Phonon noise in thin metal films in an advanced energy down-conversion stage

We have identified an important, new source of line broadening in single photon detectors that work on the principle of absorption in a thin metal film. Phonon down-conversion noise arises through the loss of high energy phonons into the substrate during the initial photon energy down-conversion stage. Because of the relatively small number of phonons initially involved in this process, the loss rate is subject to large fluctuations due to the statistical nature of the energy exchange processes. We have modelled the phonon down-conversion noise that arises in the final stage of the down-conversion cascade, during which the deposited energy is converted into predominantly electronic excitations. At this stage of down-conversion in thin films the cascade phonon energy is sufficiently small that the escape interfaces are accessible for all phonons. Solving the system of coupled integral equations for the interacting electron and phonon systems, we have derived explicit expressions for the variance of the deposited energy. We have compared the results with other known noise contributions for the two foremost types of single optical photon detectors, based on superconducting tunnel junctions and transition edge sensors.