  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.
