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On Geometric Phase from Pure Projections
The geometric phase is usually treated as a quantity modulo 2\pi, a
convention carried over from early work on the subject. The results of a series
of optical interference experiments involving polarization of light, done by
the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question
the usefulness of such a definition of the geometric phase in that it throws
away useful and measurable information about the system, for example strengths
of singularities giving rise to the geometric phase. Such singularities have
been directly demonstrated by phase-shift measurement in interference
experiments. In this paper, two recent polarization experiments (Hariharan
et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43
(1996)p.165) are analysed and compared with previous experiments and
potentially detectible singularities in these experiments pointed out.Comment: Latex, 15 pages, 6 figures; ([email protected]
Observable Dirac-type singularities in Berry's phase and the monopole
The physical reality and observability of 2n\pi Berry phases, as opposed to
the usually considered modulo 2\pi topological phases is demonstrated with the
help of computer simulation of a model adiabatic evolution whose parameters are
varied along a closed loop in the parameter space. Using the analogy of Berry's
phase with the Dirac monopole, it is concluded that an interferometer loop
taken around a magnetic monopole of strength n/2 yields an observable 2n\pi
phase shift, where n is an integer. An experiment to observe the effect is
proposed.Comment: 12 pages Latex, 3 postscript figures; submitted to Physical Review
Letters 15 September 2000; revised 19 November 200
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