Poisson transition rates from time-domain measurements with finite bandwidth

TL;DR

This paper develops a quantitative correction method for accurately estimating true transition rates in Poisson two-level systems from finite bandwidth time-domain measurements, supported by simulations and experimental data.

Contribution

It introduces a straightforward model to correct for bandwidth limitations, enabling precise determination of actual transition rates from limited measurements.

Findings

Finite bandwidth causes significant underestimation of transition rates.

The correction method accurately retrieves true rates from simulated data.

Experimental data confirms the effectiveness of the correction approach.

Abstract

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus is ten times faster than the process under study. We derive here a quantitative form for this correction using a straightforward state-transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.