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International Journal of Geometric Methods in Modern Physics

Intelligent spin states constructed from SU q(2) coherent states

M. Reboiro, Osvaldo Civitarese

Published May 4, 2015• 2 citations
Publisher

Abstract

It is shown that q-deformed Coherent Spin States (CSS), belonging to the SU q(2) representation, behave as Intelligent Spin States (ISS). The proof is based on the calculation of spin-squeezing observables, for both CSS and ISS.
DOI
10.1142/s0219887815600233

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The Robertson–Schrödinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.