  The dark count rate (DCR) is a key parameter of single-photon detectors. By
introducing a bulk optical band-pass filter mounted on a fiber-to-fiber optical
bench cooled at 3 K and blocking down to 5 micrometer, we suppressed the DCR of
a superconducting nanowire single-photon detector by more than three orders of
magnitude. The DCR is limited by the blackbody radiation through a signal
passband of 20 nm bandwidth. The figure of merit, system detection efficiency,
and DCR were 2.7 x 10^11, 2.3 %, and 0.001 Hz, respectively. Narrowing the
bandwidth to 100 GHz suppresses the DCR to 0.0001 Hz and the figure of merit
increases to 1.8 x 10^12.
