  Polar discontinuities occurring at interfaces between two different materials
constitute both a challenge and an opportunity in the study and application of
a variety of devices. In order to cure the large electric field occurring in
such structures, a reconfiguration of the charge landscape sets in at the
interface via chemical modifications, adsorbates or charge transfer. In the
latter case, one may expect a local electronic doping of one material: one
sparkling example is the two-dimensional electron liquid (2DEL) appearing in
SrTiO$_3$ once covered by a polar LaAlO$_3$ layer. Here we show that tuning the
formal polarisation of a (La,Al)$_{1-x}$(Sr,Ti)$_x$O$_3$ (LASTO:$x$) overlayer
through chemical composition modifies the quantum confinement of the 2DEL in
SrTiO$_3$ and its electronic band structure. The analysis of the behaviour in
magnetic field of superconducting field-effect devices reveals, in agreement
with $ab\ initio$ calculations and self-consistent Poisson-Schr\"odinger
modelling, that quantum confinement and energy splitting between electronic
bands of different symmetries strongly depend on interface charge densities.
These results not only strongly support the polar discontinuity mechanisms with
a full charge transfer to explain the origin of the 2DEL at the celebrated
LaAlO$_3$/SrTiO$_3$ interface, but also demonstrate an effective tool for
tailoring the electronic structure at oxide interfaces.
