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

The temporal mode of a single photon is considered more and more important in quantum information processing. On one hand, qubits or multi-dimension qudits can be constructed in photonic temporal mode, which are advantageous in long-distance transportation compared to other degrees of freedom, and thus have important applications in photonic quantum processing. On the other hand, to achieve a maximum efficiency in quantum memory, the temporal mode of a single photon is important in the matter-light coupling. Here we utilize cavity-free homodyne detection scheme for reconstructing the temporal density matrix of the subnatural-linewidth single photons generated from a cold atomic cloud. The characterization of the pure temporal-spectral state of narrowband single photons paves the way for exploiting the temporal-spectral degree of freedom to develop photonic quantum information processing.