Time dependence of tunnel statistics and the energy resolution of superconducting tunnel junctions

Abstract

Multiple tunneling of quasiparticle charge carriers in a superconducting tunnel junction (STJ) enhances the signal generated by a photon absorption event. It is also an additional source of noise, responsible for a substantial degradation of the energy resolution. Although tunneling is a binomial chance process, governed by a constant tunneling probability, the resulting cumulative statistics of tunnelled quasiparticles depend on time. In particular, the variance of the total number of tunneled quasiparticles reaches a minimum after a finite integration time, corresponding to a minimum in the spectral linewidth. Since the intrinsic energy resolution of the present generation of STJs is mainly limited by the scatter on the number of tunneled quasiparticles, the improvement of the tunnel noise can be experimentally tested by variation of the pulse integration time. An analytical theory is developed that describes the relation between the tunnel noise and the transfer function of the pulse integration hardware for an STJ characterized by a quasiparticle tunnel and loss time in each electrode. We present experiments that demonstrate that the noise contribution from multiple tunnelling is not constant during the time that the quasiparticles are present in the STJ, and that by proper filtering of the STJ pulses the tunnel noise can be optimized at a level which lies well below the canonical tunnel limit.