Universal decay cascade model for dynamic quantum dot initialization

Dynamic quantum dots can be formed by time-dependent electrostatic potentials, such as in gate- or surface-acoustic-wave-driven electron pumps. In this work we propose and quantify a scheme to initialize quantum dots with a controllable number of electrons. It is based on a rapid increase of the electron potential energy and simultaneous decoupling from the source lead. The full probability distribution for the final number of captured electrons is obtained by solving a master equation for stochastic cascade of single electron escape events. We derive an explicit fitting formula to extract the sequence of decay rate ratios from the measurements of averaged current in a periodically driven device. This provides a device-specific fingerprint which allows us to compare different architectures, and predict the upper limits of initialization accuracy from low precision measurements.