  Heralded single photons (HSPs) generated by spontaneous parametric
down-conversion (SPDC) are useful resource to achieve various photonic quantum
information processing. Given a large-scale experiment which needs multiple
HSPs, increasing the generation rate with suppressing higher-order pair
creation is desirable. One of the promising ways is to use a pump laser with a
GHz-order repetition rate. In such a high repetition rate regime, however,
single-photon detectors can only partially identify the pulses. Hence, we
develop a simple model to consider that effect on the spectral purity, and
experimentally demonstrate a high-visibility Hong-Ou-Mandel interference
between two independent HSPs generated by SPDC with 3.2 GHz-repetition-rate
mode-locked pump pulses. The observed visibility of 0.88(3) is in good
agreement with our theoretical model.
