Modeling shallow confinement in tunable quantum dots

This paper proposes a universal microscopic model for the shallow confinement regime of single-electron tunneling devices. We consider particle escape from a quantum well generically emerging as a bifurcation in a smooth electrostatic potential and develop a set of analytic and numerical approximations for the ground-state tunneling and thermally activated escape rates. These approximations are applied to the problem of electron capture by a closing tunnel barrier where the competition between the closing speed and the escape rate defines a scaling relation for the capture fidelity. Effective one-dimensional cubic potential approximation leads to a universal form of this scaling relation in terms of device-independent dimensionless depth and speed parameters. Using temperature and magnetic-field dependence predictions, we show how to infer the energy scales of cubic longitudinal and quadratic transverse confinement. Finally, we derive an intrinsic quantum speed bound for adiabatic protection of the ground-state tunneling and show that the latter can potentially be exploited up to the breakdown of confinement with a practical speed limit set by reaching the quantum uncertainty of the barrier height before the onset of nonadiabatic excitation. These results contribute to mapping out the physical limits of single-electron quantum technologies for electrical metrology and sensing.