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Observing pancharatnam phases and amplitudes

Apoorva G. Wagh, Veer Chand Rakhecha

Published Jan 1, 2001• 0 citations
Publisher

Abstract

In the mid-l950s, Pancharamam [l] propounded an exact prescription for the phase acquired in a completely general evolution of a quanta1 system. Without any loss of generality, we highlight this phase prescription here for spin-polarized neutrons, a two-state system, and describe an interferometric experiment observing phases and associated interference amplitudes in noncyclic evolutions.

DOI
10.1080/10448630108244961

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A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].

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In the mid-l950s, Pancharamam [l] propounded an exact prescription for the phase acquired in a completely general evolution of a quanta1 system. Without any loss of generality, we highlight this phase prescription here for spin-polarized neutrons, a two-state system, and describe an interferometric experiment observing phases and associated interference amplitudes in noncyclic evolutions.
We demonstrate that Pancharatnam's relative phase for mixed spin−1/2-{1/2}−1/2 states in noncyclic SU(2) evolution can be measured polarimetrically.
A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep 1998)] to measure the noncyclic phase associated with a precessing neutron spin in a neutron interferometer, as given by the Pancharatnam criterion, is presented. It is pointed out that since the experiment measures, not the noncyclic phase itself, but a quantity derived from it, it misses the most interesting feature of such a phase, namely the different sign associated with states lying in the upper and the lower hemispheres, a feature originating in the existence of a phase singularity. Such effects have earlier been predicted and seen in optical interference experiments using polarization of light as the spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].