Not yet reviewed by Pith; the record is open.

Ultrashort time-domain spectroscopy and field-resolved spectroscopy of molecular fingerprints are gold standards for detecting samples' constituents and internal dynamics. However, they are hindered by the Nyquist criterion, leading to prolonged data acquisition, processing times, and sizable data volumes. In this work, we present the first experimental demonstration of compressed sensing on field-resolved molecular fingerprinting by employing random scanning. Our measurements enable pinpointing the primary absorption peaks of atmospheric water vapor in response to terahertz light transients while sampling beyond the Nyquist limit. By drastically undersampling the electric field of the molecular response at a Nyquist frequency of 0.8 THz, we could successfully identify water absorption peaks up to 2.5 THz with a mean squared error of 12 * 10^-4. To our knowledge, this is the first experimental demonstration of time-domain compressed sensing, paving the path towards real-time field-resolved fingerprinting and acceleration of advanced spectroscopic techniques.