PHASE JUMPS AND DISCONTINUITIES IN THE EVOLUTION OF 2-STATE SYSTEMS

Analogies between propagation of classical light waves and the propaga tion of electron waves in condensed matter has made possible, in recen t years, the experimental study of several interesting quantum mechani cal phenomena through optics experiments, which are simpler to impleme nt and interpret. A similar approach has enabled us to study, with the use of the two polarization states of light in optical interference e xperiments, the evolution of the phase of the wavefunction of a quantu m mechanical two-state System and predict new effects. For example our experiments to observe ''4 pi spinor symmetry'' in the polarization s ystem show, for the first time, that the sign of the pi-phase shift ch anges discontinuously as a function of the, parameters of the experime nt as a result of nodal singularities in the parameter space, which ca n be directly observed in our experiments in terms of a net, measurabl e phase shift in going around a circuit enclosing the singularity. The possibility of a continuous monitoring of the phase of an evolving wa ve in an interference experiment, along with the use of Pancharatnam's criterion for the phase difference between two different quantum mech anical states for the theoretical calculation of such phase shifts has produced experimental results that raise important questions regardin g the phase variable. in particular, the usual practice of treating ph ase changes equal to 2n pi as being unphysical and unimportant is ques tioned by these results. The time evolution operator of an evolving, c onservative two-state system is an SU(2) matrix, occurring in eigenmod e problems in optics, condensed matter and elsewhere in physics. Some consequences of degeneracies in this operator as a function of the par ameters of the system are discussed.