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Promoting the sensitivity of mid-infrared (MIR) spectroscopy to the single-photon level is a critical need for investigating photosensitive biological samples and chemical reactions. MIR spectroscopy based on frequency upconversion is a compelling pioneer allowing high-efficiency MIR spectral measurement with well-developed single-photon detectors, which overcomes the main limitations of high thermal noise of current MIR detectors. However, noise from other nonlinear processes caused by strong pump fields hinders the development of the upconversion-based MIR spectroscopy to reach the single-photon level. Here, a broadband MIR single-photon frequency upconversion spectroscopy is demonstrated based on the temporal-spectral quantum correlation of non-degenerate photon pairs, which is well preserved in the frequency upconversion process and is fully used in extracting the signals from tremendous noise caused by the strong pump. A correlation spectrum broader than 660 nm is achieved and applied for the demonstration of sample identification under a low incident photon flux of 0.09 average photons per pulse. The system is featured with non-destructive and robust operation, which makes single-photon-level MIR spectroscopy an appealing option in biochemical applications.

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In this paper, we reconstructed the positive operator-valued measure (POVM) of a photon-number-resolving detector (PNRD) based on a multi-pixel photon counter (MPPC) by means of quantum detector tomography (QDT) at 791 nm and 523 nm, respectively. MPPC is a kind of spatial-multiplexing PNRD with a silicon avalanche photodiode (Si-APD) array as the photon receiver. Experimentally, the quantum characteristics of MPPC were calibrated at 2 MHz at two different wavelengths. The POVM elements were given by QDT. The fidelity of the reconstructed POVM elements is higher than 99.96%, which testifies that the QDT is reliable to calibrate MPPC at different wavelengths. With QDT and associated Wigner functions, the quantum properties of MPPC can be calibrated more directly and accurately in contrast with those conventional methods of modeling detectors.