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

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

2003-05-15

arxiv.org/abs/quant-ph/0305083v2

Phys. Rev. A 68, 042109 (2003)

Physics

Quantum Physics

New title, minor corrections, journal reference added

Scientific paper

10.1103/PhysRevA.68.042109

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 spin$-{1/2}$ proposed by Wagh and Rakhecha [Phys. Lett. A {\bf 197}, 112 (1995)] to spin $j\geq 1$ undergoing noncyclic SO(3) evolution. We demonstrate that the output intensity for higher spin values is a polynomial function of the corresponding spin$-{1/2}$ intensity. We further propose a general method to extract the noncyclic SO(3) phase and visibility by rigid translation of two $\pi /2$ spin flippers. Polarimetry on higher spin states may in practice be done with spin polarized atomic beams.

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