Modelling shallow confinement in tuneable quantum dots as a 1D cubic potential*

One physical system which realizes the generic model of an electron tunneling through a barrier into and out of a potential well is a tuneable barrier quantum dot. Pushing many of its applications to the limits of their fastest possible operation requires the tunneling of the electron to be as fast as possible which inevitably pushes the dot to the brink of losing its confining properties. The focus of our study is this shallow regime of confinement where the dot can hold a single electron in a single or a couple of discrete states. By considering the one-dimensional cubic potential we hope to describe universal properties of the weakly confined electron that would characterize it independently of the specific device realizing the confinement.

By comparing our cubic model predictions with data counting single electron capture events in dynamically modulated quantum dot experiments we, indeed, confirm universality across multiple dot realizations and driving protocols. Moreover, we show theoretically that the correspondence between the cubic model and experiment should increase with increasing magnetic field. We illustrate this with a comparison to experimental data from precision current sources. Finally, using the cubic potential we develop a model for the temperature dependence of the electron escape rate which is verified by comparison to data from another field of nano-electronics - Josephson junctions.