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Universal decay cascade model for dynamic quantum dot initialization

Dynamic quantum dots can be formed by time-dependent electrostatic potentials in nanoelectronic devices, such as gate- or surface-acoustic-wave-driven electron pumps. Ability to control the number of captured electrons with high precision is required for applications in fundamental metrology and quantum information processing. In this work we propose and quantify a scheme to initialize quantum dots with a controllable number of electrons. It is based on the stochastic decrease in the electron number of a shrinking dynamic quantum dot and is described by a nuclear decay cascade model with "isotopes" being different charge states of the dot. Unlike the natural nuclei, the artificial confinement is time-dependent and tunable, so the probability distribution for the final "stable isotopes" depends on the external gate voltage. 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 to compare different devices and architectures, and predict the upper limits of initialization accuracy from low precision measurements.