  Superconducting nanowire single-photon detectors are an ideal match for
integrated quantum photonic circuits due to their high detection efficiency for
telecom wavelength photons. Quantum optical technology also requires
single-photon detection with low dark count rate and high timing accuracy. Here
we present very low noise superconducting nanowire single-photon detectors
based on NbTiN thin films patterned directly on top of Si3N4 waveguides. We
systematically investigate a large variety of detector designs and characterize
their detection noise performance. Milli-Hz dark count rates are demonstrated
over the entire operating range of the nanowire detectors which also feature
low timing jitter. The ultra-low dark count rate, in combination with the high
detection efficiency inherent to our traveling wave detector geometry, gives
rise to a measured noise equivalent power at the 10^(-20) W/Hz^(1/2) level.
