Mid-Infrared Single-Photon Compressive Spectroscopy

Sensitive mid-infrared (MIR) spectroscopy plays an indispensable role in various photon-starved conditions. However, the detection sensitivity of conventional MIR spectrometers is severely limited by excessive noises of the involved infrared sensors, especially for multi-pixel arrays in parallel spectral acquisition. Here, we devise and implement an ultra-sensitive MIR single-pixel spectrometer, which relies on high-fidelity spectral upconversion and wavelength-encoding compressive measurement. Specifically, a MIR nanophotonic supercontinuum from 3.1 to 3.9 $\mu$m is nonlinearly converted to the near-infrared band via synchronous chirped-pulse pumping, which facilitates both the precise spectral mapping and sensitive upconversion detection. The upconverted signal is then spatially dispersed onto a programmable digital micromirror device, before being registered by a single-element silicon detector. Consequently, the spectral information can be deciphered from the correlation between encoded patterns and recorded measurements, which results in a spectral resolution of 0.5 cm$^{-1}$ under an illumination flux down to 0.01 photons/nm/pulse. Moreover, we demonstrate faithful reconstructions at sub-Nyquist sampling rates by using the compressive sensing algorithm, which leads to a 95\% reduction in data acquisition time. The presented single-pixel computational spectrometer features wavelength multiplexing, high throughput, and efficient sampling, which thus paves a new way for sensitive and fast spectroscopic analysis at the single-photon level.