  Subnatural-linewidth single-photon source is a potential candidate for
exploring the time degree of freedom in photonic quantum information science.
This type of single-photon source has been demonstrated to be generated and
reshaped in atomic ensembles without any external cavity or filter, and is
typically characterized through photon-counting technology. However, the full
complex temporal mode function(TMF) of the photon source is not able to be
revealed from direct photon counting measurement. Here, for the first time, we
demonstrate the complete temporal mode of the subnatural-linewidth single
photons generated from a cold atomic cloud. Through heterodyne detection
between the single photon and a local oscillator with various central
frequencies, we recover the temporal density matrix of the single photons at
resolvable time bins. Further we demonstrate that the reduced autocorrelation
function measured through homodyne detection perfectly reveals the pure
temporal-spectral state of the subnatural-linewidth single photons.
