Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron Interferometer

Abstract

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial geometric phase. The interpretation of this experiment, namely to ascribe a geometric phase to this particular state evolution, has met severe criticism from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic evolution manifests the correctness of the interpretation of the previous experiment by means of an explicit calculation of the non-cyclic geometric phase in terms of paths on the Bloch-sphere.

4 pages, revtex4

References in corpus (6)

• Geometric phases for mixed states in interferometry
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Off-Diagonal Geometric Phases
• Off-diagonal geometric phase for mixed states
• Berry phase in entangled systems: a proposed experiment with single neutrons
• Observation of off-diagonal geometric phase in polarized neutron interferometer experiments

Cited by in corpus (11)

• Berry phase in atom optics
• Engineering of triply entangled states in a single-neutron system
• General complex Spin Weak Values obtained in Matter-Wave Interferometer Experiments
• Observation of nonadditive mixed state phases with polarized neutrons
• Multifold paths of neutrons in the three-beam interferometer detected by tiny energy-kick
• Improvement of the polarized neutron interferometer setup demonstrating violation of a Bell-like inequality
• Geometric effects in non-equilibrium electron transfer statistics in adiabatically driven quantum junctions
• Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics
• New Aspects of Geometric Phases in Experiments with polarized Neutrons
• An experimental test of the geodesic rule proposition for the non-cyclic geometric phase
• Contribution of the basis-dependent adiabatic geometric phase to noncyclic evolution