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Noncyclic mixed state phase in SU(2) polarimetry

Larsson, P, Sjöqvist, E

Published May 22, 2003• 10 citations
OpenAlex

Abstract

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

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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.

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Observing pancharatnam phases and amplitudes

Apoorva G. Wagh, Veer Chand Rakhecha

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.

Neutron News•Jan 1, 2001•0 citations
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.
The polarimetric test of Pancharatnam's relative phase for spin−1/2-{1/2}−1/2 proposed by Wagh and Rakhecha [Phys. Lett. A {\\bf 197}, 112 (1995)] is extended to spin jgeq1j\\geq 1jgeq1 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-{1/2}−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\\pi /2pi/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> 1j>~1j> 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.