From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the ‘quantum Cheshire Cat’: if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat’s nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.

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.

A method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently, Vallone and Dequal [ Phys. Rev. Lett. 116, 040502 (2016)] showed theoretically that weak measurements are not a necessary condition to determine the weak value. Here, we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system’s quantum state was characterized via direct measurements, using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones for tomographic accuracy. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems.

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, in particular, 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.

Entanglement between degrees of freedom, namely between the spin, path, and (total) energy degrees of freedom, in a single-neutron system is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger (GHZ)\char21{}like state and coherently manipulated relative phases of two-level quantum subsystems. An equality derived by Mermin was applied to analyze the generated GHZ-like state: We determined the four expectation values and finally obtained M=2.558\ifmmode\pm\else\textpm\fi{}0.004$\leqslant${}$\llap{\not\;}${}2. This demonstrates a violation of Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, clearly contradicts the noncontextual assumption and confirms quantum contextuality.