We report the Hong–Ou–Mandel (HOM) interference, with visibility of 91%, produced from two independent single photons retrieved from collective atomic excitations in two separate cold-atom clouds with high optical depths of 90. The high visibility of the HOM dip is ascribed to the pure single photon in the Fock state that was generated from a dense-cold-atom cloud pumping by a short pulse. The visibility is always the same regardless of the time response of the single-photon detectors. This result experimentally shows that the single photons retrieved are in a separable temporal state with their idler photons.