Energy-time entangled photons are critical in many quantum optical phenomena
and have emerged as important elements in quantum information protocols.
Entanglement in this degree of freedom often manifests itself on ultrafast
timescales making it very difficult to detect, whether one employs direct or
interferometric techniques, as photon-counting detectors have insufficient time
resolution. Here, we implement ultrafast photon counters based on nonlinear
interactions and strong femtosecond laser pulses to probe energy-time
entanglement in this important regime. Using this technique and single-photon
spectrometers, we characterize all the spectral and temporal correlations of
two entangled photons with femtosecond resolution. This enables the witnessing
of energy-time entanglement using uncertainty relations and the direct
observation of nonlocal dispersion cancellation on ultrafast timescales. These
techniques are essential to understand and control the energy-time degree of
freedom of light for ultrafast quantum optics.Comment: 12 pages (5 main, 7 supplementary material) 4 main figure