  Many quantum advantages in metrology and communication arise from
interferometric phenomena. Such phenomena can occur on ultrafast time scales,
particularly when energy-time entangled photons are employed. These have been
relatively unexplored as their observation necessitates time resolution much
shorter than conventional photon counters. Integrating nonlinear optical gating
with conventional photon counters can overcome this limitation and enable
subpicosecond time resolution. Here, using this technique and a Franson
interferometer, we demonstrate high-visibility quantum interference with two
entangled photons, where the one- and two-photon coherence times are both
subpicosecond. We directly observe the spectral and temporal interference
patterns, measure a visibility in the two-photon coincidence rate of
$(85.3\pm0.4)\%$, and report a CHSH-Bell parameter of $2.42\pm0.02$, violating
the local-hidden variable bound by 21 standard deviations. The demonstration of
energy-time entanglement with ultrafast interferometry provides opportunities
for examining and exploiting entanglement in previously inaccessible regimes.
