Markov chain Monte Carlo Detector Tomography applied to a NbTiN nanobridge

We demonstrate the use of a flexible and highly accurate Markov chain Monte Carlo Quantum Detector Tomography method as a minimization algorithm to best describe the response of an efficient $120 nm$ wide NbTiN superconducting nanobridge single photon detector. Separation of the internal quantum efficiency and external quantum efficiency is possible due to the difference in saturation behavior of an ideal 1-photon threshold detector as compared to a detector with non-unity 1-photon internal quantum efficiency. From a statistical analysis of our measurements (at $T=4.23\pm0.01K$, $I=29.4\pm0.1\mu A$, $I/I_\text{switch}=0.90\pm0.01$) we find an external quantum efficiency $\eta=(1.60\pm0.05)\cdot10^{-6}$, a 1-photon internal quantum efficiency $p_1=0.568\pm0.008$ and unity multi-photon (2 or more) internal quantum efficiency.