Experimental Demonstration of Continuous Variable Polarization Entanglement

Abstract

We report the experimental transformation of quadrature entanglement between two optical beams into continuous variable polarization entanglement. We extend the inseparability criterion proposed by Duan et al. [9] to polarization states and use it to quantify the entanglement between the three Stokes operators of the beams. We propose an extension to this scheme utilizing two quadrature entangled pairs for which all three Stokes operators between a pair of beams are entangled. PACS numbers: 42.50.Dv, 42.65.Yj, 03.67.Hk The polarization state of light has been extensively studied in the quantum mechanical regime of single (or few) photons. The demonstration of entanglement of the polarization states of pairs of photons has been of particular interest. This entanglement has facilitated the study of many interesting quantum phenomena such as Bell's inequality [1]. Comparatively, research on continuous variable quantum polarization states has been cursory. Recently, however, interest in the field has increased due to the demonstration of transfer of continuous variable quantum information from optical polarization states to the spin state of atomic ensembles [2]; and to its potential for local oscillator-free continuous variable quantum communication networks. A number of theoretical papers have now been published [3,4], of particular interest is the work of Korolkova et al. [5] which introduces the new concept of continuous variable polarization entanglement, and proposes methods for its generation and characterization. Previous to the work presented here however, only the squeezing of polarization states had been experimentally demonstrated [2,6,7].In this paper we report the experimental transformation of the commonly studied and well understood entanglement between the phase and amplitude quadratures of two beams (quadrature entanglement) [8] onto a polarization basis. Quadrature entanglement can be characterized using the inseparability criterion proposed by Duan et al. [9]. We generalize this criterion to an arbitrary pair of observables and apply it to the Stokes operators that define quantum polarization states. We experimentally generate entanglement of Stokes operators between a pair of beams, satisfying both the inseparability criterion, and the product of conditional variances which is a signature of the EPR paradox [10]. Interacting this entanglement with a pair of distant atomic ensembles could entangle the atomic spin states. We also analyze the polarization state generated by combining two quadrature entangled pairs. We show that if the quadrature entanglement is strong enough to beat a bound √ 3 times lower than that for the inseparability criterion, then all three Stokes operators can be simultaneously entangled.The polarization state of a light beam can be described as a Stokes vector on a Poincaré sphere and is determined by the four Stokes operators [11]:Ŝ 0 represents the beam intensity whereasŜ 1 ,Ŝ 2 , andŜ 3 characterize its polarization and form a cartesian axis system. If the Stokes ve...

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