November 29, 2016
Published by Stephan Sponar
*Topological Phases*

In the language of *quantum mechanics* a pure physical state is represented by a state vector in Hilbert space. From this state one can calculate the probability of finding the particle at a specific place with a certain spin. Furthermore, the state vector carries *phase* information, property that cannot be measured in an intensity measurement. However, a **phase difference **between states vectors is a physical quantity, giving rise to the phenomenon of *interference*. Phase accumulation is, at first sight, a consequence of *dynamics* of the state evolutions. In addition to and independent of this dynamical phase Sir *Micheael V. Berry* discovered in the beginning of the eighties of the last century a phase due to the *geometrical* (or *topological*) origin of the state evolution. The peculiarity of *Berry’s* *geometric phase* phase lies in the fact that it does *not* depend on the dynamics of the system, but purely on the *evolution path* of the state in parameter space.

November 29, 2016
Published by Stephan Sponar
The influence of the geometric phase on a Bell measurement expressed in terms of the **Clauser-Horne-Shimony-Holt (CHSH)** inequality, is observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, *polar* and * azimuthal *adjustment of the Bell angles, are realized and analyzed in detail.

November 29, 2016
Published by Stephan Sponar
The effect of **spin–rotation** coupling is measured for the first time with neutrons. The coupling of spin with the angular velocity of a rotating spin turner can be observed as a phase shift in neutron interferometry and polarimetry. After the neutron’s spin is rotated by through a rotating magnetic field, different phase shifts are induced for ‘up’ and ‘down’ spin eigenstates. This phase difference results in the rotation of the neutron’s spin-vector, which turns out to depend solely on the frequency of the rotation of the magnetic field. The experimental results agree well with the solutions acquired by the **Pauli–Schrödinger ** equation.