Single-photon frequency conversion and multi-mode entanglement via constructive interference on Sagnac Loop

Based on constructive interference in Sagnac waveguide loop, an efficient scheme is proposed for selective frequency conversion and multifrequency modes W entanglement via input-output formalism. We can adjust the probability amplitudes of output photons by choosing parameter values properly. The tunable probability amplitude will lead to the generation of output photon with a selectable frequency and W photonic entanglement of different frequencies modes in a wide range of parameter values. Our calculations show the present scheme is robust to the deviation of parameters and spontaneous decay.