  Harnessing the quantum interference of photon-pair generation processes,
infrared quantum absorption spectroscopy (IRQAS) can extract the infrared
optical properties of a sample through visible or near-infrared photon
detection without the need for an infrared optical source or detector, which
has been an obstacle for higher sensitivity and spectrometer miniaturization.
However, experimental demonstrations have been limited to wavelengths shorter
than 5 um or in the terahertz region, and have not been realized in the
so-called fingerprint region of 1500- 500 cm^-1 (6.6 to 20 um), which is
commonly used to identify chemical compounds or molecules. Here we report the
experimental demonstration of quantum Fourier transform infrared (QFTIR)
spectroscopy in the fingerprint region, by which both absorption and phase
spectra (complex spectra) can be obtained from Fourier transformed quantum
interferograms obtained with a single pixel visible-light detector. As
demonstrations, we obtained the transmittance spectrum of a silicon wafer at
around 10 um (1000 cm^-1) and complex transmittance spectrum of a synthetic
fluoropolymer sheet, polytetrafluoroethylene, in the wavelength range of 8 to
10.5 um (1250 to 950 cm^-1), where absorption due to symmetric and asymmetric
stretching modes of C-F bonds is clearly observed. The signal-to-noise ratio
per unit spectral width and unit probe light intensity of our QFTIR
spectroscopy method outperforms conventional FTIR spectroscopy by a factor of
10^2. These results open the way for new forms of spectroscopic devices based
on quantum technologies.
