Tomography of the Temporal-Spectral State of Subnatural-Linewidth Single Photons from Atomic Ensembles

Subnatural-linewidth single photons are generated from atomic ensembles and temporally reshaped as desired so that their temporal modes are eligible for constructing qubits. However, the photon-counting measurement scheme most commonly used in the time-bin basis does not directly give the complex coefficients between time-bins. On the other hand, a mode-sensitive measurement technique, such as homodyne tomography, is hard to implement since a mode-restricting cavity is not allowed in this reshaped photon source. Here, we utilize a cavity-free homodyne detection scheme for reconstructing the temporal-density matrix for the subnatural-linewidth single photons generated from a cold atomic cloud. The characterization of the pure temporal-spectral state of subnatural-linewidth single photons paves the way for exploiting the temporal-spectral degree of freedom to develop photonic-quantum information processing.