Optical kinetic inductance detectors (OKIDs) are a type of superconducting single photon detector whose signal corresponds to the number of quasiparticles that are excited when the detector absorbs a photon. OKIDs whose absorptive element is made out of β-phase Tantalum (β-Ta), a disordered superconductor, exhibit faster than exponential (supra-exponential) decay of its pulse-shaped single photon response. Faster decay generally corresponds to a higher density of quasiparticles. These pulses cannot be explained by the equations typically used to describe how these quasiparticles decay in a process called recombination. One possible explanation is that the high degree of disorder of β-Ta causes the diffusion of quasiparticles through the material to be slow, which leads to a high local density of quasiparticles, causing the faster decay. The usual model for this recombination does not include this diffusion.
In this thesis, we model the OKID’s single photon pulse with a local model of the recombination process, that does include this diffusion. To this end, we analyze the downconversion process, which describes the generation of particles due to a photon absorption. This analysis therefore gives information on the initial conditions of the recombination process. Next, we study and solve this diffusion and recombination model.
Next, we test the response pulse predicted by this model against measurement data of the single photon pulses of a β-Ta OKID, for different photon energies. We show that the model must assume that an unfeasibly high number of quasiparticles is excited in order to reproduce the data. Furthermore, the pulses generated by the model exhibit a dependence on the absorbed photon energy, which is not observed in the data. Therefore we reason that the model must be missing some photon energy dependent effect. We reason that this energy dependence could lie in the downconversion process, or that it could lie in the responsivity of the OKID.
We also investigate the pulses of OKIDs that are designed with an absorber composed of multiple small elements of β-Ta, which constrain the quasiparticles in space. We measure the correspondence of the size of the β-Ta elements and the decay time of the response pulse. We show that the decay time increases for larger elements, until it saturates. This behavior is also predicted by our model. We therefore conclude that the diffusion indeed plays a significant role in the cause of supra-exponential decay.