  It is challenging to implement genuine free running single photon detectors
for the 1550 nm wavelength range with simultaneously high detection efficiency
(DE), low dark noise, and good time resolution. We report a novel read out
system for the signals from a negative feedback avalanche diode (NFAD) which
allows useful operation of these devices at a temperature of 193 K and results
in very low dark counts (~100 CPS), good time jitter (~30 ps), and good DE
(~10%). We characterized two NFADs with a time correlation method using photons
generated from weak coherent pulses (WCP) and photon pairs produced by
spontaneous parametric down conversion (SPDC). The inferred detector
efficiencies for both types of photon sources agree with each other. The best
noise equivalent power of the device is estimated to be 8.1 x 10^(-18) W
Hz^(-1/2), more than 10 times better than typical InP/InGaAs SPADs show in free
running mode. The afterpulsing probability was found to be less than 0.1% per
ns at the optimized operating point. In addition, we studied the performance of
an entanglement-based quantum key distribution (QKD) using these detectors and
develop a model for the quantum bit error rate (QBER) that incorporates the
afterpulsing coefficients. We verified experimentally that using these NFADs it
is feasible to implement QKD over 400 km of telecom fibre. Our NFAD photon
detector system is very simple, and is well suited for single-photon
applications where ultra-low noise and free-running operation is required, and
some afterpulsing can be tolerated.
