Weak values obtained in neutron optical experiments

Neutron interferometric experiments have long been established as an almost ideal tool to investigate fundamental phenomena in quantum mechanics: in particular, those experiments, where interference effects of matter waves of massive particles are involved, have served as elegant demonstrations related to the foundations of quantum mechanics. This technique enabled many text-book experiments of quantum physics such as demonstrations of 4? spinor symmetry of 1/2-spin, spin superposition, gravitationally induced phase and non-inertial motional effects. In addition, utilizing interference effect between two spin eigenstates, an alternative method using neutron polarimeters has turned out to be another useful tool for investigations of quantum mechanical two-level system. This apparatus is used for phase measurements, like topological phase measurements, particularly in cases where high stability and efficiency are called for. In this project, following our recent successful investigations of foundations of quantum mechanics with neutrons, we proceed with investigations of weak values, i.e., extended values attained in quantum measurements from conventional measurement results obtained via strong interaction, with neutron`s matter waves. Four major research targets are proposed: (i) Implementation of extracting weak values of matter waves via weak measurements as well as other strategies, i.e., without weak measurements and weak interactions (ii) Studies of weak values as a complex number in the neutron experiments as well as those of which-path information in relation to arguments of wave-particle duality (iii) Studies of paradoxical phenomena in quantum mechanics relevant to weak values (iv) Studies of weak values in terms of information in quantum measurements and as results of extended quantum measurements In the previous project "Double, triple and quadruple entanglement of neutrons" (July 2009 ~), we accomplished the experimental implementation of a multi-partite entangled state in neutron interferometers and polarimeters. In addition, a neutron polarimetric experiment confirmed the violation of the old error-disturbance uncertainty relation by Heisenberg and the validity a new universally valid formation. On the basis of these achievements, we believe that investigations of weak values with neutron`s matter waves are now feasible: appropriate development of some needed optical elements will enable the proposed experiments. Moreover, we hope that these experiments will exhibit new aspects of quantum measurements which are more abundant in available information than those in classical physics. In all cases experimental investigation will have priority and theoretical support will be provided from collaborations with other groups, in Austria, Japan, France, India and worldwide. The aim of the project is to contribute also to the impressive progress of quantum optics and quantum information/communication technology by the use of the specific properties of neutrons as an elementary matter wave system.

Since the early stage of the development of quantum theory, peculiarities predicted by this theory have fascinated and even confused not only the interested public but also physicists. One example is wave-particle duality, where particles such as neutrons, electrons and molecules propagating through the double-slit situation exhibits interference fringes at the final screen. Non-local effects, not in a sense of quantum kinematics observed in two-particle correlation but in a sense of quantum dynamics described by quantum equation of motion, are clearly observed in the double-slit experiments. For the investigations of fundamental phenomena in quantum mechanics, interferometer experiments with neutrons have been established as a powerful technique. Moreover, an alternative method using a neutron polarimeter was developed to enable phase measurements, particularly in cases where high stability and efficiency are called for. The present project is aimed to study dynamical properties of a massive-particle quantum system, i.e., neutrons, on the fundamental level. In the first experiment, weak measurement of neutrons -spin is realized in neutron interferometer experiment; path degree of freedom is weakly coupled with neutrons spin and utilized as a meter system. We successfully extracted real and imaginary components, as well as its modulus of the weak value of -spin. This is the first realization of the weak measurement with massive-particle beams, where purely quantum mechanical treatment is valid. This experiment is followed by the demonstration of so-called quantum Cheshire-Cat effect (named after Cheshire-Cat appearing in Alices Adventures in Wonderland by Lewis Carrol) in a Mach-Zehnder type interferometer as an example of counterintuitive and paradoxical phenomena in quantum mechanics; quantum particle behaves as if a particle and its property are spatially separated. The results of our perfect-crystal neutron interferometer experiment suggest that the whole system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other. This result is reported in wide spectrum of public relations such as BBC News, national and international newspapers and popular science magazine. Furthermore, confined contextuality together with quantum pigeonhole effect is investigated by performing the path weak measurement of neutrons in the interferometer. Above mentioned experiments are all feasible after appropriate development of some optical elements used in the interferometer experiments. As a whole, the project offered significant advance of the studies of quantum dynamics with neutrons matter-waves optical setup. In particular, noteworthy successes are achieved, ranging from experimental determination of the weak value to extended studies of dynamical behavior of quantum particles, e.g., emerging in quantum Cheshire-Cat and pigeonhole phenomenon, as well as more accurate and precise reconstruction of a quantum state with the aid of weak values.