MANIFESTATIONS OF GEOMETRICAL AND DYNAMIC PHASES FOR THE PHOTON UNDER CYCLIC AND NONCYCLIC EVOLUTIONS

Abstract

We review the geometrical phases in a non planar Mach-Zehnder interferometer as a non adiabatic Ahaxonov-Anandan phase shift. Light traveled interferometer's arms along paths twisted in the three spatial dimensions. Both arms were arranged symmetrically, having opposite senses of handedness. By considering the light at the asymmetrical second exit of the interferometer, we prove that the process needs not to be cyclic to exhibit geometrical phases. We also prove that a purely dynamical phase shift does not affect the relative fringe shifts associated with geometrical phases. The method of distinguishing geometrical and dynamical phases is to perform the same experiment with opposite helicities.