Investigation of quantum mechanical phenomena with neutrons

Neutron optical experiments have long been established as an almost ideal tool to investigate quantum mechanical phenomena with massive particles. In particular, those experiments where interference effects of matter waves are involved, have served as elegant demonstrations related to the foundations of quantum mechanics. In addition to interferometry, utilizing two spin eigenstates, neutron polarimetry has turned out to be another useful tool for investigations of quantum mechanical two-level system, i.e., SU(2) quantum system. We consider the dynamics of a quantum system governed by a parameterized Hamiltonian: varying this parameter along a path C in parameter space, a normalized eigenstate acquires, in addition to a dynamical phase, a further phase factor. This extra phase is called `geometric`, since it only depends on the evolution path C of quantum states. An application of the geometric phase for robust quantum information processing and a controlled phase gate has been suggested. Neutron interferometer as well as the polarimeter experiments have contributed to the investigation of the geometric phases so far. Such geometrical phenomena of quantum mechanics are a subject to be investigated in this project. Namely, we are proposing several kinds of, e.g. with cyclic/non-cyclic as well as identical/non- identical spinor evolutions, neutron interferometric and polarimetric experiments to study geometrical and topological phenomena, which will bring insights and reveal more prospects of geometrical and topological aspects of quantum mchanical phenomena. Attention has been paid to the time evolution of open quantum systems. It is easily shown that the maps describing such dissipative prosesses preserve positivity of the elements of the density matrix. Recently, the question whether a much stronger condition, namely, complete positivity, is necessary for this map has been discussed in the literature. (Complete positivity is particular important in quantum communication and information, since this ensures the positivity of the density matices representing both local and non-local systems.) We are now proposing a neutron polarimetric experiment to test complete positivity and are proceeding to seek a case where complete positivity is violated.

Neutron optical experiments have long been established as an almost ideal tool to investigate quantum mechanical phenomena with massive particles. In particular, those experiments where interference effects of matter waves are involved, have served as elegant demonstrations related to the foundations of quantum mechanics. In addition to interferometry, utilizing two spin eigenstates, neutron polarimetry has turned out to be another useful tool for investigations of quantum mechanical two-level system, i.e., SU(2) quantum system. We consider the dynamics of a quantum system governed by a parameterized Hamiltonian: varying this parameter along a path C in parameter space, a normalized eigenstate acquires, in addition to a dynamical phase, a further phase factor. This extra phase is called `geometric`, since it only depends on the evolution path C of quantum states. An application of the geometric phase for robust quantum information processing and a controlled phase gate has been suggested. Neutron interferometer as well as the polarimeter experiments have contributed to the investigation of the geometric phases so far. Such geometrical phenomena of quantum mechanics are a subject to be investigated in this project. Namely, we are proposing several kinds of, e.g. with cyclic/non-cyclic as well as identical/non- identical spinor evolutions, neutron interferometric and polarimetric experiments to study geometrical and topological phenomena, which will bring insights and reveal more prospects of geometrical and topological aspects of quantum mchanical phenomena. Attention has been paid to the time evolution of open quantum systems. It is easily shown that the maps describing such dissipative prosesses preserve positivity of the elements of the density matrix. Recently, the question whether a much stronger condition, namely, complete positivity, is necessary for this map has been discussed in the literature. (Complete positivity is particular important in quantum communication and information, since this ensures the positivity of the density matices representing both local and non-local systems.) We are now proposing a neutron polarimetric experiment to test complete positivity and are proceeding to seek a case where complete positivity is violated.