Polarization-entangled photon pairs with factorable spectra engineered by using an uneven four-stage nonlinear interferometer

We report the generation of polarization-entangled photon pairs in the 1550 nm band by pumping an uneven nonlinear interferometer loop with two orthogonally polarized counterpropagating pump pulses. The uneven nonlinear interferometer, providing a more ideal interference pattern due to the elimination of secondary maxima, consists of four pieces of dispersion-shifted fibers sandwiched with three pieces of standard single-mode fibers, and the lengths of the nonlinear fibers follow the binomial distribution. The mode number of the photon pairs deduced from the measured joint spectrum is similar to 1.03. The collection efficiency of the photon pairs is found to be similar to 94% (after background noise correction). The directly measured visibility of two-photon interference of the polarization-entangled photon pairs is similar to 92%, while no interference is observed in the direct detection of either the signal or idler photons.