Universal scaling of adiabatic tunneling out of a shallow confinement potential

The ability to tune quantum tunneling is key for achieving selectivity in manipulation of individual particles in quantum technology applications. In this work we count electron escape events out of a time-dependent confinement potential, realized as a dynamic quantum dot in a GaAs/AlGaAs heterostructure. A universal scaling relation of the escape probability as a function of potential barrier rise time and depth is established and developed as a method to probe tunneling rates over many orders of magnitude reaching the limit of shallow anharmonic confinement. Crossover to thermally activated transport is used to estimate the single time-energy scale of the universal model. In application to metrological single-electron sources, calibrated control signals greatly extend the accessible dynamical range for probing the quantization mechanism. Validation of the cubic potential approximation sets a foundation for microscopic modeling of quantum tunneling devices in the shallow confinement regime.