Neutron interference experiments have long been serving us as an almost ideal strategy to study foundations of quantum mechanics with matter-waves. Above all, interferometric experiments using massive particles, i.e. neutrons, enable investigations of fundamental phenomena in quantum mechanics with beam separation in the order of several centimeters, i.e., actually quantum interference experiments on the macroscopic scale. This technique allowed us many text-book experiments of quantum physics such as demonstrations of 4p spinor symmetry of 1/2-spin, spin superposition, gravitationally induced phase and non-inertial motional effects. Moreover, 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 quantum-mechanical measurements, particularly in cases where high stability and efficiency are called for.
In this project, following our recent successful investigations and exploiting the technique developed in previous experiments, we proceed studies of uncertainty relations in various forms with neutron’s matter-waves. Furthermore, interferometer experiments enable to extend the concept of uncertainty relation and give new insights of wave-particle duality. Three major research targets are set:
(i) Implementation of incompatible spin measurements suitable for the study of further-developed and tight error-disturbance uncertainty relation by Ozawa and Branciard.
(ii) Studies of information-theoretic uncertainty relation in a form with binary entropy function, where “error correction operation” is a key issue of the studies from the theoretical and experimental points of view.
(iii) Studies of extended uncertainty relation for path/distinguishability and wave/fringe-amplitude in double-slit situations, where new insights concerning the wave-particle duality are anticipated.
In the previous project “Double, triple and quadruple entanglement of neutrons” (July 2009 ~ October 2013), 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. It is worth noting here that this experiment stimulated the studies of uncertainty relation theoretically and experimentally. On the basis of these achievements, we believe that we can proceed further experimental studies of new uncertainty relations, namely by using neutron’s matter-waves. Moreover, we hope that studies with neutron interferometers enable to extend the uncertainty relation for double-slit situations and bring new insight of wave-particle duality.
In all cases experimental investigation will have priority and theoretical support will be provided from collaborations with other groups, in Japan, Australia, and worldwide. The aim of the project is to contribute also to the impressive progress of quantum optics, quantum information/communication technology and quantum metrology by the use of the specific properties of neutrons as an elementary matter wave system.
