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 $2.291\pm 0.008\nleqq 1$ clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.

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 ultracold neutrons, it is demonstrated that the geometric phase contributions to dephasing due to adiabatic field fluctuations vanish for long evolution times.

We present an overview of recent investigations of photopolymerizable nanocomposite photonic materials in which, thanks to their high degree of material selectivity, recorded volume gratings possess high refractive index modulation amplitude and high mechanical/thermal stability at the same time, providing versatile applications in light and neutron optics. We discuss the mechanism of grating formation in holographically exposed nanocomposite materials, based on a model of the photopolymerization-driven mutual diffusion of monomer and nanoparticles. Experimental inspection of the recorded grating’s morphology by various physicochemical and optical methods is described. We then outline the holographic recording properties of volume gratings recorded in photopolymerizable nanocomposite materials consisting of inorganic/organic nanoparticles and monomers having various photopolymerization mechanisms. Finally, we show two examples of our holographic applications, holographic digital data storage and slow-neutron beam control.

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 $200\mu \mathrm{m}$. They open up a profound perspective for next generation neutron-optical devices with the capability to tune or modulate the neutron diffraction efficiency.