  Time- and number-resolved photon detection is crucial for photonic quantum
information processing. Existing photon-number-resolving (PNR) detectors
usually have limited timing and dark-count performance or require complex
fabrication and operation. Here we demonstrate a PNR detector at
telecommunication wavelengths based on a single superconducting nanowire with
an integrated impedance-matching taper. The prototyping device was able to
resolve up to five absorbed photons and had 16.1 ps timing jitter, <2 c.p.s.
device dark count rate, $\sim$86 ns reset time, and 5.6% system detection
efficiency (without cavity) at 1550 nm. Its exceptional distinction between
single- and two-photon responses is ideal for coincidence counting and allowed
us to directly observe bunching of photon pairs from a single output port of a
Hong-Ou-Mandel interferometer. This detector architecture may provide a
practical solution to applications that require high timing resolution and
few-photon discrimination.
