Quantum detector tomography for two-dimensional superconducting nano-detectors

Abstract

Quantum tomography is a well-established characterization tool [1]. The major goal of this technique is to reconstruct the quantum state of an incident light by measuring statistical distribution of the clicks produced by the detector in response to arriving photons. If the statistics of light is known, the method can be applied to detectors. Thus, quantum detector tomography (QDT) adds a new dimension to the application area of detectors non-resolving the photon number. So far QDT was successfully applied to characterize superconducting nanodetectors with a small active area [2] comparable to the size of the local nonequilibrium state which is produced by the absorbed photon. Another restriction of the established QDT technique is the width of the spectral detection threshold broadened by fluctuations inherent to the detection mechanism [3]. Here we propose a mathematical approach allowing for QDT characterization of multiphoton two-dimensional detectors which exhibit position dependent detection efficiency and relatively broad detection threshold. The proposed modification of QDT incorporates the solution of the partition problem for photon distribution over active detector area. Applicability of our approach was demonstrated with superconducting nanostrips from magnesium diboride (MgB2). The plot shows the count rate of a straight nanostrip with a length of 100 micrometers, a width of 150 nm, and a thickness of 8 nm at several bias currents as function of the mean number of photons per pulse impinging the strip area. The strip was exposed to pulsed light with the wavelengths 800 nm at a repetition rate of 8x10^7 sec-1. At the smallest current, the count rate follows the power law with the exponent 2 which decreases to almost 1 at the largest current. The best fit, however, was obtained for thresholds in the form of the error function centered at three, four and five photon energies (from top to bottom) with the variance equal to the squared photon energy. Centering the threshold to the energy of just one photon results in the saturated count rate as function of the mean photon number.