Quantum theory describes the behavior of a system at atomic and smaller scales. At the beginning of the 20th century, the theory was developed and became one of the most successful theories in physics; for a wide range of the field, the validity of the theory has been verified with high accuracy by experiments. From the beginning, however, quantum mechanics has also supplied an extraordinary and even counter-intuitive view of nature: contrary to its success, the predictions by quantum theory are governed by a probability law and its logic is different from that in classical physics, to which we have become accustomed to in our ordinary lives. In trying to understand phenomena predicted by quantum theory, one should leave off accustomed ideas about reality, causality, locality and so on. One of the most astonishing phenomena displayed by a quantum system is wave-particle duality. Particles such as electrons, neutrons, and positrons can behave in non-locally located waves; wave-particle duality postulates that all particles exhibit both wave and particle properties. Moreover, the Schrödinger’s cat thought experiment is an example of the ability of quantum theory to present counterfactual phenomena.
Quantum mechanics predicts that particles like neutrons can exhibit non-local wave properties in certain circumstances. The neutron interferometer, with a monolithic structure of a silicon perfect crystal, was invented in 1974. In this type of the interferometer, separated coherent beams are produced by an amplitude division and the beam separation reaches typically several centimeters. The split beams are recombined and coherently superposed after travelling through some regions of the interferometer, where phase, amplitude and spin are manipulated by various interactions. The advent of the perfect crystal neutron interferometer in 1974 opened up a new era of fundamental studies of quantum mechanics with matter-waves . A schematic view of a skew-symmetric neutron interferometer made of a perfect Si-crystal and Si-crystal and pictures of divers sorts of interferometers are depicted in Fig. 1.
(a) A sketch of the interferometer: an incident beam is split into two beam paths at the first plate and recombined at the last plate. Two beams leaving from the interferometer exhibit typical intensity modulation dependent on the relative phase of the two beams in the interferometer. (b) Pictures of a variety of neutron interferometers.
Recently, Progress of Theoretical and Experimental Physics (PTEP) published a new review article, entitled “Fundamental phenomena of quantum mechanics explored with neutron interferometers” by Klepp, Sponar and Hasegawa. The instruments described in the article are not limited by the neutron interferometer but some amount is attributed to the neutron polarimeter. The neutron polarimeter is an instrument where a polarized neutron beam goes through several spin-manipulations and the spin vector is measured at the last stage. By considering the up- and the down-spin states as eingenstates of a basis, this apparatus can be regarded as that to observe (quantum) interference effects between these spin eigenstates. The authors of the article have exploited this consideration for their investigations of a variety of quantum mechanical phenomena.
In the review, the authors started by describing the neutron optical instruments and techniques used in the experiments. In the following chapter, “historical” neutron optical experiments are explained; for instance, the 4π-symmetry of the spin-1/2 wavefuntion, gravity-induced phases, and
Aharonov-Bohm phases are explained. In chapters 4 and 5, studies of quantum contextuality/entanglement and geometric phases are described, and several tests of alternative quantum theories and various studies of geometric phases are described. In chapter 6, other quantum-optical experiments, including the study of the error-disturbance uncertainty relation, are plainly expressed. As a whole, emphasis is put on the understanding of important concepts of quantum mechanics, such as superposition, entanglement, and quantum contextuality, which will help readers to develop deeper insight regarding quantum mechanics.
 H. Rauch, S.A. Werner, Neutron Interferometry, Clarendon Press, Oxford (2000).
 J. Klepp, S. Sponar, and Y. Hasegawa, Prog. Theor. Exp. Phys. (2014) 082A01.