New aspects of geometric phases in experiments with polarized neutrons

Abstract

Abstract. Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a JaynesCummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.

Bell inequalities under non-ideal conditions

“…Bell-like quantities have also been measured in experiments which involve a single quantum system instead of two quantum systems [42][43][44][45].…”

On the geometric phases in entangled states

“…The geometric phase was first studied by Ehrenberg [1], Kato [2], Pancharatnam [3], Longuet-Higgins et al [4], Aharonov and Bohm [5] and later generalized by Berry in 1984 [6]. Geometric and topological phases play a considerable role in physics and a vast literature exist today covering many plausible applications in different fields [7][8][9][10][11][12][13][14][15][16]. On the other hand, entanglement is another striking aspect of quantum mechanics and its dates back to the article published by Einstein et.al.…”