Analysis of elliptically polarized, maximally entangled states
Résumé
We demonstrate high quality polarization entanglement at telecom wavelength, based on guided-wave technology. The fully fibered setup relies on a type-II periodically poled Lithium Niobate waveguide (PPLN/W) emitting pairs of cross-polarized photons (H,V) at 1310 nm. These photon pairs are sent onto a simple 50/50 fiber-optic coupler, leading to an entangled state of the form |Ψ>=(1/21/2)*(|Ha,Vb>+|Va,Hb>) in the coincidence basis, which is eventually distributed to "users" (a,b) through standard optical fibers. Along these distribution channels, the entangled state acquires an unknown phase between its two components leading to an "elliptically polarized" maximally entangled states |Ψ>=(1/21/2)*(| Ha,Vb>+eiφ|Va,Hb>), in which φ is a non random phase, and (a,b) represent the two channels at the output of the emitting source. For such a state, the usual settings used for optimal violation of the Bell inequality are no longer adapted. Thanks to the use of a phase compensator, namely a Soleil-Babinet birefringent system, we demonstrate experimentally that any phase can be compensated, leading to a maximal violation of the Bell inequality when the standard settings are used. Alternatively, we propose here a theoretical approach that allows, when applied to those particular states, determining the phase, and finding new analysis parameters towards optimizing the Bell inequality violation. After introducing our formalism in its generic form, we will show that it can be applied to several existing systems capable of either compensating or analyzing the phase.