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Subnatural-linewidth single-photon source is a potential candidate forexploring the time degree of freedom in photonic quantum information science.This type of single-photon source has been demonstrated to be generated andreshaped in atomic ensembles without any external cavity or filter, and istypically characterized through photon-counting technology. However, the fullcomplex temporal mode function(TMF) of the photon source is not able to berevealed from direct photon counting measurement. Here, for the first time, wedemonstrate the complete temporal mode of the subnatural-linewidth singlephotons generated from a cold atomic cloud. Through heterodyne detectionbetween the single photon and a local oscillator with various centralfrequencies, we recover the temporal density matrix of the single photons atresolvable time bins. Further we demonstrate that the reduced autocorrelationfunction measured through homodyne detection perfectly reveals the puretemporal-spectral state of the subnatural-linewidth single photons.

Tomography of the temporal-spectral state of subnatural-linewidth single photons from atomic ensembles