Short answer: A photon-number-resolving (PNR) detector tells how many photons arrived in a pulse, not just whether any did. Superconducting transition-edge sensors (TESs) are the platform in all three papers here: a 2005 paper reports 88% efficiency at 1550 nm with noise-free photon-number resolution, a 2022 Nature Photonics paper reports resolving 0 to 100 photons by multiplexing TESs, and a New Journal of Physics paper uses a TES system to analyse quantum-dot single-photon sources. These are laboratory detectors that operate at low temperature.
Why count photons
The 2005 Physical Review A paper says high-efficiency detectors that determine the number of photons in a pulse have applications in physics studies, including post-selection-based entanglement protocols for linear optics quantum computing and Bell experiments that close the detection and communication loopholes together. The 2022 paper adds that avalanche photodiodes are very sensitive to distinguishing single-photon events from vacuum but cannot differentiate between larger photon-number events, and that photon-number resolution is desirable for computation, sensing and cryptography.
Transition-edge sensors
The 2005 paper reports fiber-coupled, noise-free, photon-number-resolving transition-edge sensors with 88% efficiency at 1550 nm. The authors say the efficiency could be made even higher at any wavelength in the visible and near-infrared without a higher dark-count rate or degraded photon-number resolution. The sensors are tungsten quantum calorimeters: the tungsten electrons act as both absorber and thermometer, and a voltage bias keeps them at the edge of the superconducting-to-normal transition, where the steep dependence of resistance on temperature provides precise thermometry.
From about 10 photons to 100
The 2022 paper says true photon-number-resolving detectors exist but are limited to resolving on the order of 10 photons, which it calls too small for several quantum-state generation methods based on heralded detection. The authors implement a detection scheme that multiplexes highly quantum-efficient transition-edge sensors to resolve photon numbers between 0 and 100. They demonstrate it with a quantum random-number generator that samples a coherent state in the photon-number basis, and say the method is robust against environmental noise, laser phase and amplitude fluctuations, loss, detector inefficiency and eavesdropping.
Testing single-photon sources
A New Journal of Physics paper uses a TES-based two-channel PNR system to access the photon-number distribution of deterministically fabricated solid-state single-photon sources based on quantum dots. It allows direct observation of the two-photon Fock state produced when indistinguishable photons interfere in a Hong-Ou-Mandel experiment. The authors report that photon indistinguishability measured with PNR detectors, (90 +/- 7)%, agrees with the (90 +/- 5)% from standard click detectors.
Limits
TES detectors run at cryogenic temperatures, and these papers describe laboratory systems. The results are specific to each setup and wavelength.
FAQ
What does a PNR detector do?
It reports how many photons arrived in a pulse rather than only whether any did.
How are photons counted here?
With superconducting transition-edge sensors, which measure the small temperature rise when light is absorbed.
How many photons can be resolved?
The 2022 paper reports 0 to 100 using multiplexed sensors, against about 10 for earlier true PNR detectors.
What efficiency was reported?
88% at 1550 nm in the 2005 paper.
Why use them on single-photon sources?
They show the photon-number distribution directly. One paper reports agreement with click-detector results.
All field notes