We demonstrate that Pancharatnam's relative phase for mixed spin $-{1/2}$ states in noncyclic SU(2) evolution can be measured polarimetrically.We demonstrate that Pancharatnam's relative phase for mixed spin$-{1/2}$ states in noncyclic SU(2) evolution can be measured polarimetrically.

May 22, 200310 citations

Measuring Pancharatnam’s relative phase for SO(3) evolutions using spin polarimetry

Peter Larsson, Erik Sjöqvist

In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework, we here extend the polarimetric test of Pancharatnam's relative phase for $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ proposed by Wagh and Rakhecha [Phys. Lett. A 197, 112 (1995)] to spin $j>~1$ undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two $\ensuremath{\pi}/2$ spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework, we here extend the polarimetric test of Pancharatnam's relative phase for $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ proposed by Wagh and Rakhecha [Phys. Lett. A 197, 112 (1995)] to spin $j>~1$ undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two $\ensuremath{\pi}/2$ spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.

arXiv:quant-ph/0305083Physical Review AOct 20, 20032 citations

We demonstrate that Pancharatnam's relative phase for mixed spin

-{1/2}

states in noncyclic SU(2) evolution can be measured polarimetrically.

j>~1

undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two $\ensuremath{\pi}/2$ spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.