  Dual-comb spectroscopy has been proven a powerful tool in molecular
characterization, which remains challenging to implement in the mid-infrared
region due to difficulties in the realization of two mutually locked comb
sources and efficient photodetection. Moreover, the detection capability of
dual-comb spectroscopy is fundamentally limited by the strong excitation
background and detector saturation. Here we introduce a variant of dual-comb
spectroscopy called cross-comb spectroscopy, in which a mid-infrared comb is
upconverted via sum-frequency generation with a near-infrared comb of a shifted
repetition rate and then interfered with a spectral extension of the
near-infrared comb. We show that cross-comb spectroscopy can have superior
signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency
compared to other dual-comb-based methods and avoid the limits of the
background excitation and detector saturation. We experimentally demonstrate a
proof-of-concept measurement of atmospheric CO2 around 4.25 $\mu$m, with a
233-$cm^{-1}$ instantaneous bandwidth, 28000 comb lines, a single-shot SNR of
167, and a figure of merit of $2.4\times10^{6} Hz^{1/2}$. Cross-comb
spectroscopy can be realized using up- or down-conversion and offers an
adaptable and powerful spectroscopic method outside the well-developed near-IR
region. This approach opens new avenues to high-performance molecular sensing
with wavelength flexibility, which can impact a wide swath of applications.
