Abstract
Heralded single photons emitted from spontaneous four-wave mixing process in a cold atomic cloud have extremely long coherence time up to microseconds, due to slow light effect of electromagnetically induced transparency (EIT). The temporal state of these single photons is typically characterized by the photon counting approach. For the first time, we utilize balanced homodyne tomography (BHT) to fully characterize the temporal state. From reconstructing its density matrix, and further verify that the temporal state shaped through EIT window is pure. To further improve the mode matching between the optical field of Anti-Stokes and the local field in BHT, the driving beam of EIT is split from the local field, and frequency shifted using an electric-optic modulator. The characterization of the pure temporal-spectral state of the single photons paves the way for exploiting the temporal-spectral degree of freedom to develop photonic-quantum information processing.
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