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Single-photon characterization by two-photon spectral interferometry

Single-photon sources are a fundamental resource in quantum optics. The indistinguishability and purity of photons emitted from different sources are crucial (necessary, essential) properties for many quantum applications to ensure high-visibility interference between different sources. The state of a single-photon source is described by the modes occupied by the single light quanta. Thus the ability to determine the mode structure of a single-photon source provides a means to assess its quality, compare different sources, and provide feedback for source engineering. Here, we propose and demonstrate an experimental scheme that allows for complete characterization of the spectral-temporal state of a pulsed single-photon source. The density matrix elements of the single-photon source are determined by spectral interferometry with a known single-photon reference. Frequency-resolved coincidence measurements are performed after the unknown single-photon source is interfered with a single-photon reference pulse. Fourier analysis of the frequency-resolved two-photon interference pattern reveals the spectral-temporal density matrix of the broadband single-photon source. We present an experimental realization of this method for pure and mixed state pulsed, single-photon sources.