Superconducting nanowire single-photon detectors are set apart from other photon counting technologies above all else by their extremely high speed, with few-ten-ps timing resolution, and recovery times $tau_Rlesssim$10 ns after a detection event. In this work, however, we identify in the conventional electrical readout scheme a nonlinear interaction between the detector and its readout which can make stable, high-efficiency operation impossible at count rates even an order-of-magnitude less than $tau_R^{-1}$. We present detailed experimental confirmation of this, and a theoretical model which quantitatively explains our observations. Finally, we describe an improved readout which circumvents this problem, allowing these detectors to be operated stably at high count rates, with a detection efficiency penalty determined purely by their inductive reset time.
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