  Temporal-spectral modes of light provide a fundamental window into the nature
of atomic and molecular systems and offer robust means for information
encoding. Methods to precisely characterize the temporal-spectral state of
light at the single-photon level thus play a central role in understanding
quantum emitters and are a key requirement for quantum technologies that
harness single-photon states. Here we demonstrate an optical reference-free
method, which melds techniques from ultrafast metrology and single-photon
spectral detection, to characterize the temporal-spectral state of single
photons. This provides a robust, wavelength-tunable approach for rapid
characterization of pulsed single-photon states that underpins emerging optical
quantum technologies based upon the temporal-spectral mode structure of quantum
light.
