Counterpropagating path-entangled photon pair sources based on simultaneous spontaneous parametric down-conversion processes of nonlinear photonic crystal

Ultra-bright source of entangled photons is an essential component in optical quantum information processing. Here we propose a counterpropagating path-entangled photon pair sources using a quasi-periodic modulated lithium niobate crystal. The nonlinear crystal designed by a dual-grid method, simultaneously phase-matched two spontaneous parametric down-conversion processes. Signal and idler modes have opposite propagation directions in the two spontaneous parametric down-conversion processes, which is the key to generating path-entangled photon pairs. Compared to copropagating entangled sources, the counterpropagating path-entangled sources result in a much narrower spectrum. The quantum state of the path-entanglement source is not only suited for quantum coding, but also to allow the implementation of complex quantum algorithms on a photonic chip.