Double, triple and quadruple entanglement of neutrons

From the very start, neutron interferometer experiments have been established as an ideal technique for the investigation of foundations of quantum mechanics with massive particles: in particular, those experiments, where interference effects of matter waves are involved, have served as elegant demonstrations related to quantum mechanical phenomena. This technique enabled to perform many text-book experiments of quantum physics such as demonstrations of 4p spinor symmetry of neutron`s 1/2-spin, spin superposition, gravitationally induced phase and non-inertial motional effects. In addition, an alternative method using neutron polarimeters was developed to make phase measurements, like topological phase measurements, possible particularly in cases where high stability and efficiency are called for. In this project, following our recent development of implementation of triple entanglement in a single-neutron system, we propose three major research targets: (i) Detailed study and further implementation of various type of double entanglement in neutrons as well as their application for studies of decoherence phenomena (ii) Detailed study and further implementation of a variety of triple entanglement in neutrons (iii) Implementation of quadruple entanglement in neutrons In a previous project "Neutron interferometric and polarimetric investigation of quantum mechanical phenomena" (June 2005 - May 2008), we accomplished the first experimental demonstration of a triply entangled GHZ state implemented in neutrons. We now have rather realistic and concrete proposals of further investigations of the three major subjects above. And, by appropriately developing some needed optical elements, we consider that the realizations of the experiments are in sight. It is worth noting that, since the entanglement of subspaces in single- particles, in particular with the use of a polarimeter setup, are easily applicable for other system than neutrons, the obtained achievements are widely valid. In all cases experimental investigation will have priority and theoretical support will be provided from collaborations with other groups, in Austria 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.

From the very start, interferometer experiments with thermal neutrons have been established as a powerful technique for the investigation of foundations of quantum mechanics: many text-book experiments of quantum physics have been performed with this technique. In addition, an alternative method using a neutron polarimeter was developed to enable phase measurements, particularly in cases where high stability and efficiency are called for. These neutron-optical approaches combine successfully quantum optics and advanced neutron optics. In both interferometer and polarimeter experiments, we dealt with multi entanglement of degrees-of-freedoms for single neutrons. Furthermore, we investigated the error-disturbance uncertainty relation by using neutron polarimeter setup Starting from the violation of a Bell-like inequality, degrees of freedoms, such as path, spin, energy and wave-vector, of neutrons in the interferometer are utilized to investigate multi-entanglement as well as quantum contextuality. In this project, we accomplished interferometric and polarimetric studies concerning tripartite Greenberger-Horne-Zeilinger (GHZ) like states. These experiments exhibited a clear difference between the classical and the quantum mechanical predictions. Furthermore, so-called (tripartite) W-like state families and GHZ-like state were generated to explore distinct types of genuine multi-partite entanglement: we have successfully confirmed different types of multi-partite entanglement in a single-neutron system. Our results show that quantum correlations can indeed manifest in different subsystems of a single physical entity. The polarimetric experiments dealing with tripartite entanglement exhibited results of very high contrast, e.g., more than 98%. This high fidelity was actually exploited for a test of realistic contextual model of quantum mechanics with matter-waves. A modified neutron polarimeter setup allowed the first experimental test of the errordisturbance uncertainty in spirit of the error and disturbance typically associated with gamma-ray microscope suggested by Heisenberg. The experimental results exhibit the violation of Heisenbergs original relation and confirm a new relation, which is recently derived and claimed generally valid. This accomplishment is widely reported, i.e., in newspapers, popular scientific journals, web, and so on: breakdown of old belief is expected to bring new insights of quantum measurements in applied and fundamental field. The project has provided significant advance of the studies of multi-partite entanglement with neutrons matter waves, in addition to the noteworthy experimental test of error-disturbance uncertainty relation. All consequences are of high value for relevant field of physics.