  We have used grazing-angle infrared spectroscopy to detect the Berreman
effect (BE) in the quasi-two-dimensional electron system (q-2DES) which forms
spontaneously at the interface between SrTiO$_{3}$ (STO) and a thin film of
LaAlO$_3$ (LAO). From the BE, which allows one to study longitudinal optical
excitations in ultrathin films like the q-2DES, we have extracted at different
temperatures its thickness, the charge density and mobility of the carriers
under crystalline LAO (sample A), and the charge density under amorphous LAO
(sample B). This quantity turns out to be higher than in sample A, but a
comparison with Hall measurements shows that under amorphous LAO the charges
are partly localized at low $T$ with a low activation energy (about 190 K in
$k_B$ units), and are thermally activated according to a model for large
polarons. The thickness of the q-2DES extracted from our spectra turns out to
be 4 $\pm 1$ nm for crystalline LAO, 7 $\pm 2$ nm for amorphous LAO.
