Weak Measurements, Phases and Entanglement in Neutron Optics

Neutron polarimetry has been established as an ideal technique for the investigation of foundations of quantum mechanics with massive particles. This is demonstrated especially in experiments where high stability and efficiency for observation of quantum mechanical phenomena are required: such as the noncommutation of the Pauli spin operator, geometric phase measurements and evidence of entanglement of different degrees of freedom in single neutron systems. In this project we propose three major research targets: 1. Development of a weak measurement procedure by means of a non-ideal Stern-Gerlach apparatus in neutron polarimetry 2. Investigation of topological phases, more precisely phases induced by non-unitary evolutions and an extension of the Sagnac effect, i.e., the Sagnac-Mashhoon effect 3. Quantum state tomographic (density matrix reconstruction) of a maximally entangled Bell state and a reconstruction of the Wigner functions of Schrödinger cat states (Neutron wave-packet tomography) Assuming the value of an observable depends on both a pre- and a post-selected state vector Aharobov and his co- workers developed a so called weak measurement scheme, yielding measurement values (weak values), which may lie far outside the usual range of the observable`s eigenvalues. An experimental demonstration using neutrons is still lacking. The second topic of our project is devoted to topological phase. Here we are interested in non- unitarity evolutions, which are usually considered in open quantum systems. A geometric phase arising from an evolution path depends only upon the path traced out by the system, but is different from the usual geometric phase from unitary evolutions. In addition a neutron polarimetric version of the Sagnac effect, which originally describes the influence of rotation on the phase of light passing through an interferometer, is considered using a slowly rotating static magnetic field. The last topic of the project is entanglement detection, where a quantum state tomography of a quantum system consisting of two qubits (spin and total energy of the neutron) requires measuring a full set of 16 operators. A high-frequency spin flipper system, where due to the exchange of energy with the radiation field (via photons) spin and energy of the neutron are manipulated, forms the basis for density matrix and reconstruction and tomographic reconstruction of the Wigner functions of Schrödinger cat states. Therefore development of a state of the art high-frequency spin-flipper system is inevitable. In this project, experimental investigations will have priority and theoretical support will be provided from collaborations with groups in Austria and worldwide. The aim of the project is to contribute to the impressive progress of quantum optics/communication technology and to better understand fundamental concepts of quantum mechanics by using specific properties of the neutron.

The dual nature of neutrons in some respect a particle, in other respect a wave is manifested by highly counterintuitive effects observed in neutron optics, which has been applied within the scope of this research project to explore foundations of quantum mechanics. Two well-established neutron optical approaches, namely neutron interferometry, where a beam of thermal neutrons is split into two sub-beams and after manipulations on the sub-beams recombined again, and neutron polarimetry, also referred to as spin interferometry, have been utilized in a series of experiments. In this project we accomplished development of a new method to determine the so called weak value of massive particles, more precisely of a neutrons spin component in an interferometric setup. The concept of weak measurements was introduced in 1988 as a minimally disturbing quantum measurement with weak values as result. Weak values have been attracting considerable attention in recent years as a powerful resource for exploring foundations of quantum mechanics, as well as a practical laboratory tool. However, unlike in the original textbook proposal, up to date all experimental applications have only been realized applying photonic systems instead of massive particles - such as the neutron. In addition, we have developed a weak value determination scheme valid for arbitrary interaction strengths. This procedure was applied to determine the neutrons path state within the interferometer, from which, in turn, a direct characterization of the initial state of the investigated quantum system, i.e., the neutrons path state, became feasible. Furthermore, these new tools allowed us to study a new counter-intuitive phenomenon, the so-called quantum Cheshire Cat, known from Alice in Wonderland: a separation of the particle (in our case neutron) from one of its intrinsic properties (neutrons spin), was performed successfully. Another achievement of this project was the first observation of the effect of spinrotation coupling of massive particles. The coupling of the neutrons spin with the angular velocity of a rotating magnetic field in manifested in phase shift that was detected in a neutron polarimeter experiment. The observed phase turned out to depend solely on the frequency of the rotation of the magnetic field. One last point: our on-going development of neutron optical elements, that are suited to be placed inside our neutron interferometer, was demonstrated in an experimental violation of Bells inequality. The finally obtained value is much higher than in our previous measurements and significantly above the limit predicted by realistic theories and therefore clearly in favor of the predictions of quantum mechanics. The project has provided a significant advance in the studies of fundamental questions in quantum physics, since our measurement results are not limited to the neutrons spin and path degree of freedom, but are in fact completely general and can be used for any two qubit (two-level) quantum system.