Continuous variable polarization entanglement, experiment and analysis

Abstract

We generate and characterise continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan {\it et al.}\cite{Duan00} and the Einstein-Podolsky-Rosen paradox criteria proposed by Reid and Drummond\cite{Reid88}, to Stokes operators; and use them to charactise the entanglement. Our results for the Einstein-Podolsky-Rosen paradox criteria are visualised in terms of uncertainty balls on the Poincar\'{e} sphere. We demonstrate theoretically that using two quadrature entangled pairs it is possible to entangle three orthogonal Stokes operators between a pair of beams, although with a bound $\sqrt{3}$ times more stringent than for the quadrature entanglement.