  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.
