, we accurately determine the refractive index profile of nanocomposite phase gratings by light and neutron diffraction measurements.

We demonstrate the use of nanodiamond in constructing holographic nanoparticle-polymer composite transmission gratings with large saturated refractive index modulation amplitudes at both optical and slow-neutron wavelengths, resulting in efficient control of light and slow-neutron beams. Nanodiamond possesses a high refractive index at optical wavelengths and large coherent and small incoherent scattering cross sections with low absorption at slow-neutron wavelengths. We describe the synthesis of nanodiamond, the preparation of photopolymerizable nanodiamond-polymer composite films, the construction of transmission gratings in nanodiamond-polymer composite films and light optical diffraction experiments. Results of slow-neutron diffraction from such gratings are also presented., Comment: Accepted for publication in Phys. Rev. Applied (2020)

Nanocomposites enable us to tune parameters that are crucial for use of such materials for neutron-optics applications such as diffraction gratings by careful choice of properties such as species (isotope) and concentration of contained nanoparticles. Nanocomposites for neutron optics have so far successfully been deployed in protonated form, containing high amounts of $^1$H atoms, which exhibit rather strong neutron absorption and incoherent scattering. At a future stage of development, chemicals containing $^1$H could be replaced by components with more favourable isotopes, such as $^2$H or $^{19}$F. In this note, we present results of Monte-Carlo simulations of the transmissivity of various nanocomposite materials for thermal and very-cold neutron spectra. The results are compared to experimental transmission data. Our simulation results for deuterated and fluorinated nanocomposite materials predict a decrease of absorption- and scattering-losses down to about 2 % for very-cold neutrons., Comment: submitted to NIMA

Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years., Comment: Review article, 63 pages, to be published in Prog. Theor. Exp. Phys. (2014), some figures replaced

Diffraction of slow neutrons by nanoparticle-polymer composite gratings has been observed. By carefully choosing grating parameters such as grating thickness and spacing, a three-port beam splitter operation for cold neutrons - splitting the incident neutron intensity equally into the plus-minus first and zeroth diffraction orders - was realized. As a possible application, a Zernike three-path interferometer is briefly discussed.

We report on successful tests of holographically arranged grating-structures in nanoparticle-polymer composites in the form of 100 microns thin free-standing films, i.e. without sample containers or covers that could cause unwanted absorption/incoherent scattering of very-cold neutrons. Despite their large diameter of 2 cm, the flexible materials are of high optical quality and yield mirror-like reflectivity of about 90% for neutrons of 4.1 nm wavelength.

For holographic gratings recorded in superparamagnetic nanoparticle-polymer composites the diffraction efficiency should -- next to grating spacing, nanoparticle concentration and grating thickness -- depend on the strength of an external magnetic field and the incident neutron spin state. As a consequence, diffraction gratings should be tunable to act as mirrors for one spin state, while being essentially transparent for the other. Thus, polarizing beam splitters for cold neutrons become feasible., Comment: Proceedings paper for the 5th European Conference on Neutron Scattering, July 2011, Prague, Czech Republic

Diffraction experiments with holographic gratings recorded in SiO$_2$ nanoparticle-polymer composites have been carried out with slow neutrons. The influence of parameters such as nanoparticle concentration, grating thickness and grating spacing on the neutron-optical properties of such materials has been tested. Decay of the grating structure along the sample depth due to disturbance of the recording process becomes an issue at grating thicknesses of about 100 microns and larger. This limits the achievable diffraction efficiency for neutrons. As a solution to this problem, the Pendell\"{o}sung interference effect in holographic gratings has been exploited to reach a diffraction efficiency of 83% for very cold neutrons., Comment: 7 pages, 3 figures, submitted to Phys. Rev. A

The preparation of neutron-optical phase gratings with light-optical holography is reviewed. We compare the relevant concepts of i) Kogelnik's theory for Bragg diffraction of light by thick volume gratings, which can be used to analyze holographic gratings with both light and neutrons, and ii) the dynamical theory of neutron diffraction. Without going into mathematical detail, we intend to illuminate their correspondence. The findings are illustrated by analyzing data obtained from reconstruction of nanoparticle holographic gratings with both light and neutrons., Comment: Proceedings of the Neutron Optics Workshop at Alpe d'Huez, France, 2010

Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles., Comment: 17 pages, 9 figures

We report a breakthrough in the search for versatile diffractive elements for cold neutrons. Nanoparticles are spatially arranged by holographical means in a photopolymer. These grating structures show remarkably efficient diffraction of cold neutrons up to about 50% for effective thicknesses of only 200 micron. They open up a profound perspective for next generation neutron-optical devices with the capability to tune or modulate the neutron diffraction efficiency., Comment: 4 pages, 2 figures

We developed an optical device for ultra-cold neutrons and investigated the influence of a tilt of its guiding components. A measurement of the time-of-flight of the neutrons through the device by means of a dedicated chopper system was performed and a light-optical method for the alignment of the guiding components is demonstrated. A comparative analysis of former experiments with our results shows the potential of such a device to test the electrical neutrality of the free neutron on the $10^{-22} q_{\rm e}$ level and to investigate the interaction of neutrons with gravity.

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase., Comment: 10 pages 9 figures

Violation of a Bell-like inequality for a spin-energy entangled neutron state has been confirmed in a polarimetric experiment. The proposed inequality, in Clauser-Horne-Shimony-Holt (CHSH) formalism, relies on correlations between the spin and energy degree of freedom in a single-neutron system. The entangled states are generated utilizing a suitable combination of two radio-frequency fields in a neutron polarimeter setup. The correlation function S is determined to be 2.333+/-0.005, which violates the Bell-like CHSH inequality by more than 66 standard deviations., Comment: 4 pages 2 figures

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)], a Bell-like state was generated and three expectation values were determined. The observed violation 2.291 +/- 0.008 > 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variables theories., Comment: REVTeX4, 4 pages, 3 figures

The geometric phase has been proposed as a candidate for noise resilient coherent manipulation of fragile quantum systems. Since it is determined only by the path of the quantum state, the presence of noise fluctuations affects the geometric phase in a different way than the dynamical phase. We have experimentally tested the robustness of Berry's geometric phase for spin-1/2 particles in a cyclically varying magnetic field. Using trapped polarized ultra-cold neutrons it is demonstrated that the geometric phase contributions to dephasing due to adiabatic field fluctuations vanish for long evolution times., Comment: 4 pages, 4 figures

In a neutron polarimetry experiment the mixed state relative phases between spin eigenstates are determined from the maxima and minima of measured intensity oscillations. We consider evolutions leading to purely geometric, purely dynamical and combined phases. It is experimentally demonstrated that the sum of the individually determined geometric and dynamical phases is not equal to the associated total phase which is obtained from a single measurement, unless the system is in a pure state., Comment: RevTex, 4 pages, 4 figures, accepted by PRL

We have observed the stationary interference oscillations of a triple-entangled neutron state in an interferometric experiment. Time-dependent interaction with two radio-frequency (rf) fields enables coherent manipulation of an energy degree of freedom in a single neutron. The system is characterized by a multiply entangled state governed by a Jaynes-Cummings Hamiltonian. The experimental results confirm coherence of the manipulation as well as the validity of the description., Comment: 4 pages, 3 figures

We present a neutron polarimetric experiment where two kinds of spinor precessions are observed: one is induced by different total energy of neutrons (zero-field precession) and the other is induced by a stationary guide field (Larmor precession). A characteristic of the former is the dependence of the energy-difference, which is in practice tuned by the frequency of the interacting oscillating magnetic field. In contrast the latter completely depends on the strength of the guide field, namely Larmor frequency. Our neutron-polarimetric experiment exhibits individual tuning as well as specific properties of each spinor precession, which assures the use of both spin precessions for multi-entangled spinor manipulation., Comment: 12 pages, 4 figures

We have measured the Pancharatnam relative phase for spin-1/2 states. In a neutron polarimetry experiment the minima and maxima of intensity modulations, giving the Pancharatnam phase, were determined. We have also considered general SU(2) evolution for mixed states. The results are in good agreement with theory., Comment: 5 pages, 4 figures, to be published in Phys.Lett.A