High coherent frequency-entangled photons at telecom band are critical in quantum information protocols and quantum tele-communication. While photon pairs generated by spontaneous parametric down-conversion in nonlinear crystal or modulation instability in optical fiber exhibit random fluctuations, making the photons distinguishable among consecutive roundtrips. Here, we demonstrate a frequency-entangled photons based on parametric instability in an active fiber ring cavity, where periodic modulation of dispersion excites parametric resonance. The characteristic wave number in parametric instability is selected by the periodic modulation of resonator, and stable patterns with symmetric gains are formed. We find that the spectra of parametric instability sidebands possess a high degree of coherence, which is verified by the background-free autocorrelation of single-shot spectra. Two photon interference is performed by a fiber-based Mach-Zehnder interferometer without any stabilization. We obtain a Hong-Ou-Mandel interference visibility of 86.3% with a dip width of 4.3 mm. The correlation time measurement exhibits a linewidth of 68.36 MHz, indicating high coherence and indistinguishability among the photon pairs. Our results proves that the parametric instability in active fiber cavity is effective to generate high coherent frequency-entangled photon pairs, which would facilitate subsequent quantum applications.
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