  The quasi two-dimensional electron gas (q-2DEG) at oxide interfaces provides
a platform for investigating quantum phenomena in strongly correlated
electronic systems. Here, we study the transport properties at the
high-mobility
(La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_{0.3}$/SrTiO$_{0.3}$
(LSAT/STO) interface. Before oxygen annealing, the as-grown interface exhibits
a high electron density and electron occupancy of two subbands: higher-mobility
electrons ($\mu_1\approx{10^4}$ cm$^2$V$^{-1}$s$^{-1}$ at 2 K) occupy the
lower-energy $3d_{xy}$ subband, while lower-mobility electrons
($\mu_1\approx{10^3}$ cm$^{2}$V$^{-1}$s$^{-1}$ at 2 K) propagate in the
higher-energy $3d_{xz/yz}$-dominated subband. After removing oxygen vacancies
by annealing in oxygen, only a single type of 3dxy electrons remain at the
annealed interface, showing tunable Shubnikov-de Haas (SdH) oscillations below
9 T at 2 K and an effective mass of $0.7m_e$. By contrast, no oscillation is
observed at the as-grown interface even when electron mobility is increased to
$50,000$ cm$^{2}$V$^{-1}$s$^{-1}$ by gating voltage. Our results reveal the
important roles of both carrier mobility and subband occupancy in tuning the
quantum transport at oxide interfaces.
