Theory and experiment of entanglement in a quasi-phase-matched two-crystal source

Abstract

We report results regarding a source of polarization entangled photon pairs created by the process of spontaneous parametric downconversion in two orthogonally oriented, periodically poled, bulk ${\mathrm{KTiOPO}}_{4}$ crystals. The source emits light colinearly at the nondegenerate wavelengths of 810 and $1550\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and is optimized for a single-mode optical fiber collection and long-distance quantum communication. The configuration favors long crystals, which promote a high photon-pair production rate at a narrow bandwidth, together with a high pair probability in fibers. The quality of entanglement is limited by chromatic dispersion, which we analyze by determining the output state. We find that such a decoherence effect is strongly material dependent, providing for long crystals an upper bound on the visibility of the coincidence fringes of 41% for ${\mathrm{KTiOPO}}_{4}$, and zero for ${\mathrm{LiNbO}}_{3}$. The best obtained raw visibility, when canceling decoherence with an extra piece of crystal, was $91\ifmmode\pm\else\textpm\fi{}0.2%$, including background counts. We confirm by a violation of the CHSH-inequality ($S=2.679\ifmmode\pm\else\textpm\fi{}0.004$ at $55\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1∕2}$ standard deviations) and by complete quantum state tomography that the fibers carry high-quality entangled pairs at a maximum rate of $55\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{THz}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{mW}}^{\ensuremath{-}1}$.